Autodesk Simulation 2012 Part-1

Autodesk® Simulation Mechanical 2012 Part 1 – Seminar Notes

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Autodesk® Simulation Mechanical 2012 – Part 1 – Seminar Notes

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© 2011 Autodesk, Inc. All rights reserved. Autodesk® Simulation Mechanical 2012 – Part 1 – Seminar Notes Except as otherwise permitted by Autodesk, Inc., this publication, or parts thereof, may not be reproduced in any form, by any method, for any purpose. Certain materials included in this publication are reprinted with the permission of the copyright holder.

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Disclaimer THIS PUBLICATION AND THE INFORMATION CONTAINED HEREIN IS MADE AVAILABLE BY AUTODESK, INC. “AS IS.” AUTODESK, INC. DISCLAIMS ALL WARRANTIES, EITHER EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO ANY IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE REGARDING THESE MATERIALS. Published by: Autodesk, Inc. 111 Mclnnis Parkway San Rafael, CA 94903, USA


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TABLE OF CONTENTS Introduction ..................................................1 Overview.................................................................................................................................... 1 Software Installation, Services, and Support ............................................................................ 1 Installing and Running Autodesk® Simulation .....................................................................1 System Requirements...........................................................................................................2 Subscription Center ...............................................................................................................4 Web Links ..............................................................................................................................4 Tutorials .................................................................................................................................4 Webcasts and Web Courses ................................................................................................5 How to Receive Technical Support ......................................................................................5 Updates..................................................................................................................................6 Background of FEA ................................................................................................................... 7 What is Finite Element Analysis? .........................................................................................7 Basic FEA Concepts .............................................................................................................7 How Does Autodesk Simulation Work? ...............................................................................9 The General Flow of an Analysis in Autodesk Simulation ................................................ 10 Stress and Strain Review ........................................................................................................ 11 Equations Used in the Solution .......................................................................................... 11 Limits of Static Stress with Linear Material Models ........................................................... 12 Mechanical Event Simulation (MES) Overcomes Limitations .......................................... 12 Hand-Calculated Example ................................................................................................. 13 Heat Transfer Review ............................................................................................................. 13 Equations Used in the Solution.......................................................................................... 13 Linear Dynamics Review......................................................................................................... 14

Chapter 1: Using Autodesk® Simulation ........................15 Chapter Objectives .................................................................................................................. 15 Navigating the User Interface.................................................................................................. 15 Commands ......................................................................................................................... 17 Using the Keyboard and Mouse ........................................................................................ 18 Introduction to the View Cube ............................................................................................ 19 Additional View Controls .................................................................................................... 20 Legacy View Controls in Autodesk Simulation .................................................................. 21 Steel Yoke Example ................................................................................................................ 22 Opening and Meshing the Model....................................................................................... 22 Setting up the Model .......................................................................................................... 23 Analyzing the Model ........................................................................................................... 27 Reviewing the Results........................................................................................................ 28 Creating an Animation........................................................................................................ 29 Generating a Report ........................................................................................................... 29

Chapter 2: Static Stress Analysis Using CAD Solid Models .....33 Chapter Objectives .................................................................................................................. 33 Archiving a Model .................................................................................................................... 33 Types of Brick Elements ......................................................................................................... 34 Generating Meshes for CAD Models ...................................................................................... 35 Creating a Mesh ................................................................................................................. 36 Model Mesh Settings – Options ......................................................................................... 37


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Table of Contents Tips for Modeling with CAD Solid Model Software for FEA.................................................... 39 Simplify CAD Solid Models with Autodesk Fusion.................................................................. 40 Working with Various Unit Systems ........................................................................................ 41 Loading Options ...................................................................................................................... 43 Load Cases ........................................................................................................................ 44 Constraint Options................................................................................................................... 46 Modeling Symmetry and Antisymmetry............................................................................. 46 Design Scenarios .................................................................................................................... 47 Load and Constraint Group ..................................................................................................... 48 Local Coordinate Systems ...................................................................................................... 49 Defining Materials and Using the Material Library Manager .................................................. 50 Adding Material Libraries and Material Properties ............................................................ 52 Examples of Loads and Constraints ....................................................................................... 54 When to Use Displacement Boundary Elements.............................................................. 54 Using Local Coordinate Systems ...................................................................................... 55 Using Surface Variable Loads ........................................................................................... 58 Exercise A: Frame – Full to Quarter-Symmetry Model Comparison .......................... 63

Chapter 3: Results Evaluation and Presentation ...............65 Chapter Objectives .................................................................................................................. 65 Background on How Results are Calculated .......................................................................... 65 How to Evaluate Results ......................................................................................................... 66 Displacement Results ........................................................................................................ 66 Stress Results..................................................................................................................... 68 Reaction Force Results ...................................................................................................... 70 Inquiring on the Results at a Node .................................................................................... 70 Graphing the Results.......................................................................................................... 71 Presentation Options ............................................................................................................... 73 Contour Plots ...................................................................................................................... 73 Image File Creation ............................................................................................................ 77 Animating FEA Results ...................................................................................................... 78 Using the Configure Report Utility...................................................................................... 79 Exercise B: Yoke – Evaluation of Results and Generation of a Report ..................... 81

Chapter 4: Midplane Meshing and Plate Elements ...............83 Chapter Objectives .................................................................................................................. 83 Meshing Options ..................................................................................................................... 83 Element Options ...................................................................................................................... 87 Plate Theory and Assumptions .......................................................................................... 87 Loading Options ...................................................................................................................... 88 Example of Defining the Element Normal Point ................................................................ 89 Result Options ......................................................................................................................... 92 Exercise C: Midplane Meshing and Plate Element Orientation ................................... 95

Chapter 5: Meshing ...........................................97 Chapter Objectives .................................................................................................................. 97 Refinement Options................................................................................................................. 97 Automatic Refinement Points............................................................................................. 97 Global Refinement Options ................................................................................................ 99 Creating Joints....................................................................................................................... 101 Creating Bolts ........................................................................................................................ 103 Mesh Convergence Testing .................................................................................................. 105 Performing a Mesh Study ................................................................................................ 106

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Table of Contents Exercise D: Yoke and Clevis Assembly ...................................................................... 107

Chapter 6 Introduction to Contact ...........................109 Chapter Objectives ................................................................................................................ 109 Uses for Contact.................................................................................................................... 109 Contact Options..................................................................................................................... 109 Setting up Contact Pairs................................................................................................... 109 Types of Contact .............................................................................................................. 110 Friction .............................................................................................................................. 112 Surface Contact Direction ................................................................................................ 112 Contact Example ................................................................................................................... 114 How to Model Shrink Fits: ................................................................................................ 114 Shrink Fit Example ................................................................................................................ 115 Case 1............................................................................................................................... 117 Case 2............................................................................................................................... 120 Result Options ....................................................................................................................... 121 Exercise E: Yoke Model with Contact ......................................................................... 123

Chapter 7 Introduction to Linear Dynamics ...................125 Chapter Objectives ................................................................................................................ 125 Modal Analysis ...................................................................................................................... 125 Lumped Masses .................................................................................................................... 126 Load Stiffening....................................................................................................................... 127 Example of Natural Frequency (Modal) Analysis ................................................................. 128 Meshing the Model ........................................................................................................... 129 Adding Constraints ........................................................................................................... 130 Defining the Materials....................................................................................................... 130 Analyzing the Model ......................................................................................................... 130 Reviewing the Results...................................................................................................... 131 Critical Buckling Analysis ...................................................................................................... 132 Setting Up a Critical Buckling Analysis ............................................................................ 133 Result Options ....................................................................................................................... 134 Other Linear Dynamics Analyses.......................................................................................... 134 Exercise F: Concrete Platform ..................................................................................... 135

Chapter 8 Steady-State Heat Transfer ........................137 Chapter Objectives ................................................................................................................ 137 3-D Radiator Example ........................................................................................................... 137 Meshing the Model ........................................................................................................... 138 Setting up the Model ........................................................................................................ 139 Analyzing the Model ......................................................................................................... 140 Reviewing the Results...................................................................................................... 141 Meshing Options ................................................................................................................... 142 Thermal Contact ............................................................................................................... 142 Element Options .................................................................................................................... 143 Rod Elements ................................................................................................................... 143 2-D Elements .................................................................................................................... 143 Plate Elements ................................................................................................................. 144 Brick and Tetrahedral Elements ...................................................................................... 145 Loading Options .................................................................................................................... 147 Nodal Loads...................................................................................................................... 147 Surface Loads .................................................................................................................. 149 Element Loads.................................................................................................................. 153 Body-to-Body Radiation ................................................................................................... 155 Autodesk® Simulation Mechanical 2012 – Part 1 – Seminar Notes

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Table of Contents Controlling Nonlinear Iterations ........................................................................................ 159 Result Options ....................................................................................................................... 161 Exercise G: Infrared Detector Model ........................................................................... 163

Chapter 9 Transient Heat Transfer ...........................165 Chapter Objectives ................................................................................................................ 165 When to Use Transient Heat Transfer .................................................................................. 165 Element Options .................................................................................................................... 165 Loading Options .................................................................................................................... 165 Load Curves ..................................................................................................................... 166 Nodal Heat Source ........................................................................................................... 167 Controlling Nodal and Surface Applied Temperatures ................................................... 168 Result Options ....................................................................................................................... 168 Exercise H: Transistor Case Model ............................................................................. 169

Chapter 10 Thermal Stress ...................................171 Chapter Objectives ................................................................................................................ 171 Multiphysics Overview........................................................................................................... 171 Performing a Thermal Stress Analysis.................................................................................. 172 Exercise I: Disk Brake Rotor Heat-up and Stress ...................................................... 175

Appendix A – Finite Element Method Using Hand Calculations ..177 Model Description and Governing Equations .................................................................. 179 Hand-Calculation of the Finite Element Solution............................................................. 181 Autodesk® Simulation Example ....................................................................................... 182

Appendix B – Analysis Types in Autodesk® Simulation .........185 Background on the Different Analysis Types ........................................................................ 187 Choosing the Right Analysis Type for Your Application ....................................................... 194 Combining Analysis Types for Multiphysics.......................................................................... 198

Appendix C – Linear Loads and Constraints ...................199 Nodal Loading .................................................................................................................. 201 Edge Loading ................................................................................................................... 206 Surface Loading ............................................................................................................... 207 Element Loading .............................................................................................................. 212 Constraints........................................................................................................................ 215

Appendix D – Material Model Options .........................219

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Introduction Overview This course will introduce you to the analysis products available within the Autodesk® Simulation Mechanical software. These capabilities include static stress with linear material models, heat transfer, and linear dynamics analyses. The course will focus exclusively on models originating from CAD solid modeling programs. You will learn the various meshing options available for creating solid and plate elements. The available load and constraint options for each of the covered analysis types will also be presented. You will learn how to evaluate the results of the analyses and how to create presentations of the results, including images, animations and HTML reports. This course is a prerequisite to the more advanced topic of Mechanic Event Simulation (MES) covered in the Part 2 training seminar.

Software Installation, Services, and Support Installing and Running Autodesk® Simulation The simulation software is distributed on DVDs with the exception of software for the Linux platform, which is distributed on CDs. In addition, the software may be downloaded from the Autodesk website. When you place the software DVD into a DVD-ROM drive, a launch dialog having four options will appear. If you want to set up the software on a client workstation, whether you will be using a license locked to a single computer or a network license, press the "Install Products" button. If using a network license, you must already have the license server software installed on a computer on the network. If you wish to create pre-configured deployments for installing the product on multiple client workstations, choose the "Create Deployments" command. If you want to set up the computer as a license server to control the number of concurrent users through a network, or, if you wish to install optional reporting tools, press the "Install Tools and Utilities" command. Finally, a fourth command on the launch screen, "Read the Documentation," leads to a screen from which you can access a ReadMe file and other installation and licensing guides. During the product installation process, you will need to specify your name, the name of your organization. You will also need to enter the product serial number and the product key. Otherwise, you will be limited to a 30-day trial period. To customize the installation location on your computer, the components to be installed, and/or to specify a network license server, you will have to press the "Configuration" button that appears on one of the screens during the installation process. Then, follow the prompts, provide the required information, and click the "Configuration Complete" button to continue the installation process. Any time after the installation, you will be able to start the software by using the available shortcut found in the "Start" menu folder, "All Programs: Autodesk: Autodesk Algor Simulation." The version number is included in the start menu folder name and shortcut. The name of the shortcut will depend upon which package has been purchased ("…Simulation Mechanical "…Simulation Multiphysics"). In the dialog that appears when the program is launched, you will be able to open an existing model or begin a new model. The simulation software will be used to create, analyze, and review the results of an analysis within a single user interface, regardless of the analysis type.


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Introduction

System Requirements We recommend the following system specifications for a Microsoft Windows® platform running Autodesk Simulation software. These specifications will allow you to achieve the best performance for large models and advanced analysis types. 32-Bit

64-Bit *

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Dual Core or Dual Processor Intel® 64 or AMD 64, 3 GHz or higher

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Dual Core or Dual Processor Intel 64 or AMD 64, 3 GHz or higher

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2 GB RAM or higher (3 GB for MES and CFD applications)

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8 GB RAM or higher

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100 GB of free disk space or higher

30 GB of free disk space or higher

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256 MB or higher OpenGL accelerated graphics card

512 MB or higher OpenGL accelerated graphics card

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DVD-ROM drive

DVD-ROM drive

Supported Operating Systems: • • • • •

Microsoft Windows 7 (32-bit and 64-bit editions) Microsoft Vista™ (32-bit and 64-bit editions) Microsoft Windows Server 2003 and Windows Server 2008 Microsoft Windows XP (32-bit and 64-bit editions) Linux **

Other Requirements (All Platforms): • • • •

Mouse or pointing device Sound card and speakers *** Internet connection *** Web browser with Adobe Flash Player 10 (or higher) plug-in ***

* We recommend usage of a 64-bit version of the operating system to run large models of any analysis type and for Mechanical Event Simulation, CFD, and Multiphysics analyses. While a 32-bit machine can be configured for larger system memory sizes, architectural issues of the operating system limit the benefit of the additional memory. ** Linux may be used as a platform for running the solution phase of the analysis only. It may be used for a distributed processing (or clustering) platform. However, pre- and post-processing is done in the graphical user interface, which must be installed and run on a Microsoft Windows platform. *** These requirements are due to the use of multimedia in our product line and the availability of distance learning webcasts, software demos, and related media. Minimum system requirements and additional recommendations for Linux platforms may be found on the Autodesk website. To navigate to the Autodesk Simulation web page, access the "Help" panel from the "Getting Started" tab. Then click on the "In-Product Help" button.

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Introduction

Autodesk Simulation Help Autodesk Simulation Help is available in two places—the In-Product Help and the Online Wiki Help, these resources contain the following information: • • • • • •

Documentation for all of the model creation options within the user interface Documentation for all of the Autodesk Simulation analysis types Documentation for all of the result options available within the user interface Essential Skills videos (Online Wiki Help only) Step-by-step examples that illustrate many modeling and analysis options Meshing, modeling, and analysis tutorials (Online Wiki Help only)

How to Access the Help Files •

Select the "Getting Started" tab. Click on the "In-Product Help" button. The title page of the Autodesk Simulation Help will appear.

•

You can navigate through the In-Product Help or Online Wiki Help via the table of contents to the left or by using the "Search" or "Index" tabs.

Features of the Help Files •

Autodesk Simulation Help is a set of compiled help files that are installed with the software but are also accessible from the Autodesk website.

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Hyperlinks and a table of contents make it easy to move quickly from topic to topic.

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The Help window contains a standard Internet browser toolbar, so you can move forward and backward and print with ease.

Figure I.1: Autodesk Simulation In-Product Help


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Introduction

Search the Help Files using Keywords •

All of the pages in the Help files can be searched based on keywords.

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The keywords are entered at the top of the "Search" tab on the left side of the In-Product Help or Online Wiki Help screen. Topics that match the search criteria are listed below.

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Keywords are used to search the Help files. You may use single or multiple keywords.

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Boolean operators (AND, OR, NEAR, and NOT) are available to enhance the search utility. Also, phrases may be enclosed in quotes to search only for a specific series of words.

Subscription Center Along with your Autodesk Simulation software purchase, you have the option of purchasing various levels of Subscription Center access and support. The Subscription Center is accessible via the "key" icon near the right end of the program title bar and also via the "Help: Web Links" menu. Through the Subscription Center, you can download software updates, service packs, and addon applications. You can access training media, such as topical webcasts. Finally, you can also submit technical support requests via the Subscription Center.

Web Links Within the Getting Started tab of the ribbon, in the HELP panel, there is a "Web Links" pullout menu. The following content can be accessed via the web links within this menu: • • • • • • •

Autodesk Simulation - product range Subscription Center Services and Support - information Discussion Group Training - course information Autodesk Labs – where you may obtain free tools and explore developing technologies Manufacturing Community

Tutorials Tutorials are available that demonstrate many of the capabilities of the Autodesk Simulation software. Each analysis is presented through step-by-step instructions with illustrations to assist the user. The tutorials are accessed from the "Help: Tutorials" command and the associated model files are in the "\Tutorials\Models" subdirectory within the program installation folder. The tutorials will appear next to the user interface. You will be able to follow the steps using the software without switching between the two windows.

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Introduction

Figure I.2: Autodesk Simulation Help panel

Webcasts and Web Courses Webcasts focus on the capabilities and features of the software, on new functionality, on accuracy verification examples, and on interoperability with various CAD solid modeling packages. These streaming media presentations are available for on-demand viewing from the Subscription Center via your web browser. Similarly, web courses are also available for on-demand viewing. Web courses are typically longer in duration than webcasts and focus on more in-depth training regarding the effective usage of your simulation software. The topics cover a wide variety of application scenarios. For a list of available webcasts and web courses, follow the "Training" link from the home page of the Subscription Center. Choose the "Autodesk Algor Simulation" or “Autodesk Simulation” product in the "Browse the Catalog" list. This leads to the Autodesk Simulation e-Learning page, in which the available webcasts and web courses are listed according to topic.

How to Receive Technical Support Technical support is reachable through several contact methods. The means you can use may depend upon the level of support that was purchased. For example, customers with "Silver" support must obtain their technical support from the reseller that sold them the software. "Gold" subscription customers may obtain support directly from Autodesk. Five ways to contact Technical Support: •

Reseller:

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Subscription Center: Access the Subscription Center from the link provided in the program interface. Click the Tech Support link on the left side of the page and then click on the "Request Support" link.

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Autodesk Phone:

(412) 967-2700 [or in USA/Canada: (800) 482-5467]

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Autodesk Fax:

(412) 967-2781

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Autodesk E-mail:

[email protected]

Obtain phone, fax, and/or e-mail information from your reseller.


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Introduction When contacting Technical Support: •

Have your contract number ready before contacting Technical Support.

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Know the current version number of your software.

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Have specific questions ready.

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Remember, Technical Support personnel cannot perform, comment on, or make judgments regarding the validity of engineering work.

Updates The software is updated with new functionality on a continual basis. The following three types of releases are provided: 1.

A major version: Indicated by the four-digit year of the software release (based upon the Autodesk fiscal year, not the calendar year)

2.

A "subscription" version: Customers with a current maintenance subscription are eligible for additional releases that may be made available between major product version releases. These are designated by the addition of the word "Subscription" after the major version number.

3.

A service pack: Incorporates minor improvements to a major or subscription release and is indicated by the letters "SP" and a service pack number after the major or subscription version number.

How to Determine the Software Version Click on the "About" button in the" Help" panel. This dialog will display the version that you are using. In addition, the program title bar and the splash screen that appears at each program launch will indicate the major version number of the software. However, as with the start menu group name and program shortcut, it will not indicate the subscription and service pack variants. How to Obtain an Update Update notifications are provided via the "Communication Center" within the user interface. The Communication Center icon is located at the right end of the program window title bar. When new information is available the state of the Communication Center icon, changes. The Communication Center provides up-to-date product support information, software patches, subscription announcements, articles, and other product information through a connection to the Internet. Users may specify how frequently the Live Update information will be polled— on-demand, daily, weekly, or monthly. When a program update notification is received, the user will be given the option of downloading and installing it.

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Introduction

Background of FEA What is Finite Element Analysis? Finite element analysis (FEA) is a computerized method for predicting how a real-world object will react to forces, heat, vibration, etc. in terms of whether it will break, wear out or function according to design. It is called "analysis", but in the product design cycle it is used to predict what will happen when the product is used. The finite element method works by breaking a real object down into a large number (1,000s or 100,000s) of elements (imagine little cubes). The behavior of each element, which is regular in shape, is readily predicted by a set of mathematical equations. The computer then adds up all the individual behaviors to predict the behavior of the actual object. The "finite" in finite element analysis comes from the idea that there are a finite number of elements in the model. The structure is discretized and is not based on a continuous solution. In any discrete method, the finer the increments, or elements, the more precise is the solution. Previously, engineers employed integral and differential calculus, which broke objects down into an infinite number of elements. The finite element method is employed to predict the behavior of objects with respect to virtually all physical phenomena: • • • • •

Mechanical stress (stress analysis) Mechanical vibration (dynamics) Heat transfer - conduction, convection, radiation Fluid flow - both liquid and gaseous fluids Electrostatic or MEMS (Micro Electro Mechanical Systems)

Basic FEA Concepts Nodes and Elements A node is a coordinate location in space where the degrees of freedom (DOFs) are defined. The DOFs of a node represent the possible movements of this point due to the loading of the structure. The DOFs also represent which forces and moments are transferred from one element to the next. Also, deflection and stress results are usually given at the nodes. An element is a mathematical relation that defines how the DOFs of one node relate to the next. Elements can be lines (beams or trusses), 2-D areas, 3-D areas (plates) or solids (bricks and tetrahedra). The mathematical relation also defines how the deflections create strains and stresses.


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Introduction Degrees of Freedom •

The degrees of freedom at a node characterize the response and represent the relative possible motion of a node.

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The type of element being used will characterize which DOFs a node will require.

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Some analysis types have only one DOF at a node. An example of this is temperature in a thermal analysis.

A structural beam element, on the other hand, would have all of the DOFs shown in Figure I.3. "T" represents translational movement and "R" represents rotational movement about the X, Y and Z axis directions, resulting in a maximum of six degrees of freedom.

Figure I.3: Degrees of Freedom of a Node Element Connectivity – Conventional Bonding Elements can only communicate to one another via common nodes. In the left half of Figure I.3, forces will not be transferred between the elements. Elements must have common nodes to transfer loads from one to the next, such as in the right half of Figure I.4. No Communication Between the Elements

Communication Between the Elements

Figure I.4: Communication through Common Nodes Element Connectivity – "Smart Bonding" With the introduction of "Smart Bonding" it is now possible to connect adjacent parts to each other without having to match the meshes (i.e., common nodes at part boundaries are no longer mandatory). This feature is available for both CAD and hand-built models and is applicable to the following analysis types: • • •

Static Stress with Linear Material Models Natural Frequency (Modal) Transient Stress (Direct Integration)

Figure I.5, is a pictorial example of two adjacent parts that may be connected via smart bonding. Smart bonding is disabled by default for both new and legacy models (that is, those 8


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Introduction created prior to implementation of the smart bonding feature). The option may be changed within the "Contact" tab of the Analysis Parameters dialog. Note that where nodal coordinates fall within the default or user-specified tolerance of each other, they will be matched in the conventional manner. Other nodes along the bonded surfaces or edges – those at a relative distance greater than the tolerance – will be connected by means of multipoint constraint equations (MPCs). Also note that the "Use virtual imprinting" option within the "Model" dialog of the mesh settings options will minimize the likelihood that smart bonding will be needed or will occur for CAD-based assemblies. This option attempts to imprint smaller parts on larger parts where they meet, forcing them to have identical meshes.

Figure I.5: Connection via "Smart Bonding" Types of Elements The actual supported and calculated DOFs are dependent upon the type of element being used. A node with translational DOFs can move in the corresponding directions and can transmit/resist the corresponding forces. A node with rotational DOFs can rotate about the corresponding axes and can transmit/resist the corresponding moments. Briefly, the general element types are as follows (more details will be given in later chapters): •

Line elements: A line connecting 2 nodes (such as beams, trusses, springs, thermal rods, and others).

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2-D elements: YZ-planar elements that are triangular or quadrilateral (3 or 4 lines enclosing an area).

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3-D plates or shells: Planar or nearly planar elements in 3-D space. Each must be triangular or quadrilateral and they represent a thin part with a specified thickness.

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Brick (solid) elements: Must be enclosed volumes with 4, 5, or 6 faces (triangular and/or quadrilateral) and with 4, 5, 6 or 8 corner nodes.

DOFs for element types: • • • • •

Truss: Translation in X, Y and Z. Beam: Both translation and rotation in X, Y and Z. 2-D: Translation in Y and Z. Plate: Five degrees of freedom – out-of-plane rotation is not considered. Brick: Translation in X, Y and Z.

How Does Autodesk Simulation Work? •

The software transforms an engineering model with an infinite number of unknowns into a finite model.

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This is an idealized mathematical model.

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The model is defined by nodes, elements, loads and constraints.


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Introduction •

The user interface can be effectively used for the design, analysis and evaluation phases of a typical design process.

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The simulation software can be extremely useful during the initial concept and design phase to identify areas that can be improved.

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The simulation software can also be used to quickly evaluate a concept, saving time and engineering resources.

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This does not necessarily replace the testing needed to evaluate a final design; however the goal is to minimize the prototype and testing stages of design.

The General Flow of an Analysis in Autodesk Simulation Create a Mesh • • • •

Start the simulation program Open your model in the FEA Editor environment Select the analysis type Create your mesh

Define the FEA Data • • •

Assign the loads and constraints Define the material Define the analysis parameters

Run the Analysis Review and Present Results • • •

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Review the desired result types Save images and animations Create presentations and HTML reports


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Introduction

Stress and Strain Review Equations Used in the Solution A complex system can be broken into a finite number of regions (elements), each of which follows the equations below:

σ= ε=

F A

σ

E

∫

L

δ = ε dx 0

F=

AE δ L

Where,


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Introduction In practice, the direct inversion is extremely difficult and sometimes unstable. In FEA, matrices can be 50,000 x 50,000 or larger. As a result, other solution methods for this linear equation have been developed. All of these methods use the basic principles of a mathematical method called Gaussian Elimination. The details of this method will not be discussed here, but may be obtained from any numerical programming text. Since differentiation cannot be performed directly on the computer, approximation techniques are used to determine the strain in the model. Since an approximation technique is used for the strains, the finer the mesh, the better the approximation of the strain. For a linear static analysis, stress has a linear relation to strain. Therefore, the stresses will have the same accuracy as the strains. For more complex analyses, more terms are needed. The equation below is needed to represent a true dynamic analysis:

{f } = [m]⋅ {x}+ [c]⋅ {x}+ [K ]⋅ {x} where the additional matrices and vectors are, m = mass, c = damping,

x = acceleration (second derivative of displacement versus time) x = velocity (first derivative of displacement versus time)

Limits of Static Stress with Linear Material Models •

Deformations are small

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Strains and rotations are small

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Changes in stiffness through the model are small

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Changes in boundary conditions are small

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Changes in loading direction with deformations are small

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Material remains in the linear elastic range

Mechanical Event Simulation (MES) Overcomes Limitations MES supports: •

Large deformations

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Changing boundary conditions

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Loads moving as the model moves or deforms

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Nonlinear material behavior

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Time-dependent loading

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Large-scale motion

Event visualization capabilities:

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Viewing results with respect to time using the Results environment

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Animation tools


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Introduction MES simulates: •

Motion

•

Impact

•

Real-time observation of deformations, stresses and strains

•

Failure due to the following: material yielding, local and structural buckling, permanent deformations - residual stress

MES capabilities are included within the Autodesk Simulation Mechanical product. It is also included within the higher-level Autodesk Simulation Multiphysics product. For information and training regarding MES, refer to the Autodesk Simulation Mechanical – Part 2 training course.

Hand-Calculated Example Refer to Appendix A for an example of displacement and stress results for a simple truss structure. A theoretical solution using fundamental equations is presented. In addition, a hand-calculated solution based on the finite element method is presented and its results compared with those obtained by the FEA software.

Heat Transfer Review Equations Used in the Solution Heat transfer, as applied to FEA, is actually a conduction problem. The heat loads are boundary conditions. The primary results are a temperature profile and the heat flux through the body of the structure. Conduction is the flow of heat in the body of the structure. This is what is being solved in an FEA problem. The properties of conduction are controlled by the part definition. Only the thermal conductivity (k) is needed for a steady-state analysis. For a transient analysis, the mass density and specific heat will also be required. The governing equation is:

 ∆T  q = kA    L  where: k = Thermal conductivity A = Area ∆T = Change in temperature L = Length The two most common loads for a thermal analysis are convection and radiation loads. These loads are applied to a surface. The equation for the heat flow due to convection is:

q = hA (Ts − T∞ ) where: h = Convection coefficient A = Area Ts = Temperature of the surface T∞ = Ambient temperature Autodesk® Simulation Mechanical 2012 – Part 1 – Seminar Notes

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Introduction

The equation for the heat flow due to radiation is:

(

q = εσA(V .F .) T∞4 − Tb4

)

where: ε = Emissivity which describes the surface finish for gray bodies. (If ε = 1.0, it is a true blackbody.) σ = Stefan-Boltzmann constant for radiation A = Area V.F. = View factor from the surface to the infinite source T∞ = Ambient temperature (in units of absolute temperature) Tb = Temperature of the node (in units of absolute temperature)

Linear Dynamics Review Equation for Dynamic Analyses The basic equation of dynamics is:

[m]{a}+[c]{v}+[k]{x}=0 where: [m] = the mass matrix {a} = the acceleration vector [c] = the damping constant matrix {v} = the velocity vector [k] = the stiffness matrix {x} = the displacement vector A natural frequency analysis provides the natural vibration frequencies of a part or assembly based on a linear eigenvalue solution. Because the above equation is solved in this linear solution, only mass and stiffness are taken into account. No damping is used. In addition, loads are ignored. As a result, actual displacement output is meaningless except to define the shape of the natural frequency mode. Note that loads are taken into account for a natural frequency with load stiffening analysis, assuming the loads produce membrane stresses that affect the stiffness of the structure. Constraints have a very significant effect on the solution. When no boundary conditions or insufficient boundary conditions are used, rigid-body movement or modes will be found. Unlike a static solution, this is acceptable in a modal analysis.

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Chapter

1

Using Autodesk® Simulation Chapter Objectives •

Introduction to the user interface Commands - Ribbon Keyboard Mouse View Cube and other view controls

•

Complete an example of using Autodesk Simulation Overview of launching a Simulation from Autodesk Inventor and creating a mesh Overview of adding loads and constraints to a model Overview of defining material properties Overview of performing an analysis Overview of reviewing results Overview of generating a report

Navigating the User Interface In this section, we will introduce you to the Autodesk Simulation user interface. This interface is the same for each of the available packages, including the Simulation Mechanical and Simulation Multiphysics products. The only difference will be with regard to which advanced features or capabilities are enabled. We will begin with an overview of the major components of the graphical user interface. Then we will discuss the Ribbon, keyboard, mouse, View Cube, and additional view controls. Please note that the behavior of the keyboard, mouse and View Cube – as discussed within this manual – are based on the default program settings for a clean installation of the product. Many of the features to be discussed are customizable via tabs and settings within the "Application Options" dialog, reachable via the "Tools: Application Options" command. Figure 1.1 on the next page, along with the legend that follows it introduces the major components of the user interface. This manual is based on Autodesk Simulation 2012. Users of other versions may encounter differences between their version and the interface described herein.


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Chapter 1: Example Using Autodesk® Simulation

Figure 1.1: Autodesk Simulation User Interface Interface Legend: A. Application Menu: Files can be opened and accessed from the Application Menu. Other commands that are available here include Merge, Export and Archive. B. Quick Access Bar: In addition to commonly used commands, customizable, the quick access bar displays the program name and version as well as providing links to the Autodesk Subscription Center and Communication Center C. Ribbon tab: The Ribbon tab is located just below the title bar and contains the pull-down menus. D. Ribbon commands: The Ribbon provides the user with quick access to many commands. E. Tree View: The tree view has unique contents for each environment of the user interface. For the FEA Editor, it shows the parts list and the units, various properties, and loads that will be used for the analysis. In the Results environment, you will see a list of results presentations and other postprocessing-specific content. The components of the analysis report will be listed in the tree view within the Report environment. F. Display Area: The display area is where the modeling activity takes place. The title bar of the window displays the current environment and the model name. The FEA Editor environment is used to create the model, add the loads and constraints and perform the analysis. The Results environment is used to view results and to create images, graphs, and animations. The Report environment will be used to produce a formal report of the analysis, including desired results presentations. View Cube and Navigate bar are also in the Display area by default. G. Miniaxis and Scale Ruler: The miniaxis shows your viewpoint with respect to the threedimensional working area. The scale ruler gives you a sense of the model size, H. Status Bar: The status bar displays important messages.

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Commands Autodesk Simulation accesses program functions through the ribbon, context menus, and quick access toolbar (QAT), in addition to the Application Menu. The available commands and menus vary for each program environment (FEA Editor, Results, and Report). The Ribbon is positioned at the top and is customizable by being able to move the panel positions within the same Ribbon tab.

Figure 1.2: Autodesk Simulation Ribbon The commands are logically grouped into panels and tabs. For example, the Mesh tab includes Mesh, CAD Additions, Structured mesh and Refinement Point panels. Each panel will have specific commands, and so on. These commands can be added to the quick access toolbar, so that they can be easily accessed. This can be done by right clicking on the command in the panel and selecting "Add to Quick Access Toolbar" as shown in figure 1.2. Most of the tabs, panels, and commands will not appear until an existing model is opened or a new model is created. Figure 1.3 shows a typical context menu accessed after clicking a surface on the model and adding a load.

Figure 1.3: Autodesk Simulation Context Menu In some cases there where will be too many commands to be all displayed on the panel. In these situations you can click on the panel options button to gain access to further commands as shown in figure 1.4.

Figure 1.4: Additional Panel commands Autodesk® Simulation Mechanical 2012 – Part 1 – Seminar Notes

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Using the Keyboard and Mouse The keyboard and mouse will both be used to operate within the user interface. The keyboard will be used to enter the required data for loads, constraints, material properties, and so on. It will also be used to modify the behavior of particular mouse operations. That is, certain keyboard keys, when held down, will change the behavior of the mouse. The software supports a number of different mouse configurations. This document assumes that the default template for a new installation is in effect. However, user settings, or those retained from a prior Autodesk Simulation installation, may cause the behavior to differ from that described herein. To ensure that your mouse actions follow the descriptions in this book, access the "Tools: Application Options: Mouse Options" dialog and choose the "Autodesk Simulation" template. The left mouse button will be used to select items. How items are selected will depend upon the selection mode chosen in the "Selection: Shape" pull-out menu or Ribbon. The type of objects that are selected (such as lines, vertices, surfaces, parts, edges, or elements) will depend upon the selection mode chosen in the "Selection: Select" pull-out menu or Ribbon. Holding down the key, while left-clicking on the object, will toggle the selection state of the clicked object. That is, unselected objects will be added to the selection set and previously selected items will be removed from the selection set. Holding down the key while left-clicking will only add clicked objects to the selection set (this will have no effect on already selected items). Finally, holding both and while leftclicking will only remove clicked objects from the selection set (this will have no effect on items that are not already part of the current selection set). Pressing the right mouse button with the cursor hovering over items in the tree view will access a context menu with commands relevant to the item under the cursor. When items are currently selected, either within the tree view or display area, the right-click context menu will display commands and options that are specifically relevant to the selected items. For example, if a surface is selected, only surface-based commands will appear in the context menu. You may right-click anywhere in the display area when items are selected to access the context menu. However, to access the context menu within the tree view area, you must right-click with the cursor positioned on one of the selected headings. If a mouse has a wheel, rolling the wheel will zoom in or out on the model. Holding down the middle mouse button or wheel and dragging the mouse will rotate the model. Pressing the key, while holding the middle button and dragging the mouse, will pan the model, moving it within the display area. Pressing the key while dragging the mouse with the middle button down will zoom in and out, making the model larger as the mouse is moved upward and smaller as it is moved downward. You will likely find the use of the middle mouse button and wheel to be more convenient than choosing a command like "Rotate" or "Pan," clicking and dragging the mouse, and then pressing to exit the command. Finally, the X, Y, or Z key on the keyboard may be held down while dragging the mouse with the middle button held down. Doing so will rotate the model, as before, but constraining the rotation to be only about the corresponding X, Y, or Z global axis direction. You may also use the left and right cursor keys on the keyboard while holding down X, Y, or Z to rotate about these axes in fixed increments (15 degrees by default). The rotation increment is customizable via the "Tools: Application Options: Graphics: Miscellaneous" dialog.

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Introduction to the View Cube As is true for the mouse, the software also supports a number of different view configurations. This document assumes that the default view options template and view navigation settings for a new installation are in effect. However, user settings, or settings retained from a prior Autodesk Algor Simulation or Autodesk Simulation installation, may cause the view orientations and behavior to differ from those described throughout this document. To ensure that your view commands follow the descriptions in this book, access the "Tools: Application Options: Views Options" dialog and choose the "Autodesk Simulation" template. Next, access the "Graphics" tab of the same "Options" dialog, select "Navigation Tools" from the items listed on the left side of the dialog, and click on the "View Cube" button. Click the "Restore Defaults" button followed by "OK" to exit the "View Cube Properties" dialog. Finally, click the "Steering Wheel" button. Click the "Restore Defaults" button followed by "OK" to exit the "Steering Wheels Properties" dialog. Click "OK" to exit the "Options" dialog. Users of other Autodesk® products, such as AutoCAD® or Autodesk® Inventor® will likely already be familiar with the View Cube and associated additional view controls. The View Cube will be located in the upper right corner of the display by default but may be relocated. The appearance will change depending upon whether the view is aligned with a global plane and whether the cursor is near the cube or not. The View Cube, in its various appearances, is shown in Figure 1.5.

(a) Cursor not near the View Cube (b) Cursor on View Cube (view not aligned to a standard face) (c) Cursor on View Cube (standard face view) Figure 1.5: View Cube Appearance The six standard view names, as labeled on the cube faces, are the Top, Bottom, Front, Back, Left, and Right. These may be selected by clicking near visible face names on the cube, as shown in Figure 1.5 (b) or by clicking the triangular arrows pointing towards the adjacent faces, as shown in Figure 1.5 (c), which shows the cursor pointing to the arrow for the Bottom view. In addition, there are clickable zones at each corner and along each edge of the View Cube. Clicking on a corner will produce an isometric view in which that particular corner is positioned near the center and towards you. Clicking an edge will produce an oblique view, rotated 45 degrees, Half-way between the views represented by the two adjacent faces. When the cursor is near the View Cube, a "Home" icon will appear above it and to the left, providing easy access to the home view. This is an isometric view having the corner between the Front, Right, and Top Faces centrally positioned and towards you by default. The home view may be redefined by right-clicking the Home icon and choosing the "Set Current View as Home" command while viewing the model positioned as desired. When one of the six standard views is active and the cursor is near the View Cube, two curved arrows will appear above and to the right of the cube, as seen in Figure 1.5 (c). These


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Chapter 1: Example Using Autodesk® Simulation are used to rotate the model to one of the four possible variants of the particular standard view. Each click of an arrow will rotate the model 90 degrees in the selected direction. When the face being viewed is changed via the View Cube, the model may move to the selected view in the manner that requires the least amount of motion. For example, say we are first looking at the Right view, with the word "Right" positioned upright (that is in the normal reading position). Now, if we click the downward arrow above the cube, the model will rotate 90 degrees to reveal the top face. The Top view will be rotated 90 degrees clockwise from the upright orientation (that is, the word "Top" will read in the vertically downward direction). Activating the "Keep scene upright" option will cause the Front, Back, Left, and Right views to automatically be oriented in the upright position (Top above, Bottom below) when changing to any of these views. You may, however, rotate the view after initial selection, if desired. Go to "Tools: Application Options: Graphics: Navigation Tools: View Cube" to locate the "Keep scene upright" setting. It is activated by default. The point of this discussion is that whenever a new face is selected using the View Cube, the resultant view rotation may differ, depending upon the prior position of the model. If the resultant orientation is not what is desired, simply click one of the curved arrows to rotate the view.

Immediately below the View Cube is a pallet of additional view controls. This consists of seven tools, each of which may be individually enabled or disabled. All are on by default. Figure 1.6 shows the view control pallet. From top to bottom, the seven tools are as follows: • • • • • • •

Steering Wheels Pan Zoom Orbit Center Previous View Next View

Each of these icons, except for the Previous and Next commands, function as a toggle—clicking it once to activate a command and again to deactivate it. Several of the tools, such as Pan, Previous, and Next are self-explanatory

Figure 1.6: Additional View Controls Pallet

Additional View Controls

The "Zoom" tool includes a fly-out menu allowing the choice of one of four different zooming modes—Zoom, Zoom (Fit All), Zoom (Selected), and Zoom (Window). The first of these causes the model to become larger as the cursor is moved upward in the display area and smaller when it is moved downward. The Fit (All) mode encloses the extents of the whole model. After selecting objects in the display area, the Zoom (Selected) tool fits the selected items into the display area. Finally, after selecting the Zoom (Window) tool, you click and drag the mouse to draw a window defines the area you wish to expand to fill the display area. The "Orbit" tool has two variants, selectable via a fly-out menu—Orbit, and Orbit (Constrained). The former allows the model to be rotated freely in any direction. The Constrained option causes the model to rotate only about the global Z-axis, similar to pressing the Z key while dragging the mouse with the middle button depressed. The "Center" tool is used to center a point on the model within the display area. Click with the mouse to specify the desired center point after selecting the Center command. This point also becomes the display pivot point, about which the model pivots when being rotated. 20


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The "Steering Wheel" tool is customizable and, in its default setting, produces the Full Navigation Wheel shown in Figure 1.7. The full navigation wheel floats above the model view, following the cursor position. It provides an additional access method for several functions found elsewhere on the view tools pallet as well as a few additional functions.

Figure 1.7: Full Navigation Wheel The "Rewind" button on the navigation wheel presents a timeline of thumbnails representing various views that have been used during the modeling session. Simply release the mouse button with the cursor positioned at the thumbnail representing the view to which you wish to jump. This is more convenient than pressing the previous or next view buttons multiple times. For additional information concerning these view controls, consult the In-Product Help or Online Wiki Help.

Legacy View Controls in Autodesk Simulation Traditional view controls and options are also provided via the View tab of the command ribbon at the top of the screen. Options for displaying or hiding the mesh or model shading may be found here as well as eight pre-defined, standard view orientations. The orientations will depend upon the currently active Views Options template (previously discussed in the "Introduction to the View Cube" section of this chapter). There is also a "User-defined Views" dialog that may be used to save, modify, or restore custom views. Additional capabilities include a local zoom feature and display toggles for the scale ruler, mini axis, and perspective mode. The "Local Zoom" feature displays a small rectangle that represents the area to be magnified. A larger rectangle shows an overlay of the magnified region. You may click on and drag the local zoom window to position it anywhere on the model within the display area. The size of the local zoom area and magnified overlay and also the zoom level can be customized via the "Application Menu: Options: Graphics: Local Zoom" dialog. For additional information concerning the legacy view controls, consult the In-Product Help or Online Wiki Help.


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Steel Yoke Example This example is an introduction to static stress analysis with linear material models. The example will give step-by-step instructions to create a mesh and analyze a three-dimensional (3-D) model of a steel yoke under an applied force. There are three sections: Setting up the model – Open the model in the FEA Editor environment and create the mesh on the model. Add the necessary forces and boundary conditions and define the model parameters. Visually check the model for errors with the Results environment. Analyzing the model – Analyze the model using the static stress with linear material models processor. Reviewing the results – View the displacements and stresses graphically using the Results environment. Use the Inventor solid model, yoke.ipt, located in the "Chapter 1 Example Model\Input File" folder in the class directory (or extracted to your computer from the solutions archive) to create a simple model of the steel yoke shown in Figure 1.8. The right half of the small hole will be fixed. A force of 800 pounds will be applied to the left half of the large hole and acting towards the left, as shown in the figure. The yoke is made of Steel (ASTM-A36). Analyze the model to determine the displacements and stresses.

Figure 1.8: Steel Yoke Model

Opening and Meshing the Model The FEA Editor environment is used to create a mesh for all solid models. You can open CAD solid models from any of the CAD solid modelers that Autodesk® Simulation supports. You can also open models of any of the universal CAD formats that are supported. Here we are going to access Autodesk® Simulation directly from Autodesk® Inventor®. "Start: All Programs: Autodesk: Autodesk Inventor 2012: Autodesk Inventor Professional 2012" "Getting Started: Launch: Open" "Autodesk Inventor Parts (*.ipt)" "Yoke.ipt" “Open” 22

Press the Windows "Start" button and access the "All Programs" pull-out menu. Select the "Autodesk" folder and then the "Autodesk Inventor 2012" pull-out menu. Choose the "Autodesk Inventor Professional 2012 software" command. Click on the "Open" button in the Launch panel. Alternatively you select “Open” from the quick access toolbar or Application Menu. Select the "Autodesk Inventor Parts (*.ipt) option in the "Files of type:" drop-down box. Select the file "Yoke.ipt” in the “Chapter 1 Example Model \Input File” directory. Press the “Open” button.


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Chapter 1: Example Using Autodesk® Simulation Mouse

Select "Yes" to accept the warning

"Add-Ins: Start Simulation: Autodesk Simulation"

Select the "Add-Ins" tab. Click on the "Start Simulation button in the "Autodesk Simulation" panel. A dialog will appear asking you to choose the analysis type for the model. From the pull-out menu, choose "Linear: Static Stress with Linear Material Models" and press the "OK" button.

"Linear: Static Stress with Linear Material Models" "OK"

The model will appear in the FEA Editor environment. "Mesh: Mesh: 3D Mesh Settings" "Mesh model" "View: Navigate: Orbit"

Mouse

Select the "Mesh" tab. Click on the "3D Mesh Settings" button in the "Mesh" panel. Press the "Mesh model" button to create a mesh with the default options. Select the "View" tab. Click on the "Orbit" button in the "Navigate" panel. Can also access Orbit from the Navigate Bar. Click left mouse button and drag the mouse to rotate the model and inspect the mesh all around it. This mesh appears to be acceptable. When done inspecting the mesh, position the model so that you can see the inside of the small hole as shown in Figure 1.9. These surfaces will be constrained. Press to exit the rotate command.

Figure 1.9: Yoke Rotated to Select Constrained Surfaces

Setting up the Model The FEA Editor environment is also used to specify all of the element and analysis parameters for your model and to apply the loads and constraints. When you initially come into the FEA Editor environment with the yoke model, you will notice a red X on certain headings in the tree view. This signifies that this data has not yet been specified. You will need to eliminate all of the red Xs before analyzing the model. Since you have created a solid mesh, the


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Chapter 1: Example Using Autodesk® Simulation "Element Type" heading in the tree view is already set to "Brick" and the default "Element Definition" parameters have been accepted. Adding Constraints Constraints describe how a finite element model is tied down in space. If an object is welded down so that it can neither translate nor rotate, the object is fully constrained. "Selection: Shape: Point"

Select the "Selection" tab. Make sure the "Point" button is selected in the "Shape" panel.

"Selection: Select: Surfaces"

Also make sure the "Surfaces" button is selected in the "Select" panel.

Mouse Mouse "Setup: Constraints: General Constraint"

Click one of the surfaces on the right side of the small hole as oriented in Figure 1.9. Holding down the key, click on the other surface on the right side of the small hole. Select the "Setup" tab. Click on the "General Constraint" button in the "Constraints" panel.. The dialog shown in Figure 1.10 will appear.

Figure 1.10: Surface Boundary Condition Dialog

"Fixed"

"OK"

24

Press the "Fixed" button. Note that all 6 of the checkboxes in the "Constrained DOFs" section to the left are activated. This means that the nodes on this surface will be totally constrained. Press the "OK" button to apply these boundary conditions. Now there will be green triangles on the nodes of the surface that was selected. This signifies a fully constrained boundary condition.


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Chapter 1: Example Using Autodesk® Simulation Adding Forces to the Model In this section, you will add the 800 lb force in the –X direction to the large hole. Click and drag using the middle mouse button to rotate the model. Position it so that you can see the surfaces of the large hole where the load is to be applied (that is, the two quarter surfaces at the left side of the hole). Click on one of the surfaces on the left interior of the large hole to select it. Holding down the key, click on the other surface on the left side of the large hole. Click on the "Force" button in the "Loads" panel.. The dialog shown in Figure 1.11 will appear.

Mouse

Mouse Mouse "Loads: Forces…"

Figure 1.11: Surface Forces Dialog

-400

"X" "OK"

"View: Navigate: Top View"

Type "-400" in the "Magnitude" field to add two forces of 400 pounds each in the negative X direction to the surfaces. This force will be evenly distributed across each surface. They will combine to produce the desired 800 pound load. Select the "X" radio button in the "Direction" section to add surface forces in the X direction. Press the "OK" button to apply these surface forces. Now there will be green arrows on the surfaces that were selected. They are pointed in the negative X direction. Select the "View" tab. Click on the options button to the bottom of "Orientation" button in the "Navigate" panel. Select "Top View" from the pull-out menu. The model should now look like Figure 1.12. The View Cube can also be used to access the views


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Figure 1.12: Yoke after Boundary Conditions and Loads are Applied Assigning the Parameters Once the model has been constructed and the loads and constraints have been applied, use the FEA Editor environment to specify material properties. Mouse "Edit Material…" "Steel (ASTM-A36)"

26

Right-click on the "Material" heading for Part 1. Select the "Edit Material…" command. The "Element Material Selection" dialog will appear. Highlight the "Steel (ASTM-A36)" item from the list of available materials as shown in Figure 1.13.


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Figure 1.13: Element Material Selection Dialog "Edit Properties" "OK" "OK" Mouse "Analysis: Analysis: Check Model" "Tools: Environments: FEA Editor" "View: Orientation: Isometric View"

Press the "Edit Properties" button to view the material properties associated with this steel. Press the "OK" button to exit the "Element Material Specification" dialog. Press the "OK" button to accept the information entered in the "Element Material Selection" dialog for Part 1. Accept the warning to override default material defined within Inventor. Select the "Analysis" tab. Click on the "Check Model" button in the "Analysis" panel. Select the "Tools" tab. Press the "FEA Editor" button in the "Environments" panel. Select the "View" tab. Click on the options button to the bottom of "Orientation" button in the "Navigate" panel. Select "Isometric View" from the pull-out menu.

Analyzing the Model

"Analysis: Analysis: Run Simulation"

Select the "Analysis" tab. Click on the "Run Simulation" button in the "Analysis" panel. When completed, the model will be displayed in the Results environment and the von Mises stress will be displayed, as shown in Figure 1.14 below. Note the maximum stress value.


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Figure 1.14: Yoke Model as Displayed in the Results Environment

Reviewing the Results "Results Contours: Stress: von Mises"

Note the maximum von Mises value.

"Results Contours: Displacement: Displacement"

Select the "Results Contours" tab. Click on the "Displacement" button in the "Displacement" panel. Note the maximum displacement magnitude.

The maximum von Mises stress and maximum deflection should closely match the values in the table below. Maximum von Mises Stress (psi)

Maximum Displacement (in)

~1,900

~0.0004

Viewing the Displaced Shape Viewing the displaced shape is always the best way to get an overall understanding of how the model reacted to the applied load. A displaced model alone or a displaced model overlaid with a undisplaced model can be displayed. 28


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"Results Contours: Displaced Options" "Transparent" Mouse

Click on options next to "Show Displaced" button in the "Displacement" panel. Then select "Displaced Options" button. Select the "Transparent" radio button in the "Show Undisplaced Model As" section. Press the button in the upper right corner of the "Displaced Model Options" dialog.

Creating an Animation " Results Contours: Captures: Start Animation" "Captures: Stop Animation"

Select the "Results Contours" tab. Click on the "Start Animation" button in the "Captures" panel. Click on the "Stop Animation" button in the "Captures" panel.

The preceding steps animated the results within the display area but did not create an animation file that we can place in our report. In the following steps, we will export an animation file that can be included in the report or copied to and played on any computer. "Animation: Save As AVI…" "von Mises Stress Animation" "Save" "No"

Click on the "Start Animate" button in the "Captures" panel. Then select "Save As AVI" option. Rather than using the default file name, type "von Mises Stress Animation" into the "File name:" field. Press the "Save" button to save the animation to an AVI file format. Press the "No" button when asked if you want to view the animation.

Generating a Report In this section, you will automatically create an HTML report using the Report Configuration Utility. "Tools: Report"

Select the "Tools" tab. Click on the "Report" button in the "Environments" panel..

"Tools: Setup: Configure"

Select the "Configure" button in the "Setup" panel. This will open the dialog shown in Figure 1.15.


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Figure 1.15: Report Configuration Utility NOTE: Clicking on any of the checkboxes will toggle the inclusion state of the item (i.e. whether it is to be included or excluded from the HTML report). When selecting included portions of the report, to modify them. Click on the item name and not on the checkbox. This will select the item without toggling the checkbox state.

Mouse

Activate the checkbox next to the "Logo" heading. This will include the default Autodesk® logo at the top of the report.

Note that you may also customize the logo by browsing to and selecting your own image file. Several different image file formats are supported. The logo size and alignment may also be adjusted by right-clicking on it and choosing the "Format Image" command. You may also select the image and then click and drag the handles that appear around the image border while it is selected to resize it. Mouse

Select the "Project Name" heading.

Mouse: Yoke Design Mouse: Analysis of Yoke under 800 lbf Loading

Click and drag the mouse to select the text, "Design Analysis" and type "Yoke Design" to replace it. Click and drag the mouse to select the text, "Project Title Here" and replace this text by typing "Analysis of Yoke under 800 lbf Loading".

Mouse

Select the "Title and Author" heading.

Your Name

Type your name into the "Author" field.

Your Department

Type your department name into the "Department" field.

Mouse

Select the "Reviewer" heading.

Person who checked model Department of person who checked the model 30

Type the name of the person who checked the model into the "Reviewer" field. Enter the name of the department of the person who checked the model into the "Department" field.


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Chapter 1: Example Using Autodesk® Simulation Passed all FEA tests

Type "Passed all FEA tests" into the "Comments" field.

Mouse

Deselect the "Executive Summary" item by clicking on the associated checkbox. This item will be excluded from the report.

NOTES: Text can be added as desired within the "Executive Summary" section using the built-in word processor features. A variety of font and paragraph styles are included, such as bullet or numbered lists, tables, tabs, and various text justification settings. The following sections are automatically generated and cannot be modified. The analyst may only include or exclude these items or alter their order of appearance within the report:

• • • • • • • • • • • • •

Summary Analysis Parameters Parts Element Material Loads Constraints Probes Rotating Frames (applicable to fluid flow analysis) Results Presentations Processor Log Files Group Code Checking – General Code Checking – Detailed

Mouse

"Tree: Add AVI File(s)..."

"von Mises Stress Animation.avi" "Open"

Deselect the "Results Presentations" checkbox. Rather than including the default image of the results window, we will include the previously generated animation. Access the TREE pull-down menu and select the "Add AVI File(s)..." command. This will allow you to include an animation file within the report. Alternately, you can right-click in the report tree area and choose the "Add AVI File" command. Browse to and select the previously created animation file "von Mises Stress Animation.avi". Press the "Open" button. A "von Mises Stress Animation" heading will appear in the report tree and it will be selected.

The default text within the "Header Text:" field will match the filename. We will leave it as is. Optional text may be placed in the report below the animation, if desired, by entering the desired text into the "Caption" field. We do not need to include a caption for this example.

Mouse

"Generate Report"

Click and drag the "von Mises Stress Animation" heading in the report tree and release it over the "Processor Log Files" heading. This will reorder the report, placing the animation immediately before the processor log files. Press the "Generate Report" button. This will automatically bring up the report, which will appear as shown in Figure 1.16 below. You can scroll through and review the full report.


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Figure 1.16: Completed Report NOTE: The default title image is the model as it currently appears within the FEA Editor environment. A different image may be substituted for this one and/or the image may be resized using the report configuration utility. To adjust the image size or alignment right-click on it and choose "Format Image" command. You may also select the image and then click and drag the handles that appear around the image border while it is selected to resize it.

A completed archive of this model (yoke.ach), including results, is located in the "Chapter 1 Example Model\Results Archive" folder in the class directory or in the copy of the solutions folders on your computer.

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Chapter

2

Static Stress Analysis Using CAD Solid Models Chapter Objectives • • • • • • • • • •

Learn about working with model archives Learn how to open and mesh CAD solid models Learn how to work with multiple unit systems Learn the types of loads available for static stress analysis Learn how to use load cases Learn the types of constraints available for static stress analysis Learn about design scenarios Learn how to use symmetry and antisymmetry Learn how to define local coordinate systems Learn how to use the Material Library Manager

Archiving a Model Before getting into the specifics of working with CAD solid models and setting up static stress analyses, let us take a moment to discuss model archives. These will be referenced throughout this manual. In the "Application" pull-down menu, there is a pull-out menu called "Archive". This menu has five choices: "Create", "Retrieve", "Manage Existing", "Repair", and "Delete" The "Create" command will allow you to create a file with an .ach extension. This file is similar to a zip file format. When you select the "Create" command and select "Save", once the filename has been specified the following dialog will appear:

Figure 2.1: Archive: Create Dialog Autodesk® Simulation Mechanical 2012 – Part 1 – Seminar Notes

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Chapter 2: Working with CAD Solid Models and Static Stress Select either the "Model only" or "Model and results" radio button to save into the archive (.ach) file. Selecting the "Model and results" radio button allows you to conveniently store the model and its results in one compressed file. There is a "Comment" field noting the location and name of the file to be saved. If you select the "Retrieve" command, then you can retrieve and uncompress an existing archive file for viewing or applying changes. You will be prompted to specify the location where the files are to be placed when extracted. You can also retrieve an archive using the "File: Open…" command by selecting "Autodesk Simulation Archive (*.ach)" as the file type to open. The "Manage Existing" command allows you to see and manage an existing archive file. The dialog lists all of the files in the archive file and allows the user to remove or update any file. If an archive file has become corrupt use the "Repair" command to fix it. You can also use the "Delete" command to delete archive files.

Types of Brick Elements There are four possible geometrical configurations that can be used to create a brick element. These are displayed in Table 2.1 Table 2.1: Brick Element Geometry Configurations

34

8-noded Brick

6-noded Wedge

5-noded Pyramid

4-noded Tetrahedral


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Chapter 2: Working with CAD Solid Models and Static Stress

Generating Meshes for CAD Models In this chapter we will cover the basics of creating meshes for CAD models. This will be sufficient for completing the exercises in the first few chapters. The topic will be covered in more detail in Chapter 5, "Meshing." Autodesk® Simulation is compatible with most FEA software products and most major CAD products. It works from native CAD files as well as STL, IGES, ACIS, and STEP files. For native CAD formats not directly supported, the models can typically be exported using one of the supported universal formats. Meshing operations are performed on solid models and 3-D plate/shell models using quadrilateral or triangular elements representing the surface of the model. The interface also offers enhanced user control over the geometric properties of the generated solid brick mesh. Users can control internal angles of quadrilaterals and quadrilateral warpage, adapting to requirements of some FEA systems. At the lowest interface level, the simulation program retrieves an existing solid model for FEA processing from another source such as a CAD solid modeler or from another finite element program. The engineer can automatically improve the mesh for more accurate and faster FEA results. At the highest level, the engineer can intervene to enhance the model, including adding local mesh refinement, adding manually constructed elements, or merging in additional parts or assemblies. CAD Solid Models Supported directly: • • • • • • • •

ACIS files (*.sat) AutoCAD (*.dwg, *.dxf) Inventor files (*.ipt, *.iam) Inventor Fusion (*.dwg) Mechanical Desktop (*.dwg) IGES files (*.igs, *.iges) STEP files (*.stp, *.step) Stereolithography files (*.stl)

Note: More files can be brought into Autodesk Simulation via Autodesk Fusion To open these models, access the "Application" pull-down menu, select the "Open" command, and select the file type you need in the CAD Files section of the "Files of type:" drop-down box. The model will be opened in the FEA Editor environment. You can also use the "Merge" command to create assembly files from multiple part or subassembly files. The models will be combined using the same position and orientation as the CAD solid models. When you first open a CAD solid model in the user interface, you may be asked if you want to use a process called "surface-knitting." Whether or not you see a surface-knitting prompt depends upon the settings under "Application Menu: Options: CAD Import." The options for the "Knit surface on import" settings are "Yes" "No" and "Ask each time." This process is required if an internal or external fluid part is to be automatically derived within Autodesk Simulation from the imported CAD geometry. It also enhances mesh matching between parts by splitting the surfaces where two parts meet so that the two intersecting surfaces and their feature lines are identical for each part. If surface-knitting is performed, it also lets the user apply a load — such as pressure or convection — to a surface that partially intersects an adjacent part without having it act on the portion of the surface where the two parts meet. In Autodesk® Simulation Mechanical 2012 – Part 1 – Seminar Notes

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Chapter 2: Working with CAD Solid Models and Static Stress other words, the load will act everywhere on the surface except where it is coincident with another part, since this portion will actually be identified by a new surface number after knitting has been completed. After the model has been imported, you will need to re-import the original model if you want to change whether to knit the surfaces or not. It is not necessary to perform surface-knitting on assemblies if the only purpose is to enhance mesh matching. Meshing features called "virtual imprinting" and "smart bonding" are sufficient to enhance connectivity between adjacent parts. Smart bonding was discussed in the "Introduction" chapter. Virtual imprinting identifies coincident surfaces between adjacent parts and meshes these intersecting regions one time, producing an identical mesh on both parts where they meet. It does not actually divide the larger surface into two subsurfaces as the surfaceknitting operation does. So, if this behavior is desired or if fluid part derivation is to be performed, you must still do surface-knitting. NOTE: By default, the surface-knitting operation is disabled for a new or clean installation of the current software version. For the purpose of this manual's exercises and examples, it will be assumed that the surface-knitting option is set to "No." If this is not the case for a given PC, either change the setting under "Application Menu: Options: CAD Import" or simply answer "No" whenever prompted unless instructed otherwise. The setting may also be changed by clicking on the "Options" button within the File: Open dialog when a CAD file type is selected.

Creating a Mesh When a CAD solid model is opened in the FEA Editor environment and the "Mesh: 3D Mesh Settings" command is chosen; the "Model Mesh Settings" dialog pictured in Figure 2.2 will appear.

Figure 2.2: Model Mesh Settings Dialog The "Solid" radio button in the "Mesh type" section will be selected. By default, the program will automatically create a surface mesh on all parts and verify that they each enclose a watertight volume. The solid mesh will be generated during the analysis phase. The options specified in the "Model Mesh Settings" dialog will be applied, by default, to all of the parts in the model. If you want to apply certain mesh settings to a specific part(s), right-click on the part(s) in the display area or on the heading(s) for the part(s) in the tree views. Select the "CAD Mesh Options…" pull-out menu and then choose the "Part…" command. A dialog identical to the "Model Mesh Settings" dialog will appear. The mesh settings specified in this dialog will only be applied to the selected part(s). This functionality will allow you to mesh certain parts as brick elements and other parts as plate elements, for example. 36


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Click on the slider bar in the "Mesh size" section and drag it to the desired mesh coarseness or fineness. Press the "Mesh model" button to create the mesh. When the mesh is complete, you will have the option to view the mesh results. Pressing the "View Mesh Results" button, within the "Mesh panel options; will access the "Meshing Results" dialog shown in Figure 2.3.

Figure 2.3: Meshing Results Dialog If the "Model" button is depressed, the mesh results for the entire model will be displayed. If the "Part" button is depressed, you will be able to toggle through the results for each part in the assembly. After you are finished reviewing the mesh results, press the "Close" button.

Model Mesh Settings – Options By pressing the "Options…" button within the "Model Mesh Settings" dialog, a different "Model Mesh Settings" dialog will appear. There are three icons on the left side of this dialog that will each access different options. •

The "Surface" icon will access options that are used to control the surface mesh.

•

The "Solid" icon will access options that are used to control the solid mesh.

•

The "Model" icon will access options that will affect all parts of the model.


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Chapter 2: Working with CAD Solid Models and Static Stress The dialog accessed by the "Surface" icon is shown in Figure 2.4.

Figure 2.4: Model Mesh Settings Dialog with the Surface Icon Active

Mesh Settings – "Surface" Section: The options within the "Surface" section of the mesh settings dialog control the size of the mesh, how to proceed when automatic mesh size reduction is necessary, and whether second order elements are to be generated. Mesh size section: Size: The value in this field controls the size of the mesh that will be applied. The type of value shown depends on the selected option in the "Type" drop-down box. If the "Percent of automatic" option is selected, this value will be a ratio of the default mesh size that was determined when the model was opened in the FEA Editor environment. If the "Absolute mesh size" option is selected, this value will be the length of one side of an element in the current units system. The actual element length will typically vary slightly from the requested size because the number of elements along an edge or across a surface must be a whole number. Type: In this drop-down box, you can choose to have the size defined as a percent of the default value calculated when the model was opened ("Percent of automatic") or an absolute size ("Absolute mesh size"). Retries section: If a successful mesh cannot be formed with the currently specified mesh size, the mesh engine will try again after reducing the size by the value in the "Retry reduction factor" field. It will repeat this process, if necessary, until the number of retries specified in the "Number of retries" field is reached. If all of the retries fail, the original mesh size will be used and any problem surfaces will not be meshed. Generate 2nd order elements: There is an option in the element definition screen to include midside nodes in the finite element solution for brick, shell, tetrahedron and certain other element types. When midside nodes are included, they are – by default – placed at the midpoint of straight 38


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Chapter 2: Working with CAD Solid Models and Static Stress lines connecting the vertices of each element. This is true even when a surface mesh lies on a curved surface of a CAD-based model. Activating the "Generate 2nd order elements" option causes midside node placement to be based on the surface of the CAD model so that they follow the curvature of the part(s). In other words, they don't have to lie along a straight line between two element corner vertices. Mesh Settings – "Model" Section: Please refer to Chapter 5 for information regarding options within this section of the mesh settings dialog. Mesh Settings – "Solid" Section: The options within the "Solid" section of the mesh settings dialog are beyond the scope of this introductory level course. Please consult the program Help files for further information. The appropriate help file section may be accessed by pressing the "Help" button within the model mesh setting dialog or via the "Contents," "Index" or "Search" command in the HELP pull-down menu.

Tips for Modeling with CAD Solid Model Software for FEA Often, some FEA issues can be avoided by employing certain modeling techniques within the CAD software used to create the solid models. For example, large assemblies can result in large numbers of elements being created and will increase setup and analysis time, making it desirable to simplify the models. There are several guidelines to consider during CAD model creation that can simplify the FEA procedures and control the size of the FEA models. •

Combine parts with the same material properties: Since each part has a single material, it is convenient to combine parts of the same material into a single part. This can be done in the CAD solid modeler. This will require you to only enter the material properties for one part instead of several.

•

Remove parts that are not relevant to the stress calculations: Some complicated assemblies can actually be legitimately simplified by eliminating some parts. The only reason some parts are in an assembly is to prevent other parts from moving in a particular direction. The effect of these parts can be replaced by properly constraining the model. Other parts are simply there to connect two parts together. This connection can be simulated by connecting the nodes of these parts.

•

Remove unnecessary details: Many assemblies have relatively small features such as fillets or holes that will not affect the stress results. These features will require a finer mesh size in their areas, which could result in significantly more elements. Removing or suppressing these features will reduce the analysis time. In the Autodesk Simulation menu, toolbar, and/or command ribbon for some of the CAD systems for which a direct transfer exists, there is a command entitled "Simply Model.". This command will allow you to quickly suppress features in your CAD model that are not necessary for the FEA model. Features that are suppressed will not be transferred to the simulation software.

•

Split surfaces: Many loads are applied to the surfaces of a model. If a load will only be applied to a portion of a CAD surface, it may be useful to split the surface in the CAD software so that the desired portion bears a unique surface identification. Another use of this would be to control how the surfaces are created along a cylindrical hole. The simulation software divides incoming cylindrical surfaces into two semicircular surfaces. These may be rotated 90 degrees from how you would need them in order to properly apply a load to 180 degrees of the cylinder, for example. Splitting the surface in the CAD software would allow you to control this and to create load application areas wherever desired.

Inventor Parameters are now available within Autodesk Simulation and can be used to modify the component directly within Autodesk Simulation Autodesk® Simulation Mechanical 2012 – Part 1 – Seminar Notes

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Simplify CAD Solid Models with Autodesk Fusion As an alternative Autodesk Fusion can be also used to simplify cad models as shown below in figure 2.5

Figure 2.5: Simplifying models in Autodesk Fusion Once the model has been simplified then the model can then be sent to Autodesk Simulation using the "Autodesk Simulation" button in the "Simulation" panel. Fusion can open many CAD format files including, Alias, CatiaV5, Pro Engineer, Rhino, Solidworks and more. Once the model is within Autodesk Simulation further editing of the model is possible using the "CAD with Fusion" button in the "Edit" panel as shown in figure 2.6.

Figure 2.6: Simplifying models in Autodesk Fusion Once the model has been further simplified the model can then be sent back to Autodesk Simulation and then model will be updated within Autodesk Simulation. Fusion is ideal for components that have no feature history or are made up neutral CAD file formats as Fusion allows direct modeling capabilities.

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Working with Various Unit Systems It is possible to define element data, material data, geometry, and loads based on multiple unit systems. The analyst need not convert all input data to the same unit system as the one used to initially construct the model. Beneath the active design scenario heading in the tree view, there is a "Unit Systems" branch. Here, the "Model Units" and various pre-defined "Display Units" are listed. Figure 2.7 shows a typical model's tree view with the Unit Systems branch highlighted.

Figure 2.7: Tree View Showing Unit Systems Branch To choose alternate display and input units, simply double-click the heading showing the desired units, or right-click and choose the "Activate" command. Pre-defined unit systems can be altered by right-clicking on the heading and choosing the "Edit" command. A unit system may be renamed either by clicking on a heading that is already selected, thus entering a name editing mode, or by double-clicking the heading and specifying new name in Description field.. The user may also create their own display unit systems which will be added to the list in the Unit Systems branch of the tree view. To do so, right-click on the top-level Unit System heading in the tree view and choose the "New…" command. A Unit System dialog will appear, as shown in Figure 2.8. Autodesk® Simulation Mechanical 2012 – Part 1 – Seminar Notes

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Figure 2.8: Unit System Dialog All data input fields have pull-down menu boxes associated with them, the available units for each item (force, length, time, temperature, and so forth). Begin by selecting the existing unit system that is closest to the desired system. To do this, first select the "Unit System" input field at the top of the dialog. A down-arrow button will appear at the right end of the field once it has been selected. Use this button to access the pull-down list of available systems and choose the one that is most similar to the system you wish to create. Then, access the list once more and choose the "Custom" option. This action will unlock all of the individual items in the "Corresponding Units" section below, so that they can be altered. By first choosing the most similar existing system, several of the fields may already bear the desired units designations for the new system, minimizing the number that you need to change. Choose the desired display and input units for the items that you wish to alter using the pulldown lists at each input field. Enter a unique name in the "Description" field for identification of the custom unit system in the model tree. To make the new unit system available, for all future FEA models, to be created on the subject computer workstation, activate the "Add to tree for new models" checkbox. If you only want this unit system to be available for the current model, leave this box unchecked. When an alternate unit system is activated, all data input screens will reflect the associated current input units. These will remain in effect until the unit system is changed once again. This facilitates inputting available model data that may be in differing unit systems. For example, you may have load data in English (in) units but your available material data may be in Metric mks (SI) or cgs units. Simply change to the appropriate unit system before accessing the input screens for the quantities or properties being defined. You will not have to manually perform the units conversions. Alternate unit systems are also available within the Results environment. For example, a model can be constructed using mm for length with loads applied based on Newtons, degrees C, and Joules. By choosing the English (in BTU) system in the Results environment, analysis results will be presented using pounds per square inch (psi) for stresses and thermal results will be shown in units of BTUs (British Thermal Units) and degrees F.

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Loading Options In static stress analysis with linear material models, there are four different categories of loading: nodal, edge, surface and element. The loading options are listed below. Loading options for thermal analysis will be covered in Chapter 8, "Steady-State Heat Transfer" and in Chapter 9, "Transient Heat Transfer." Nodal loading: •

Nodal Force: Will apply a force along any vector to the selected nodes.

•

Nodal Lumped Mass: Will apply the effects of a mass concentrated at the point of attachment. For the mass moment of inertia (rotational inertia) about a given axis to have effect, the element type must support rotational DOFs.

•

Nodal Moment: Will apply a moment about any vector to the selected nodes. The nodes must be on an element type that supports rotational DOFs.

•

Nodal Prescribed Displacement: Applies a displacement along any vector to the node.

•

Nodal Temperatures: Applies a temperature to the selected node for use in a thermal stress analysis. Temperature data can also be mapped from a thermal analysis.

•

Nodal Voltages: Applies a voltage to the selected nodes for use in a piezoelectric analysis. Voltage data can also be mapped from an electrostatic analysis.

Edge loading: •

Edge Force: Applies nodal forces to the nodes on an edge so that the magnitude is evenly distributed over the length.

•

Edge Prescribed Displacement: Applies nodal displacement boundaries to each node on the edge.

Surface loading: •

Surface Force: Evenly distributes a force over the surface.

•

Surface Variable Load: Applies a pressure that will vary with position according to a mathematical function. Refer to the example at the end of this chapter.

•

Surface Pressure/Traction: Applies pressures either normal to a surface or along a specified direction.

•

Surface Hydrostatic Pressure: For brick elements, this applies a hydrostatic pressure which is zero at a specified Y-elevation and increases linearly in the -Y direction. The model must be oriented with the +Y direction being vertically upward. For plate elements, the model and hydrostatic pressure may have any orientation (see the "Hydrostatic Pressure Loads" heading under the "Loading Options" section of Chapter 4).

•

Surface Prescribed Displacement: Applies nodal displacement boundaries to each node on the surface.

•

Surface Temperature: Applies nodal temperatures to each node on the surface.

•

Surface Voltage: Applies nodal voltages to each node on the surface.


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Chapter 2: Working with CAD Solid Models and Static Stress Element loading: •

Accelerations/gravity: Will apply an acceleration load to the entire model. The parts must have a mass density defined.

•

Centrifugal loads: Will apply a centrifugal load perpendicular to a global axis to the entire model. The parts must have a mass density defined.

For additional details about the application and definitions of any of these preceding loads, refer to Appendix C. NOTE: Nodal loads may be defined at a remote point not on the model geometry and attached to a set of model nodes, edges, or surfaces using automatically generated line elements. Refer to the help files for additional information regarding the application of remote loads and constraints. Loads applied to nodes, edges or surfaces can be copied and duplicated on other nodes, edges, or surfaces. This can be done by clicking on the load and right-clicking in the display area. Select the "Copy" command. Right-click on the node, edge or surface where you want to duplicate the load, and select the "Paste" command

Load Cases When applying most loads, there is a "Load Case / Load Curve" field. This field will control which load case the load is applied in. Each load case will be analyzed separately. For example, if you want to see the effect of a 100 pound force applied in the X direction and a separate 500 pound force applied in the Y direction, you can place these forces in load case 1 and load case 2. If you also want to see the combined effect, you can copy these forces and apply them both in load case 3. When the analysis is performed, there will be three sets of results in the Results environment. You can toggle through the load cases using the "Next" and "Previous" options in the "Load Case Options" panel in the "Results Contours" tab. Certain loads need load case multipliers in order to be applied. For instance, if you apply a pressure or a surface force, you need to assign a value in the "Pressure" column of the "Load Case Multipliers" table in the "Multipliers" tab of the "Analysis Parameters" dialog. This dialog is accessed either by selecting the "Parameters" button in the "Model Setup" panel in the "Setup" tab or by right-clicking on "Analysis Type" heading in the tree view and selecting the "Edit Analysis Parameters …" command. This multiplier is a global multiplier for all of your pressures and surface forces in your model. If you entered 1,000 psi for the pressure and put a load case multiplier for pressure of 2.0, your actual pressure in the model for that load case will be 2000 psi. The value in the "Index" column refers to the load case number There are seven multipliers in the "Analysis Parameters" dialog for a static stress analysis: Pressure:

This multiplier will multiply all pressures, tractions, surface forces, surface variable loads and beam distributed loads.

Accel/Gravity: This multiplier will multiply the acceleration loads defined under the "Accel/Gravity" tab. Rotation:

This multiplier will multiply the rotation rate specified under the "Centrifugal" tab.

Angular Accel: This multiplier will multiply the angular acceleration specified under the "Centrifugal" tab. 44


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Boundary:

This multiplier will multiply the magnitude of all displacement boundary elements.

Thermal:

This multiplier does NOT directly multiply the magnitude of the temperature applied to each of the nodes in a model. Rather, it multiplies the thermal load as defined by the equation: Thermal Load = (Coefficient of Thermal Expansion) * (Nodal Temperature – Stress Free Reference Temperature) So, the difference between the nodal temperature and the stress-free reference temperature (defined in the "Element Definition" dialog) is being multiplied. Therefore, a thermal multiplier of 2 will result in exactly double the stress relative to a thermal multiplier of 1, even for parts with non-zero stress free reference temperatures.

Voltage:

This multiplier will multiply the magnitude of the voltage applied to each of the nodes in a model.

You can combine these multipliers in any order and can turn off loads for different load cases by entering a zero for that column. Refer to Figure 2.9 for an example.

Figure 2.9: Analysis Parameters Dialog The load case multipliers shown in Figure 2.7 would be used to model the following situations: 1.

Only surface applied forces, pressures, and/or traction loads applied.

2.

No load except for gravity.

3.

No load except for thermal loads.

4.

All loads listed in preceding items 1 through 3.

5.

1.5 times the surface applied forces, pressures, and/or traction loads combined with gravity and 1.25 times the thermal load.


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Constraint Options In static stress analysis with linear material models, constraints can be applied to the model in three ways: to nodes, edges or surfaces. If a constraint is applied to a surface or edge, constraints will be applied to each node on the surface or edge. General Constraint: Will constrain the node to which they are applied against translation or rotation along the specified direction. Pin Constraint: Pin constraint can be applied to only a surface on the model. Pin constraint will allow too restrict the motion in the radial, tangential and axial directions about the coordinate system defined by the circular surface selected. Pin constraints are often used to simulate pin connection. 3D Spring Support: Will apply stiffness against translation or rotation along a global direction. 1D Spring Support: Will apply stiffness against translation or rotation along any vector. More details about constraints in Appendix C

Modeling Symmetry and Antisymmetry One way to simplify models is to use symmetry or antisymmetry. If the loading, geometry and results of a model are symmetric about a plane, only the part of the model on one side of that plane needs to be analyzed. However, in order to get correct results, the proper constraints must be applied at the symmetry plane. When modeling symmetry, the out-ofplane translation and the two in-plane rotations must be constrained. This is described in Figure 2.10. If the geometry is symmetric, but the loading and results are antisymmetric, you can apply antisymmetric constraints along the symmetry plane. When modeling antisymmetry, the two in-plane translations and the out-of-plane rotation must be constrained. This is described in Figure 2.11.

Figure 2.10: Symmetrical Model

Figure 2.11: Antisymmetrical Model

For additional details about the application and definitions of any of these constraints, refer to Appendix C.

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Design Scenarios A design scenario is a set of parameters for a model. Multiple design scenarios can be present for a single model file. Any parameter can be changed between design scenarios. The only limitation is that a single file cannot have different CAD models between design scenarios. The mesh parameters can change, but not the actual CAD geometry. For hand built models, each design scenario can contain unique geometry. The results for each design scenario will be kept separate. Therefore different analysis types can be performed on a single model in separate design scenarios and the results can be easily loaded for each analysis type. Figure 2.12 shows a tree view with three design scenarios.

Figure 2.12: Tree View with Three Design Scenarios In this case, three design scenarios were used because pressure loads follow a global multiplier. Therefore a model cannot have pressure in one location in load case 1 and another location in load case 2. For a static stress analysis, design scenarios are not a complete substitute for multiple load cases. Since design scenarios are actually separate models, the entire analysis will be performed twice for two design scenarios. Multiple load cases can be solved in the same analysis. It is recommended that multiple load cases be used if: •

Geometry, mesh and element parameters are the same. This includes plate thickness and beam or truss cross-sectional properties.

•

The loading consists of loads which can be placed in individual load cases such as nodal forces or moments.

•

The loading consists of loads which can be scaled by a single value in different load cases. For example, all pressure loads can be scaled by a different pressure multiplier in each load case.


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Chapter 2: Working with CAD Solid Models and Static Stress It is recommended the multiple design scenarios be used if: •

Geometry, mesh or element input is different for each situation.

•

The loading consists of loads that cannot be adequately controlled by load cases. For example gravity can only be applied in one direction. This direction can be changed in a new design scenario. Also pressures and distributed loads can be turned on or off in different areas of the model using design scenarios.

•

Different analysis types will be performed.

Only one design scenario can be active at a time. The heading for the active design scenario will be bold in the tree view. Design Scenario 3 is active in the model shown in Figure 2.10 on the proceeding page. A new design scenario can be created by right-clicking on the heading for the active design scenario and selecting the "New" or "Copy" command. If the "New" command is selected, you will be asked to specify an analysis type for the new design scenario. If the model has an associated CAD model, only the CAD geometry will be present in the new design scenario. If the model is a hand built model, nothing will be present in the new design scenario. If the "Copy" command is selected, all of the current parameters including geometry will be present in the new design scenario. Any changes that are made will only affect the new design scenario. The original design scenario will not be changed. You can activate an inactive design scenario by right-clicking on the heading for the design scenario in the tree view and selecting the "Load" command, or by double-clicking the heading.

Load and Constraint Group It can be seen in Figure 2.12, that there is a "Load and Constraint Group" heading for each design scenario. Whenever a single load or multiple loads are applied to a model in a single command, a new FEA object group will be created. A new heading will appear under the "Load and Constraint Group " heading in the tree view. The name of the heading will be the type of load that is applied. For example, if you apply fixed nodal boundary conditions to one part of a model, a "Nodal Boundary Conditions" heading will appear in the tree view. Under this heading will be an individual heading for each individual boundary condition. If you then apply nodal boundary conditions to another area of the model, a new heading will be created. If the loads and boundary conditions are applied in a logical manner, this organization will make it easy to make changes in the future because they will all remain grouped together. Loads and constraints can be moved between FEA object groups after they are created by either dragging the heading in the tree view or by right-clicking on the load or constraint and selecting the "Move to Group…" command. If the "Move to Group…" command is selected, a dialog will appear that will allow you to select the target FEA object group or create a new FEA object group. If all of the loads or constraints in an FEA object group are identical, you can change the parameters of them at the same time by right-clicking on the heading for the FEA object group and selecting the "Edit" command. The changes will be applied to each load or constraint in the FEA object group. If there are multiple types of loads and constraints in an FEA object group or they have different values, you will not be able to modify the FEA object group.

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Chapter 2: Working with CAD Solid Models and Static Stress Only loads and constraints that are valid for the current analysis type can exist in a design scenario. For example, a convection load cannot exist in a design scenario with a static stress analysis type. Therefore it is strongly recommended that you use separate design scenarios when performing multiple analysis types on a model. For example, if you are performing a steady-state heat transfer analysis and will use the temperature profile in a subsequent thermal stress analysis, these should be set up in separate design scenarios. If you change the analysis type from steady-state heat transfer to static stress, the thermal specific loads will be deleted. For this reason, if you try to change the analysis type, a prompt will appear asking you if you want to copy the current parameters into a new design scenario for the new analysis type or delete any parameters not relevant to the new analysis type.

Local Coordinate Systems By default, any load or constraint that is applied along a direction is applied with respect to the global coordinate system (X, Y, Z). Sometimes this is not adequate to properly model a situation. In these cases a local coordinate system can be applied. You can create a local coordinate system by right-clicking on the "Coordinate Systems" heading in the tree view and selecting the "New…" command. The dialog shown in Figure 2.13 will appear.

Figure 2.13: Creating Coordinate System Definition Dialog Three types of local coordinate systems are available in the "Coordinate System Type" drop-down box: "Cylindrical", "Rectangular" and "Spherical". Once the type of local Autodesk® Simulation Mechanical 2012 – Part 1 – Seminar Notes

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Chapter 2: Working with CAD Solid Models and Static Stress coordinate system is selected, you must specify three points. These will correspond to the points A, B and C in the image. You can either enter the coordinates for these points or you can select them in the display area by pressing the "Select A," Select B," or "Select C" button. You can select all three in quick succession by pressing the "Interactive" button. The axes will appear as you select the three points in interactive mode. The last thing to do is type a name in the "Description" field. Once a local coordinate system is defined, you can apply it to any nodes, edges, or surfaces in the model by selecting the desired geometry and right-clicking in the display area. Select the desired coordinate system in the "Coordinate Systems" pull-out menu. Any directional loads applied to items to which a local coordinate system has been assigned will be applied according to the local directions. If the local coordinate system is cylindrical, the X, Y and Z values will refer to the R, θ, and Z directions, respectively. If the local coordinate system is spherical, the X, Y and Z values will refer to the R, θ, and φ directions, respectively. You may define multiple local coordinate systems and have them applied concurrently to differing portions of the model. If a coordinate system is defined but not applied to any specific nodes, edges, or surfaces, then it will have no effect on the model except within the Results environment, where all displacements, stresses, forces, or moments may be displayed according to any one of the local coordinate systems.

Defining Materials and Using the Material Library Manager Material properties must be defined for each part in the model. This is done by right-clicking on the "Material" heading for that part in the tree view and selecting the "Edit Material…" command. A dialog will appear allowing you to define the relevant properties. Not all of the properties are necessary for every model. For example, you only need to define the modulus of elasticity, the Poisson's ratio, and a coefficient of thermal expansion if you are performing a thermal stress analysis – optionally include the density if an acceleration or gravity load is to be specified. For a stress analysis without thermal effects, the coefficient of thermal expansion is not needed. Some element types support multiple material models. The material model is defined in the "Material model" drop-down box in the "Element Definition" dialog which is accessed by right-clicking on the "Element Definition" heading for that part in the tree view and selecting the "Edit Element Definition..." command. A table with all of the material models available for each element is available in Appendix D. The material library manager allows tracking of predefined or user defined materials by use of a database format. Material data can be imported or exported to and from XML files. Many of the material properties have been provided by MatWeb®. To access the library manager from the FEA Editor environment, select the "Tools" then click on the "Manage Material Library" button in the "Options" panel. The dialog shown in Figure 2.14 will appear:

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Figure 2.14: Material Library Manager Dialog A pre-defined database called the Autodesk Simulation Material Library already exists. This database cannot be altered. To view the different material properties select a material (Aluminum 6061-T6; 6061-T651 for example). The material properties will appear in the table to the right. This table contains the information for the defined material. In the "Material Identification" section, the material library and the material model are identified. The material model is selected when the entry for the material is added. This will be discussed later. Also in this section are the material name and material description. The rest of the table contains the material properties associated with the material model selected. For Aluminum 6061-T6; 6061-T651 the material model selected was "Standard". As seen in Figure 2.12, properties for the "Standard" material model include general properties (mass density and damping), elastic, thermal, electrical and plastic properties. Not all information is needed for every analysis. For example, if a new material for a static stress analysis is needed, then you should only need to enter data for the elastic properties. Since this is a material from the Autodesk Simulation Material Library, editing properties is not allowed. The next section will describe how to enter properties for user materials. The database format for the libraries is a FoxPro (.dbf) file format. These files can be changed with the Material Library Manager, FoxPro or Visual Basic.


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Adding Material Libraries and Material Properties To create a library, press the "New …" button at the top of the dialog. The dialog shown in Figure 2.15 will appear.

Figure 2.15: Create Library Dialog This dialog allows the user to create the name of the new library. In the "File name" field enter a library name and then press the "Save" button. The next dialog will appear.

Figure 2.16: Create Library Dialog This dialog is a prompt to enter a description for the library. For example, in the predefined library, the description is "Autodesk Simulation Material Library". After typing in a description press the "OK" button to return to the "Material Library Manager" dialog. Notice that a new tab exists for the new library. This is set as the active library. To add a material, right-click on the heading for the library in the tree view and select the "Add New Material" command. The dialog shown in Figure 2.17 will appear.

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Figure 2.17: New Material Dialog Type the name of the material in the "Material name" field. Choose the type of material model in the "Material model" drop-down box and select a unit system in the "Unit System" drop-down box. If the material is entered in one unit system and the model is in a different unit system, the software will automatically make the appropriate conversions. This means that the material information can be in "English (in)" and the model can be in "Metric mks (SI)". In the "Material Description" field, enter a description of the material that is being added. It is suggested that a reference to the source of information for the material should be entered in the "Material source description" field. Once this information is specified, press the "OK" button. The screen shown in Figure 2.18 will appear.

Figure 2.18: Material Property Entry Dialog for a Standard Material Model


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Chapter 2: Working with CAD Solid Models and Static Stress The next step is to enter the material properties needed. You can then repeat the process to add more materials to the library. Once you are finished, close the Material Library Manager. NOTE: It is also possible to create new libraries or to save materials to a user library directly from the material applicator screen (that is, without having to use the material library manager).

Examples of Loads and Constraints When to Use Displacement Boundary Elements Figure 2.19 shows an example of where displacement boundary elements may be used. When the foundation collapses, the bottom of the structure will move. However, the structure will not move the entire 0.5" because of the stiffness of the bolts. Therefore a stiffness must be applied to the displacement boundary element to properly model this situation.

Figure 2.19: Sample Displacement Boundary Element Application Another example is any situation where you know the deformation or displacement to be imparted to a given design but do not know the force required to achieve it. For example, say you are shouldering a roller bearing against a dished or conic washer. The washer acts like a spring to keep the assembly tight and free of clearance. You know that you are to compress the washer axially by 0.05 inches. Enter this movement as a displacement boundary condition and the program will tell you the resultant forces and stresses.

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Using Local Coordinate Systems To illustrate the use of a local coordinate system, we will use a simple model of a cube with a hole running through it. A meshed archive of this model (Cube.ach) is located in the "Chapter 2 Example Models\Input File" folder in the class directory or in the copy of the solutions folders on your computer. We want to apply nodal forces to the interior of the hole so that they are normal to the surface. We could calculate the normal vector at every location along the circumference and apply the nodal forces individually. A better way would be to create a cylindrical coordinate system with the origin at the center of the hole. We can then apply the forces in the radial, R, direction. "Start: All Programs: Autodesk: Autodesk Algor Simulation 2012: Autodesk Simulation 2012" "Getting Started: Launch: Open" "Autodesk Simulation Archive (*.ach)" "Cube.ach"

Press the Windows "Start" button and access the "All Programs" pull-out menu. Select the "Autodesk" folder and then the "Autodesk Algor Simulation 2012" pull-out menu. Choose the "Autodesk Simulation 2012 software" command. Click on the "Open" button in the Launch panel. Alternatively you select “Open” from the quick access toolbar or Application Menu. Select the "Autodesk Simulation Archive (*.ach)" option in the Autodesk Simulation Files section of the "Files of type:" drop-down box. Select the file "Cube.ach" in the "Chapter 2 Example Models\Input File" directory. Press the "Open" button.

"Open" "OK"

"View: Navigate: TopView"

Select the location where you want the model to be extracted and press the "OK" button. Select the "View" tab. Click on the options button to the bottom of "Orientation" button in the "Navigate" panel. Select "TopView" from the pull-out menu. The model should now look like Figure 1.10. The View Cube can also be used to access the views. The model will appear as shown in Figure 2.20.

Figure 2.20: Model in FEA Editor Environment Autodesk® Simulation Mechanical 2012 – Part 1 – Seminar Notes

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Chapter 2: Working with CAD Solid Models and Static Stress We must first determine the location of the center of the hole. "Selection: Shape: Point"


"Selection: Select: Vertices"

Also make sure the "Vertices" button is selected in the "Select" panel.

Mouse

Click on the bottom left corner of the cube in the XY view.

Mouse

Right-click in the display area.

"Inquire"

Select the "Inquire" command. A tool tip will appear with the coordinates of the selected vertex. It is (0, 0, 2).

Mouse

Click on the upper right corner of the cube in the XY view.

Mouse


"Inquire"

Select the "Inquire" command. A tool tip will appear with the coordinates of the selected vertex. It is (2, 2, 2).

Since the hole is at the center of the cube, we can determine that the centerline of the hole is at X=1 and Y=1. Mouse "Cylindrical"

Double-click on the "Coordinate Systems" heading in the tree view. Select the "Cylindrical" option in the "Coordinate System Type" drop-down box.

Referring to the image in the dialog, Points A and B can be any two points along the centerline of the hole. We will use (1, 1, 0) for point A and (1, 1, 1) for point B. Point C must be in the plane perpendicular to the vector from point A to point B. We will use (2, 2, 0). 1 1 0 1 1 1 2 2 0

Type "1" in the first field for "Point A", press , type "1", press and type"0". Type "1" in the first field for "Point B", press , type "1", press and type"1". Type "2" in the first field for "Point C", press , type "2", press and type"0".

Center of Hole

Type "Center of Hole" in the "Description" field.

"OK"

Press the "OK" button.

Next, we are going to select the two edges that will use the cylindrical coordinate system and assign this coordinate system to them.

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"Selection: Select: Edges"

Select the "Edges" button in the "Select" panel.

Mouse

Select one of the edges of the hole

Keeping the key pressed select the other 3 circular edges

Mouse


"Coordinate Systems: Id 1: Center of Hole"

Select the "Coordinate Systems" pull-out menu and select the "Id 1: Center of Hole" command.


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"View: Appearance: Nodal Coordinate System "

If small miniaxes are not already visible at the selected nodes; Select the "View" tab. Make sure the "Nodal Coordinate System" button is selected in the "Appearance" panel options.

Small miniaxes will be visible on each selected vertex. The red axis (indicating the local x–direction) should point away from the center of the circle, as shown by the radial miniaxis lines in Figure 2.21. Next, we can add an edge load.

Figure 2.21: Model with Local Coordinate System Defined

"Setup: Loads: Force"

With the edges of the hole's still still selected, Select the "Setup" tab. Select the "Force" button in the "Loads" panel

10

Type "10" in the "Magnitude" field.

"Y"

Select the "Y" radio button in the "Direction" section. This corresponds to the tangential direction.

"OK"


The forces will appear tangential to the surface as shown in Figure 2.22.

Figure 2.22: Model with Forces Applied


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Chapter 2: Working with CAD Solid Models and Static Stress A completed archive of this model (Local coord.ach) is available in the "Chapter 2 Example Models\Results Archives" folder in the class directory or in the copy of the solutions folders on your computer. An alternate method of defining cylindrical coordinate systems is to draw construction lines across the center of the hole or similar round feature, one at each end of the feature, and to divide these two lines into two increments each. The line command can be accessed from the "Draw" panel with the "Draw" tab. Be sure that the "Use as Construction" option is enabled so that you're not adding actual FEA entities but merely reference geometry. To divide the lines, you must be in "Select Construction Objects" mode, select the lines, rightclick, and choose the "Divide..." command. Next, place construction vertices at the midpoints of the construction lines using the "Construction Vertex" command. This method provides two vertices along the centerline of the hole that can easily be selected when defining the coordinate system. When using this method it is best to specify an existing part number for the construction lines. This will prevent the addition to the model tree of a part with no actual FEA entities. Such an "empty" part would need to be deactivated prior to performing the analysis.

Using Surface Variable Loads Surface variable loads can be used when a load follows a known function across a surface. A classic example would be a bearing load where the force profile is parabolic. This will be practiced in a future exercise. For now we will attempt to apply a load to a side of the cube model that we used previously to demonstrate the creation of local coordinate systems. We want this load to have a magnitude of 55 psi at the top of the block (Z=2) and decrease linearly along the Z axis to 8 psi at the bottom (Z=0). A diagram of this load is shown in Figure 2.23.

Figure 2.23: Diagram of the Surface Variable Force We will continue using the "Cube" model from the prior example. If this model is not still open, reopen it.

"View: Navigate: Right View"

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Select the "View" tab. Click on the options button to the bottom of "Orientation" button in the "Navigate" panel. Select "Right View" from the pull-out menu.


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"Selection: Shape: Point"




Mouse

Click on the surface facing the screen.

"Setup: Loads: Variable Pressure"

Select the "Setup" tab. Click on the "Variable Pressure" button in the "Shape" panel options. The dialog shown in Figure 2.24 will appear.

Figure 2.24: Surface Variable Load Dialog From the given minimum and maximum loads and positions we can derive the equation for the pressure as a function of z. The equation is P=23.5z+8. When defining the equation, the x, y and z coordinates will be represented by the variables r, s and t, respectively. You can use basic operators such as +,-,*,/, () and ^. Pressing the "Available Primitives >>" button will allow you to access several common functions. "Normal to Surface"

Select the "Normal to Surface" radio button.

Linear Pressure

Type "Linear Pressure" in the "Active function" field.

23.5*t+8

Type "23.5*t+8" in the "Expression (Use 'r', 's', and 't' as variables)" field.

"View"

Press the "View" button.

"T Z"

Select the "T Z" radio button. A graph will appear as shown in Figure 2.25. This shows a force increasing from 8 to 55 from z=0 to z=2.


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Figure 2.25: Variable Load Graph "Close"

Press the "Close" button.

"OK"


Mouse

Right-click on the "Material" heading in the tree view.

"Edit Material…"

Select the "Edit Material…" command.

"Steel (ASTM-A36)"

Highlight the "Steel (ASTM-A36)" item from the list of available materials.

"OK"


"Analysis: Analysis: Check Model"

Select the "Analysis" tab. Click on the "Check Model" button in the "Analysis" panel. Select the "View" tab. Click on the options button to the bottom of "Orientation" button in the "Navigate" panel. Select "Front View" from the pull-out menu.

"View: Navigate: Front View"

The model will now appear as shown in Figure 2.26. You can see the force vectors increasing in the positive Z direction.

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Figure 2.26: Surface Variable Load in the Results Environment You will notice that the arrow at the very top of the surface is shorter than the arrows immediately below it. This is because when two elements share a node, the nodal forces receive a partial contribution from each of the adjacent element faces. These are combined into one force at the shared node and displayed as such in the Results environment. Nodes along surface edges and at corners represent fewer element faces. For a uniform pressure on a perfectly uniform mesh, corner nodes will see half of the force that the other nodes along the edge will see and one-fourth of the force that the interior nodes will see. Similarly, noncorner edge nodes will see half the force that the interior nodes will see. A completed archive of this model (Surf var load.ach) is available in the "Chapter 2 Example Models\Results Archives" directory in the class directory or in the copy of the solutions folders on your computer.


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Exercise A Frame – Full to Quarter-Symmetry Model Comparison Brick Elements Concepts that will be illustrated: • • • •

Merging two CAD solid models into a single FEA model Applying pressure loads Applying symmetry constraints Comparing full model results to symmetry model results

Objective:

Mesh and analyze the frame shown below. Analyze the whole model and a quartersymmetry version of the model, side-by-side, and verify that the results are the same.

Geometry:

Start with the file Exercise A (Full).step and then merge in the second file Exercise A (Quarter).step. Both files are in the "Exercise A\Input Files" folder of the class directory or in the copy of the solutions folders on your computer. By merging the two together, they can be solved simultaneously and compared more easily.

Mesh:

For a precise comparison, use a relatively small, absolute mesh size of 0.15 inch.

Constraints:

Fully fix the holes at the top of each part (half-holes in the case of the symmetry version). Apply proper symmetry boundary conditions for the quarter-symmetry model.


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Chapter 2: Working with CAD Solid Models and Static Stress Loads:

Apply a 10,000 psi pressure normal to one surface of each part, as indicated in the preceding diagram.

Element:

Brick

Material:

Steel (ASTM-A36)

Results:

Assembly Description

Maximum von Mises Stress (psi) *

Maximum Displacement Magnitude (in)

Full Model

30,765

0.00759

Quarter-Symmetry Model

30,743

0.00759

* – Note that the stress variation between the two parts is less than onetenth of 1% (0.07%, in fact). This small variation can easily be explained by the differences in the surface and/or interior meshes of the two solids.

A completed archive of the combined full and quarter models, Exercise A (Complete).ach, is available in the "Exercise A\Results Archives" folder in the class directory or in the copy of the solutions folders on your computer.

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Chapter

3

Results Evaluation and Presentation Chapter Objectives • • • • • • •

Learn how the results of the analysis are calculated Learn how to evaluate the displacement, stress and reaction force results Learn how to inquire on results at specific locations Learn how to create graphs of results Learn how to customize presentations of the results Learn how to generate image and animations of the results Learn how to generate an HTML report of the results

Background on How Results are Calculated As was explained in the Introduction, the equation that is solved during the analysis is

{x} = [K ]−1{ f } where the stiffness matrix, [K], and the force vector {f} are known from the geometry and the loads. Once the displacement vector {x} has been determined, the distribution of the displacements and then the strains are determined. Once the strain values are known, the stress can be calculated from the relationship:

σ = εE This displacement-based finite element solution process – whereby a distribution is derived from nodal displacements, the strains are derived from the distribution, and the stresses are finally calculated from the strains – is generally referred to as "stress recovery." In summary, the displacements are the first result to be solved. Once the displacements are known, the strains and then the stresses can be calculated. Typically, a rather coarse mesh can provide fairly accurate structural displacement results. However, the strains and stresses calculated from these coarse mesh displacement values may not be accurate enough. A finer mesh will improve the accuracy of the stress results, even though the displacement results are relatively insensitive to the change in mesh size.


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Chapter 3: Results Evaluation and Presentation

How to Evaluate Results Evaluation of results is done in the Results environment. Once the analysis is performed, the model will be automatically transferred to the Results environment. To enter the Results environment at any other time first select the "Tools" tab then click on the "Results" button in the "Environments" panel. Alternatively you can select the "Results" tab at the top of the tree view browser Upon attempting to enter the Results environment for a previously run model, you may receive a pop-up warning stating that the existing results do not match the current model. This can occur if you visited an element or material data screen or the analysis parameters dialog and clicked "OK," rather than canceling out of the dialog, even if you changed no input. If you are sure that the results still correctly reflect the current model setup, click the "Yes" button in the pop-up message box to proceed to the results environment. If the Results environment is not available (that is, it is grayed-out) but you are certain that the results have been output and that they are consistent with the current model setup; you can use the "Check Model" command, available from the "Analysis" panel within the "Analysis" tab, to view the model in the Results environment. Alternate Display Unit Systems As discussed in the previous chapter, several pre-defined unit systems are available in both the FEA Editor and Results environments. In addition, custom unit systems may be defined and, optionally, made available for all future models. Regardless of the model units, the results can be presented in any other pre-defined or user-defined unit system by simply activating the desired Display Units listed within the tree view. For more information regarding the creation of custom unit systems or modifying existing unit systems, refer to "Working with Various Unit Systems" in Chapter 2.

Displacement Results As mentioned previously, the first result to review is the displacements. If the displacements look incorrect, there is most likely an error in the setup of the model. If the displacements look correct, the stresses can then be reviewed. To review the displacement contours, access the "Results Contours" tab and then click on the "Displacement" button in the "Displacement" panel. The "Magnitude" command will display the magnitude of the displacements at each node. The magnitude, D, is calculated by the equation:

D = D x2 + D y2 + D z2 Where Dx, Dy and Dz are the components of the displacement in the global directions. Note that this will always be a positive value. The contours of the individual components can also be displayed by selecting the appropriate command in the "Displacement" panel. Another way to verify the displacement results is to view the deflected shape. This is useful to visually verify that the deflections are in the logical direction. To view the deflected shape, select the "Displaced Options" button from the "Displacement" panel. The dialog shown in Figure 3.1 will appear.

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Figure 3.1: Displaced Model Options Dialog Displaced Model section Show Displaced Model: If this checkbox is activated, the displaced shape of the model will be shown in the display area. If any contour is currently being shown, the displaced shape will continue to show the contour. Scale Factor section As an Absolute Value: If this radio button is selected, the actual displacement values will be multiplied by the value in the "Scale Factor" field to create the displaced model display. A value of "1" in the "Scale Factor" field will show the true displaced shape of the model. As a Percentage of Model Size: If this radio button is selected, the scale factor used to multiply the actual displacements will be based on the size of the model. The slider bar can be used to get a reasonable scale factor. Show Undisplaced Model As section Do Not Show: If this radio button is selected, the undisplaced model will not appear in the display area. Mesh: If this radio button is selected, a wireframe mesh representing the undisplaced model will appear to be used as a reference. Mesh on Top of Displaced Model: If this radio button is selected, a mesh representing the undisplaced model will be drawn on top of the shaded model representing the displaced model. Transparent: If this radio button is selected, a transparent shaded representation of the undisplaced model will appear to be used as a reference. The level of the transparency can be controlled using the "Results Options: View Settings: Transparency Level" command.


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Stress Results Once the displacement results have been checked, the stresses should be reviewed. Which are available from the "Stress" panel within the "Results Contours" tab. von Mises: This command will set the results display to be the equivalent von Mises stress. The von Mises stress can be displayed for element types with area (2-D, plate and membrane) and volume (bricks). The equation used to calculate the von Mises stress is:

[

] (

2 0.5 (S x − S y ) + (S y − S z ) + (S z − S x ) + 3 S xy + S yz2 + S zx2 2

2

2

)

where Sx, Sy and Sz are the normal stresses in the global directions and Sxy, Syz and Sxz are the shear stresses. In terms of the principal stresses S1, S2 and S3:

[

0.5 ( S1 − S 2 ) + ( S 2 − S 3 ) + ( S 3 − S1 ) 2

2

2

]

Note from the equations that the von Mises value is always positive. Tresca*2: The Tresca*2 stress can be displayed for solid element types. This method extracts the maximum shear stress from a given stress tensor. The Tresca equation is:

0.5 * MAX [ S1 − S 2 , S 2 − S 3 , S 3 − S1 ] where S1, S2 and S3 are the principal stresses. The value reported is twice the maximum shear stress. Thus, yielding would occur when the reported Tresca*2 value reaches the yield stress. Note that by definition, the Tresca stress is always positive. Refer to the Mohr's circle in Figure 3.2 for a graphical representation. Minimum Principal: This command will set the results display to calculate the minimum principal stress (S3). The principal stress can be displayed for element types with area and volume. Positive (+) indicates tension and negative (-) indicates compression. Refer to the Mohr's circle in Figure 3.2 for a graphical representation. Intermediate Principal: This command will set the results display to calculate the intermediate principal stress (S2). This is the stress in the direction normal to the minimum and maximum principal stresses. The principal stress can be displayed for element types with area and volume. Positive (+) indicates tension and negative (-) indicates compression. Refer to the Mohr's circle in Figure 3.2 for a graphical representation. Maximum Principal: This command will set the results display to calculate the maximum principal stress (S1). The principal stress can be displayed for element types with area and volume. Positive (+) indicates tension and negative (-) indicates compression. Refer to the Mohr's circle in Figure 3.2 for a graphical representation.

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Figure 3.2: Mohr's Circle Stress Tensor: The commands in this pull-out menu display the component of the stress in the chosen direction. Technically, it uses the double dot product with the stress tensor or local stress components. The stress tensor can be displayed for element types with area and volume. If the "Use Element-Local Results" button is not active within the "Settings" panel within the "Results Contours" tab, you will be able to select between the following global stresses. If this option is active, the following choices will display the local stress tensors mentioned in the individual descriptions. 1.) XX: Stress tensor component showing the normal stress in the global X direction. Positive (+) indicates tension; negative (-) indicates compression 2.) YY: Stress tensor component showing the normal stress in the global Y direction. Positive (+) indicates tension; negative (-) indicates compression. 3.) ZZ: Stress tensor component showing the normal stress in the global Z direction. Positive (+) indicates tension; negative (-) indicates compression. 4.) XY: Stress tensor component showing the shear stress in the global XY direction. (X indicates the direction normal to the face, and Y indicates the direction of the shear stress.) 5.) YZ: Stress tensor component showing the shear stress in the global YZ direction. (Y indicates the direction normal to the face, and Z indicates the direction of the shear stress.) 6.) ZX: Stress tensor component showing the shear stress in the global ZX direction. (Z indicates the direction normal to the face, and X indicates the direction of the shear stress.)


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Chapter 3: Results Evaluation and Presentation Factor of Safety: You can display the factor of safety values for any stress result by selecting the "Safety Factor" button within the "Stress" panel. The ratio of the allowable stress value to the current stress value will be displayed at each node. By default, the yield stress of the materials will be used as the allowable. You can modify these values using the "Set Allowable Stress Values" option from the "Safety Factor" button, within the "Results Contours" tab.

Reaction Force Results Another useful result type is the reaction force. It is important to verify that the reaction forces at the boundary conditions are equal to the forces that were applied to the model so that a force balance exists. You can access the reaction force values by selecting the "Reactions" button within the "Other Results" panel, within the "Results Contours" tab. Six reaction types will appear. Each reaction can be plotted as the magnitude or a component. These results can also be found in the "ds.l" text file within the numbered design scenario subfolder under the filename.ds_data folder. Reaction Force: This command will display the internal force reaction at each node. Note that this is not the support reactions. You can either have the magnitude of the reaction force displayed or the individual components along the global axes. Applied Force: This command will display the force applied to each node. You can either have the magnitude of the applied force displayed or the individual components along the global axes. Residual Force: This command will display the residual force at each node (sum of applied and reaction). This is what most engineers call the support reactions. You can either have the magnitude of the residual force displayed or the individual components along the global axes. Reaction Moment: This command will display the internal moment reaction at each node. Note that this is not what most people consider to be the support reactions. You can either have the magnitude of the reaction moment displayed or the individual components along the global axes. Applied Moment: This command will display the moment applied at each node. You can either have the magnitude of the applied moment displayed or the individual components along the global axes. Residual Moment: Displays the residual moment at each node (sum of applied and reaction). This is what most people consider to be the support reactions. You can either have the magnitude of the residual force displayed or the individual components along the global axes.

Inquiring on the Results at a Node It is often necessary to know the exact value of the result being displayed at a particular node. In order to do this, first select the necessary result contour on the model. Then, to make the selection easier, select the "Selection" tab and then the desired method in the "Shape" panel. Then select "Vertices" button in the "Select" panel. Now click on the node where you are interested in determining the exact results. Then select the "Results Inquire" tab and then click on the "Current Results" button in the "Inquire" panel. The "Inquire: Results" dialog will appear with the current display results for the selected node. The data in this dialog can be saved to a text file by pressing the "Save Values" button. The results for multiple nodes can be displayed by holding down the key during selection. The average, sum, and other calculations can be performed on sets of data by selecting the desired

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Chapter 3: Results Evaluation and Presentation option in the "Summary" drop-down box. Calculating the sum of the results of several nodes is useful for evaluating the reaction force results. Another option for determining the exact value of a result at a particular node is to use the probe feature. This can be accessed by selecting the "Probe" button in the "Probes" panel, within the "Results Inquire" tab. Now as the mouse moves over nodes, a probe will appear with the currently displayed result value at that node.

Graphing the Results For static stress analyses with linear material models, the results at a node can be viewed in a bar graph format. There are two general uses for this; one is to compare the results at multiple nodes and the other is to compare the results of a single node in multiple load cases. Note that for nonlinear analyses (not covered within this course), line graphs showing results as a function of time can be created. In order to graph the results, select the node(s) and right-click in the display area. Select the "Graph Value(s)" command to create a graph of the selected node using default settings. If you had multiple nodes selected when this command was executed, a bar graph will appear for each node and for each load case. You may also choose the "Embed Graph" command if you wish the graph to appear within the current contour plot window instead of within a new window. This will allow you to view the contour of a model and the results of a particular node, or nodes, simultaneously. Embedded graphs may be moved or resized by right-clicking on the graph's heading in the tree view and choosing the "Move/Resize" command. Then click and drag the graph to reposition it or click and drag its handles to resize it. Choosing the "Modify" command opens the graph in its own window, where the various attributes of the plot may be altered (such as the font style and size, plotting method, grid options, legend style, and so on) or the graph may be exported in a variety of formats. Whenever a graph is created, whether in a separate window or embedded in a contour plot, it will be listed as an additional presentation in the tree view. Previously defined "Curve" presentations (such as graphs) can be embedded into a contour plot presentation window, even though the option to embed the graph had not been chosen when it was created. To embed an existing curve, right-click on the presentation heading of the desired curve, select the "Embed in Presentation" pull-out menu, and select the target presentation. A heading will appear under the "Embedded Presentation" heading in the tree view for the target presentation. When you select the target presentation, the original contour plot and its embedded graph will be shown. The embedded graph can be moved or resized in the same manner as previously described. In some situations, it may be desired to combine the results of multiple nodes. One situation would be to sum the reaction forces. If this is desired, select the nodes and right-click in the display area. Select the "Edit New Graph…" command. A graph will appear. Also the "Edit Curve" dialog will appear. You can select the desired function to graph in the "Multiple Nodes:" drop-down box: •

Maximum: This option will graph the maximum result value from the selected node set at each time value.

•

Maximum Magnitude: This option will take the absolute value of the result value from the selected node set and display the maximum value at each time value. The sign of the value will be reapplied. For example, if the result values are 1, -3, 5 and -6, the value reported would be -6.

•

Mean: This option will graph the average result value of the selected node set at each time value.


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Chapter 3: Results Evaluation and Presentation •

Minimum: This option will graph the minimum result value from the selected node set at each time value.

•

Range: This option will graph the difference between the maximum result value and minimum result value from the selected node set at each time value.

•

Sum: This option will graph the sum of the result values of the selected node set at each time value.

If you select a node and right-click in the display area after a graph has been created, the "Add Curve(s) to Graph" pull-out menu will appear in addition to the previously discussed command. You can select any existing graphs in this pull-out menu and the select nodes will be added to the graph. Note this command is also available from the "Results" panel Path Plots Results for nodes lying along a path, such as along the edge or centerline of a part or through the thickness of a part, may be graphed. In this case, the abscissa (that is, the horizontal scale) may be represented as the distance magnitude along the path of the selected nodes or the X, Y or Z distance components along the nodal path. After selecting a series of nodes, click on the "Create Path Plot" button in the "Graphs" panel within the "Results Inquire" tab. The dialog shown in Figure 3.3 will appear with the selected nodes listed.

Figure 3.3: Path Plot Definition Dialog Choose the desired radio button within the "Plot Against" section to specify which values to use for the abscissa. If you want the scale values to reflect the original, undisplaced coordinates of the nodes, deactivate the "Use Displaced Coordinates" checkbox. Finally, right-click on the "Nodes" list and choose the desired sorting method so that the graph's data points will be properly ordered and meaningful. You may sort the nodes according to the X, Y or Z coordinates. In addition, you may select individual node numbers within the list and manually move their position up or down within the list. As with regular results graphs, you may add nodes to a previously created path plot. Simply select the desired nodes, right-click in the display area, access the "Add Path Plot to Graph" pull-out menu, and choose the appropriate graph. Nodes added to a path plot are displayed as an additional path plot curve on the graph. That is, they are not appended to the prior curve. If you need to change the order of the nodes or what value to plot against, right-click on the appropriate heading under "Path Plots" in the tree view and choose the "Edit…" command. This will bring up the dialog shown previously in Figure 3.3, with the newest set of nodes now listed.

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Presentation Options There are many components that are involved in creating a presentation from an analysis. The Results environment has tools that will assist in creating images and animations that can then be assembled into a report. In the tree view, there is a heading called "Presentations". The saved presentation of "Stress" is loaded by default upon entering the Results environment. Any of the presentations under the "Saved Presentations" heading can be applied to the model by right-clicking on the heading for that presentation and selecting the "Activate" command. Once a presentation is activated, it will appear under the "Presentations" heading. All factors that contribute to the appearance of the model in the display area are saved in the presentation. Each loaded presentation is a separate window. To display the presentation, click on the appropriate heading in the tree view. All windows, including presentations, can be viewed together using the "Arrange" button in the "Windows" panel within the "View" tab, for example in a tiled or cascade formation. To delete a presentation from the list, close the window using the "X" button. To save the current window to a presentation, right-click on the heading in the tree view and select either the "Save with Model" or "Save with System" command. If the "Save with Model" command is selected, the presentation will be available whenever the current model is opened. If the "Save with System" command is selected, the presentation will be available for all models.

Contour Plots Annotations Annotations can be used to add text to the display area to provide descriptive comments about the results that are being presented. There are three annotations that are automatically created from the analysis. These are placed in the lower left-hand corner of the display area. These are listed under the "Annotations" heading for each presentation in the tree view. A new annotation can be created by right-clicking on the "Annotations" heading for the desired presentation and selecting the "Add…" command. The "Annotation" dialog shown in Figure 3.4 will appear. Text can be typed into the "Annotation text" field. A standard Windows font selection dialog can be accessed by pressing the "Font" button. After you press the "OK" button, you will be able to place the annotation anywhere in the display area by left-clicking. The part of the annotation specified by the radio buttons in the "Preview and text justification" section will be placed where you click. An existing annotation can be moved to a new location by right-clicking on the heading for that annotation in the tree view and selecting the "Move" command.


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Figure 3.4: Annotation Dialog Probes The ability to probe on the results at the nodes in a model using the "Results Inquire: Inquire: Current Results" button was described previously in this chapter. Probes can also be used for presentation purposes, which can be accessed by clicking on the "Probe" button in the "Probes" panel within the "Results Inquire" tab. When a probe appears over a node, you can right-click in the display area and select the "Add Probe" command. A probe displaying the result value and pointing to the node will remain on the node. If you want to remove a probe, right-click in the display area, and select "Delete All Probes" command. Any probes that are added in this manner will be included in any images or animations generated. Probes can be automatically added to the nodes with the minimum and maximum result values for the currently displayed result using the "Maximum" and "Minimum" button within the "Probes" panel. These probes will be included in any images or animations generated. Slice Planes A slice plane can be added to a model to look at the results on the interior mesh. A slice plane can be added to a model by selecting the options button below "Slice Planes" in the "View Setting" panel in the "Results Options" tab. Then select the "Add Slice Plane" option, the three global planes and the isometric option will be available. Once a plane is selected, the orientation of the plane can be modified using the commands in the "Slice Planes" pull-out menu. The "Rotate About I", "Rotate About J" and "Rotate About Origin" commands will allow you to change the angle at which the plane is oriented. The I axis is the red axis on the slice plane. The J axis is the green axis on the slice plane. The origin is located where the I and J axes meet on the slice plane. The location of the slice plane along the normal axis can be controlled using the "Translate Normal" command. The "Flip" command will hide the elements on the opposite side of the slice plane. Once the slice plane is defined to your specifications, you can right-click on the heading for the particular slice plane and select the "Hide" command. This will cause the translucent plane to disappear from the view. The

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Chapter 3: Results Evaluation and Presentation slice plane will still be in effect. To deactivate the effect of the slice plane, right-click on the heading for the particular slice plane and select the "Deactivate" command. Customizing the Legend Box The legend box is an important component to the presentation. Many aspects of the legend box can be customized by selecting the options button to the left of the "Legend Properties" button and selecting "Setup" in the "Settings" panel within the "Results Contours" tab. The dialog shown in Figure 3.5 will appear.

Figure 3.5: Plot Settings Dialog Contour Colors tab: The "Presets" drop-down box provides several color sets that can be used for the contour colors on the models. You can also select individual colors by activating the "Custom" checkbox and use the options available in the "Color Settings" section. Legend Properties tab: The "Position" section will allow you to select where in the Display area the legend box will be placed. The "Appearance" section will allow you to customize the font styles, the number of tick marks and the number of significant digits to use for the legend box. Range Settings tab: By default, the highest and lowest result values will be used as the maximum and minimum values for the legend box. The intermediate values will be evenly spaced between these. By deactivating the "Automatically calculate value range" checkbox in the "Current Range" section, you can enter specific values for the maximum and minimum values in the legend box. The "Threshold" section can be used to highlight only areas of the model above or below a specific value. Vector Plots tab: The options in this tab are used to control the size of the arrows used when a result is displayed as a vector plot. This will show the direction of the results at each node. Probe Settings tab: This tab will allow you to control the font of the text in probes and to control how the probe appears with respect to the rest of the model.


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Chapter 3: Results Evaluation and Presentation Customizing the Model in the Display area The display of the model is also an important component to the presentation. By default, the model is displayed with the mesh. Sometimes, displaying the model without the mesh will result in an image that is more easily interpreted. The display of the model can be controlled by selecting the options pull-down menu below "Visual Style" button in the "Appearance" panel within the "View" tab. The "Shaded with Features" command will shade the entire model but will only display the feature lines. This will result in an outline of the model with the result contour shading. The "Shaded" command will only shade the model; no lines will be displayed. Another important feature is the orientation of the model. You can orient the model in any manner using the various buttons in the "View" tab and the "Navigate bar". Once you have an acceptable view, you can save this view to be easily accessed in the future. This can be done by selecting the Navigate Panel options and then selecting the "User-Defined Views" command. The dialog shown in Figure 3.6 will appear.

Figure 3.6: User-Defined Views Dialog To save the current view you must give it a new name. First, click on the "" item in the "Description" field. The "Rename" button will become available. Press the "Rename" button. Type in a descriptive name, press the key, and press the "OK" button to exit the dialog. The saved views will be available for this model within either the FEA Editor or the Results environments. To restore a previously defined view, select the desired view name and click on the "Apply View" button. If you want to update a previously defined view to match the current viewpoint, select the view name in the "Description" field that is to be redefined and then press the "Save View" button. The current view will overwrite the definition of the selected view name.

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Image File Creation In the Results environment, images of the results from the analysis can be saved in standard image formats. Once the display area is set to the desired settings, you can select the "Application menu" and then select "Export" pull-out menu and then the "Image command. Alternatively you can select the "Save Image" button in the "Captures" panel. The mouse cursor will have the image of a camera. You can use the mouse to select a rectangle enclosing the part of the display area that you want to be saved to the image file. If you want to save the entire display area, press the key. The dialog shown in Figure 3.7 will appear.

Figure 3.7: Save Image as Dialog Enter a name for the image file in the "File name:" field. Select the picture format that you want the image saved as in the "Save as type:" drop-down box. Select the size of the image in the "Image attributes" section. When the settings are acceptable, press the "Save" button


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Animating FEA Results An animation of the displaced shape of a static stress analysis can be created and viewed in the Results environment using the "Start" button in the "Captures" panel. The parameters can be set up using "Setup" command from the "Animate" button options in the "Captures" panel. The dialog shown in Figure 3.8 will appear, was "Setup" command is selected.

Figure 3.8: Animation Settings Dialog In the "Frame Rate Control" section, you can press the appropriate button to have the animation created to your specifications. If you press the button next to "Creates an Animation that runs from no displacement to current displacement", an animation will be created starting from the undisplaced shape and will progress in even steps to the current displacement shown in the display area. If you press the button next to "Creates a looping animation that runs from no displacement to current displacement and back to none again", an animation will be created starting from the undisplaced shape and will progress in even steps to the current displacement shown in the display area and then will return to the undisplaced shape, again in even steps. If you press the button next to "Creates a sinusoidal animation that cycles between positive and negatively scaled current displacements", an animation will be created starting from the undisplaced shape and will progress in even steps to the current displacement shown in the display area. The animation will then proceed to the same scaled displacement but in the opposite direction of that in the display area. Specify the number of frames that you want to be used in the animation in the "Number Of Frames To Generate" field. The deflections will be divided evenly into this many divisions. If you have a results contour on the model, you can have the values change during the animation by activating the "Animate Results" checkbox. If this checkbox is activated, the results will be evenly scaled throughout the animation. Once the settings are acceptable, press the "OK" button. Use the "Animation: Start Animation" command to generate the animation. The animation will play in the display area. You can use any dynamic viewing commands as the animation is playing. You can save the animation as a video using the "Save as AVI" command from the "Animate" button options in the "Captures" panel.

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Using the Configure Report Utility Select the "Report" button from the "Environments" panel within the "Tools" tab. to move into the Report environment. The Report environment will allow you to easily create HTML reports that include all of the input parameters and analysis results as well as user-defined content. A "Master Report" and a report for each individual FEA design scenario will be created. Any images or animations that were created may be included in the reports. In addition, an image from each currently loaded results presentation will automatically be captured and added to the design scenario reports. These automatic presentation images may be deactivated if desired. Right-click on either the "Master Report" heading or the "HTML Report" heading in the tree view and select the "Configure Report" command. The "Configure Report" dialog will appear. You may also access the utility by pressing the "Configure" button in the "Setup" panel within the "Report" tab. The tree on the left side of the dialog lists all of the predefined sections of the report. Selecting a given heading (by clicking on the heading itself and not the associated checkbox), accesses the editing screen for that topic. If there are no editable items associated with the topic, a message in the right frame will indicate that the item "…can be re-ordered but not edited." To re-order the report, simply click and drag one of the headings to a different vertical position within the tree list. If an item is not checked, no message or editing screen will appear when the heading is selected and the topic will be excluded from the HTML report. The inclusion/exclusion state of each item may be toggled by simply clicking on the appropriate checkboxes. Some of the editing screens contain self-explanatory fields for entering data, such as the author's name and department. Other screens, like the one used for entering the "Project Name" or the "Executive Summary," have a built in word processor that supports a number or fonts, styles, tabs, numbered or bullet lists, text frames, imbedded images, and tables. Placeholder text or labels within these dialogs can be selected and overwritten with the author's desired text. Page breaks can be added ahead of any section by right-clicking on a heading and choosing the "Add Page Break" command. Also within the right-click, context menu (and the TREE pull-down menu) are commands to add sections to the report for including user-defined images, animations, *.HFS or *.WRL files (virtual reality images that can be rotated, panned, and zoomed), and/or additional text sections. You may also rename or delete report sections. Changes to the report may be saved selecting "Report" tab and choosing the "Save as Report Template" command. This menu is only visible when an editable section of the report is currently selected. When finished, choose the Generate Report command from the same menu or press the "Generate Report" button. The HTML report will automatically appear within the Report environment. In the directory on the computer where the FEA model is located there will be a filename.ds_data folder. Within this folder there will be numbered subfolders, one for each design scenario that exists within the subject model. There will also be a "Master Report" subfolder that contains all of the HTML master report files and attachments. Within each numbered design scenario folder there will be a "ds_rpt" subfolder. This folder contains all of the files and attachments for the subject design scenario's HTML report. These "ds_rpt" folders can be zipped up and sent to other persons for review. The recipient need not have the simulation software installed on their computer to view the report. It will be displayed via the default web browser.


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Exercise B Yoke – Evaluation of Results and Generation of a Report Brick Elements Concepts that will be Illustrated: • • • •

Applying a surface variable load Creating a local coordinate system Reviewing reaction forces Creating a path plot

Objective:

Knowing what we have learned in the last two chapters, we will refine our analysis of the yoke that was performed in Chapter 1. Review the reaction forces. Generate a report that includes an image of the von Mises stress contour, an animation of the deflections, and a path plot of the stresses along one of the straight edges at the top of the slot.

Geometry:

Use the file Exercise B.step in the "Exercise B\Input File" folder of the class directory or in the copy of the solutions folders on your computer. Use the default mesh settings.

Loading:

Use a surface variable load to apply the 800 lbf to the left half of the hole. The load should have a magnitude of 0 at the ends of the diameter and should have a parabolic profile.

Constraints:

Only constrain the radial and axial translation at the small hole. The tangential direction is free. Constrain only the half that is expected to have a reaction.

Element:

Brick

Materials:

Steel (ASTM-A36)

Questions:

Are the specified constraints adequate for a statically stable model? If not, what can be done to achieve this? How do these results compare to the results of the Chapter 1 example? If the loads are developed by pins or shafts passing through the holes, which result is more realistic? Do the support reactions sum to 800 lbf? Autodesk® Simulation Mechanical 2012 – Part 1 – Seminar Notes

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Results: Maximum von Mises Stress (psi)

Maximum deflection (in)

2,074

0.00044

A completed archive of this model (Exercise B.ach) is available in the "Exercise B\Results Archive" folder in the class directory or in the copy of the solutions folders on your computer.

Derivation of the Pressure vs. Position Function In order to calculate the equation, we must first determine the projected area over which the pressure will be applied. For the yoke, it will be over the diameter of the hole, which is from y = -1 to y = 1. The product of the area under the pressure curve and the depth of the yoke must equal the desired 800 lbf. The equation for a parabola with the dimensions shown below is:

A=

4ah 3

For the yoke, a = 1 and h = Pmax. The depth of the yoke where the load is applied is 1.5 in. Therefore we can solve for Pmax using the equation

4 in * 1 * Pmax * 1.5 in 3 = 400 psi

800 lbf = Pmax

The equation of the parabola will take some form of

P = ey 2 + by + c We know three points on the parabola: P = 400, y = 0; P = 0, y = -1; P = 0, y = 1. Using these we can calculate that e = -400, b = 0, c = 400. Therefore the equation is: P = -400y2 + 400

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Chapter

4

Midplane Meshing and Plate Elements Chapter Objectives • • • •

Learn how to create midplane meshes of thin parts Learn when to use plate elements Learn how to use element normal points to properly orient pressure loads on plate elements Learn how to evaluate results that are specific to plate elements

Meshing Options When importing solid models that have thin parts, it is often better and simpler to analyze them using plate elements. Autodesk® Simulation can be used to convert thin CAD solid models to plate elements. A plate element is drawn at the midplane of the part. Entire assemblies or individual parts in assemblies can be converted to plate elements. An assembly where plate elements can be used for one of the parts is shown in Figure 4.1. This model is a manifold connected to two flanges. The manifold can be modeled with plate elements and the flanges with brick elements. This model, Manifold Assembly.step, is located in the "Chapter 4 Example Model\Input File" folder in the class directory or in the copy of the solutions folders on your computer. We will use an absolute mesh size of 0.75" for all parts.

Figure 4.1: Assembly to be Modeled Partly with Plate Elements


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Chapter 4: Midplane Meshing and Plate Elements "Start: All Programs: Autodesk: Autodesk Algor Simulation 2012: Autodesk Simulation 2012" "Getting Started: Launch: Open" "STEP (*.stp, *.ste, *.step)" "Manifold Assembly.step" "Open" "Use STEP file units" "OK" "Linear: Static Stress with Linear Material Models" "OK"

Press the "Open" button. A "Select Length Units" dialog will appear. Choose "Use STEP file units" from the pull-down menu and click the "OK" button. A dialog will appear asking you to choose the analysis type for the model. From the pull-out menu, choose "Linear: Static Stress with Linear Material Models" and press the "OK" button.

"Mesh: Mesh: 3D Mesh Settings"

Select the "Mesh" tab. Click on the "3D Mesh Settings" button in the "Mesh" panel.

“Options…”

Press the "Options…" button.

Mouse "Absolute mesh size"

Access the "Type" pull-down menu and select the "Absolute mesh size" option.

0.75

Enter "0.75" in the "Size" field.

"OK"

Press the "OK" button to exit the options dialog.

"OK"

Press the "OK" button to exit the model mesh settings dialog.

Mouse "Part…"

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Press the Windows "Start" button and access the "All Programs" pull-out menu. Select the "Autodesk" folder and then the "Autodesk Algor Simulation 2012" pull-out menu. Choose the "Autodesk Simulation 2012 software" command. Click on the "Open" button in the Launch panel. Alternatively you select “Open” from the quick access toolbar or Application Menu. Select the "STEP (*.stp, *.ste, *.step)" option in the CAD Files section of the "Files of type:" drop-down box. Select the file "Manifold Assembly.step " in the "Chapter 4 Example Models\Input File" directory.

Right-click on the "CAD Mesh Options" heading for Part 1 in the tree view. Select the "Part…" command. We will now be able to specify the mesh settings for only the manifold.

"Midplane"

Select the "Midplane" radio button.

"Options…"



Access the "Type" pull-down menu and select the "Absolute mesh size" option.

0.75

Enter "0.75" in the "Size" field.

"Midplane"

Select the "Midplane" icon. The dialog shown in Figure 4.2 will appear with the options specific to a midplane mesh. We do not need to change any of the default options but they are discussed below the figure.


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Chapter 4: Midplane Meshing and Plate Elements

Figure 4.2: Part Mesh Settings Dialog with the Midplane Icon Active Thickness control section User-specified maximum thickness: By default the midplane mesh process will search for surface pairs that are within an automatically calculated or a user-specified distance from each other. We will call this distance the maximum thickness. When these outer surface pairs are found, the location of the midplane of the region is determined and the mesh is placed at this location. The program default is to use the automatically calculated maximum thickness, which is determined as a function of the initial surface mesh. If this maximum thickness value is smaller than the part thickness at any region, that region will be missing from the resultant midplane mesh. In such cases, you can enable the "Userspecified maximum thickness" option and enter a value greater than the maximum thickness of the part or parts to be midplane meshed. This option may also be used to intentionally exclude thicker regions of a part from the midplane mesh. Maximum allowed thickness variation: If this checkbox is activated, the midplane mesh process will only convert the mesh on a part to a midplane if the difference between the maximum thickness and the minimum thickness in the part is less than the value specified in this field. Use junction method: If this checkbox is activated, a chordal axis transform (CAT) algorithm will be used to generate the midplane mesh. This may result in a better approximation of the midplane for models containing complex geometries such as junctions and intersections. "OK" "OK" "Mesh: Mesh: Generate 3D Mesh"

Press the "OK" button to accept the default settings and to close the mesh options dialog. Press the "OK" button to accept these parameters for the manifold part and to close the mesh settings dialog. Select the "Generate 3D Mesh" button in the Mesh panel.


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Chapter 4: Midplane Meshing and Plate Elements All three parts will be surface meshed. The midplane mesh engine will convert the surface mesh into a midplane mesh for the manifold part. The flanges remain as solid objects. By analyzing the manifold we can see that the manifold has no thickness. You can also see that the nodes where the manifold meets the flanges have been matched so that the loads will be transferred between the parts. If mesh sizes between plate and solid parts are significantly different, smart bonding may at times be used to connect the components without matching the nodal locations. This is also dependent upon other mesh settings, such as the "Use virtual imprinting" option that was previously discussed. It is important to note that not all combinations of midplane and solid models are acceptable. Figure 4.3 shows an acceptable configuration and an unacceptable configuration.

Figure 4.3: Midplane and Solid Combinations The configuration on the left is acceptable because the midplane of the gusset will be in contact with the top of the plate. The configuration on the right will not work because the midplane of the plate will not be in contact with the bottom of the gusset. Therefore the nodes on the parts will not be matched. The midplane mesh can be extended in the plane of the elements at the edges in order to match the parts. The nodes cannot be stretched out of the plane, nor can the node of the solid mesh be moved in order to match the parts. Mouse "Edit Element Definition…"

Right-click on the "Element Definition" heading for Part 1 in the tree view. Select the "Edit Element Definition…" command. The dialog shown in Figure 4.4 will appear.

Figure 4.4: Element Definition Dialog for Plate Elements 86


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Chapter 4: Midplane Meshing and Plate Elements By default, unique thickness values will automatically be assigned to each individual plate element within a midplane-meshed part. This can be verified by checking the model and inquiring on the element information for selected plate elements within the Results environment. If the "Use mid-plane mesh thickness" option is deactivated, the average thickness for the part will be calculated and displayed in the thickness column. This thickness will then be applied to all elements within the part. The user may also specify the thickness on a per-surface basis, if desired. Choosing the "Surface-based" option from the "Properties" pull-down list will expand the table to list each surface of the midplane-meshed part. The thickness, normal point coordinates and other data can then be entered for each surface.

Mouse

Deactivate the "Use mid-plane mesh thickness" checkbox. The average thickness calculated for the part will be displayed in the "Thickness" column.

Mouse

Activate the "Use mid-plane mesh thickness" checkbox.

"OK"


"File: Save"

Click on the "Save” button in the quick access toolbar.

We will continue developing this example model later on in this chapter.

Element Options Plate Theory and Assumptions

Figure 4.5: Plate Theory Figure 4.5 shows the DOFs associated with plate elements. Please take note that the out-ofplane rotation (Rz) is not taken into account because of the plate theory. Thus, plate elements have 5 DOFs. Limits of Plate Theory • • •

No warpage is accounted for in the undeformed element Stress through the thickness is not truly linear for thicker plates The theory is based on a square element with 90-degree corners

NOTE: Violation of these limitations does not mean you will get wrong results. It simply means that you should check your results.


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Chapter 4: Midplane Meshing and Plate Elements Plate Formulations 1.

Veubeke (Standard) • •

2.

Reduced Shear • •

3.

This uses the reduced shear integration Hsieh, Clough and Tocher (HTC) plate bending theory is used (Constrained Linear Strain Triangle, CLST)

Linear Strain • •

4.

This is the most accurate This is very sensitive to warpage of the elements

Without the reduced shear integration terms HTC plate bending theory is used (CLST)

Constant Strain •

HTC plate bending theory is used (CLST)

Assumptions • • • • • •

The thickness is small relative to the overall length and width of the model Small displacements and rotations Plane sections remain planar Linear stress distribution through the thickness The plate element is initially flat; that is, all points are in the same plane The out-of-plane rotations are negligible

Loading Options The loading options for plate elements are almost identical to those for brick elements, as discussed in Chapter 2. The only addition is the control for the orientation of normal surface pressure, hydrostatic pressure, and surface force loads. For plate elements, this is controlled by an element normal point. This is an arbitrary point in space defined in the "X Coordinate", "Y Coordinate" and "Z Coordinate" fields in the "Element Normal" section of the "Orientation" tab of the "Element Definition" dialog. A positive normal or hydrostatic surface load or surface force will be applied normal to the face of each element and will push against the side of the element that is facing the element normal point. A negative normal or hydrostatic surface load or surface force will act in the opposite direction. See Figure 4.6 for a visual explanation.

Figure 4.6: Element Normal Point

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Chapter 4: Midplane Meshing and Plate Elements Hydrostatic Pressure Loads: One additional option for plate elements is that hydrostatic pressure loads can be applied in any orientation. The model does not need to be oriented with gravity acting in the -Y direction. The plane representing the surface of the fluid will be defined by a point on the surface and a vector normal to the surface. The normal vector should point into the fluid, that is, in the direction of increasing depth and gravity.

Example of Defining the Element Normal Point To illustrate the use of the element normal point, we will continue using the manifold assembly from the prior midplane meshing example. If this model is not currently loaded, reopen the file, Manifold Assembly.fem, saved at the end of the midplane meshing example. By default, the element normal point will be set to the global coordinate origin (0, 0, 0). We will add a pressure load to all of Part 1 and see how the loads are oriented. We will then make necessary corrections to the element normal point definitions and recheck the model. "View: Orientation: Isometric View" "Selection: Select: Parts" Mouse "Selection: Subentities: Surfaces" "Setup: Loads: Pressure"

Select the "View" tab. Click on the options button to the bottom of "Orientation" button in the "Navigate" panel. Select "Isometric View" from the pull-out menu. Select the "Selection" tab and then click on the "Parts" button in the Select" panel. Select Part 1 in the display window. Then Right Click mouse. Then click on the "Surfaces" button in the Subentities" pull out panel. Select the "Setup" tab. Click on the "Pressure" button in the "Loads" panel.

20

Enter "20" in the "Magnitude" field.

"OK"


Before we can check the model, we will need to define the material for the plate and brick parts. Mouse "Steel (ASTM – A36)"

Double-click on the "Material" heading under Part 1 in the tree view. Expand the Steel folder and then expand the ASTM folder. Select "Steel (ASTM-A36)" within the Autodesk Simulation Material Library.

"OK"


Mouse

Select the "Material" heading under Part 2 in the tree view.

Mouse

Holding the key, also select the "Material" heading under Part 3 in the tree view.

Mouse

Right-click on one of the selected headings.

"Edit Material…"

Choose the "Edit Material…" command.

"Steel (ASTM – A36)"

Expand the Steel folder and then expand the ASTM folder. Select "Steel (ASTM-A36)" within the Autodesk Simulation Material Library.

"OK"



Select the "Analysis" tab. Click on the "Check Model" button in the "Analysis" panel.


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Chapter 4: Midplane Meshing and Plate Elements It will initially be difficult to tell whether the orientations are correct or not because some of the load vectors will be rendered attached to the model at the arrow head end and some will be attached at the tail end. We will make the vector orientations consistent so that critiquing the model will be easier. "Tools: Options: Application Options"

Select the "Tools" tab and then click on the "Application Options" button in the "Options" panel.

Mouse

Go to the "Results" tab within the Options dialog.

"Global FEA Objects Preferences…"

Press the "Global FEA Objects Preferences…" button.

"All arrows point at point of attachment" "OK" "OK"

Under the "Arrow Pointing" heading, activate the "All arrows point at point of attachment" option for the "Current" model (left radio button). You do not need to change the default setting. Press the "OK" button to close the Global FEA Objects Preferences dialog. Press the "OK" button to exit the Options dialog. The model should now appear as shown in Figure 4.7.

Figure 4.7: Pipe Model in FEA Editor Environment Notice how the pressure is acting against the outside of half of each pipe leading out to the flanges. Clearly, the origin is not a suitable location for the element normal point for these two surfaces. A more intuitive location for these normal points would be somewhere along the centerline of each pipe. This is already true for the middle pipe, since its axis passes through the coordinate origin. There are two ways to correct the orientation: 1. 2.

Make each outlet pipe a unique part number by modifying the attributes of the lines comprising them. Then, each outlet pipe can have a unique, part-based element normal point. Specify surface-based element properties for Part 1. In this way, the surfaces comprising the two outlet pipes may have unique element normal point definitions.

We will now demonstrate the latter approach. The centerlines of the two outlet pipes are at Z = +/- 7.5" and lie in the XZ plane. You may identify the surface numbers of the outlet pipes by selecting one surface at a time, right-clicking, and choosing the "Inquire" command. A pop-up tool tip will identify the part and surface numbers. The half-surfaces comprising the +Z pipe are 5 and 14. The half-surfaces of the -Z pipe are 4 and 15. 90


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"Tools: Environments: FEA Editor" "Element Definition…"

Select the "Tools" tab. Press the "FEA Editor" button in the "Environments" panel. Double-click the "Element Definition" heading under Part 1 in the tree view.

Note that the "Properties" setting defaults to "Part-based." Therefore, the data entered into the table will apply to the entire part. As an alternative, it is possible to change this setting to "Surface-based," in which case each unique surface can have different properties. Access the pull-down menu in the "Properties" field and choose the "Surface-based" option. Enter "-7.5" in the "Normal Point (Z)" column for Surface 4 and for Surface 15. Enter "7.5" in the "Normal Point (Z)" column for Surface 5 and for Surface 14.

Mouse "Surface-based" -7.5 7.5 "OK"



Select the "Analysis" tab. Click on the "Check Model" button in the "Analysis" panel. Select the "View" tab. Select the options below "Visual Style" button in the "Appearance" panel. Select the "Features" option. The model will now appear as shown in Figure 4.8.

"View: Appearance: Visual Style"

Figure 4.8: Model in Results Environment You can now see that the pressure is properly applied to all surfaces of the manifold. A completed archive of this model (Manifold Assembly.ach) is available in the "Chapter 4 Example Model\Results Archive" folder in the class directory or in the copy of the solutions folders on your computer.


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Result Options When a plate element model is initially loaded into the Results environment, the midplane will be displayed. The actual thickness of the plate elements can be shown by right-clicking on the heading for a plate element part in the tree view and selecting the "3-D Visualization" command. For result options that are specific to plate elements, access the options pull-down menu in the "Settings" panel within the "Results Contours" tab. Then select the "Plate Option" button. The "Plate Display Options" dialog shown in Figure 4.9 will appear.

Figure 4.9: Plate Display Options Dialog Bending/Membrane section: Total Stress/Strain: If this radio button is selected, the total top/bottom stress or strain will be displayed. The total stress consists of the axial stresses, shear stresses, and bending stresses. The stresses are displayed on the visible side. The "Reverse Sides in Plot" checkbox can be activated to view the stresses on the other side. Bending Stress/Strain: If this radio button is selected the bending stresses or strains (SB11, SB22 and SB12) will be used for all stress calculations including von Mises, Tresca, maximum principal and minimum principal stresses. Membrane Stress/Strain: If this radio button is selected, the membrane stresses or strains due to axial stress (SM11, SM22) and shear stress (SM12) are used for all stress calculations including von Mises, Tresca, maximum principal and minimum principal stresses.

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Chapter 4: Midplane Meshing and Plate Elements Two-Sided Display section Both Sides: If this radio button is selected, the results of both the top and bottom sides of the plates will be displayed. Therefore different contours will be displayed on the opposite sides of the plate. If the "Reverse Sides in Plot" checkbox is activated, the top and bottom sides will be reversed. This will allow you to view the results on the opposite side of the plates without rotating the model. Top Side Only: If this radio button is selected, the results on the top side of the plate will be displayed on both sides of the plate elements. Bottom Side Only: If this radio button is selected, the results on the bottom side of the plate will be displayed on both sides of the plate elements.


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Exercise C Midplane Meshing and Plate Element Orientation Plate Elements Concepts that will be Illustrated: • • • •

Creating a midplane mesh Modeling with plate elements Properly defining plate element orientations Applying pressures to plate elements

Objective:

Generate a plate model of the duct and nozzle assembly shown below, apply an internal pressure throughout the assembly, and analyze it.

Geometry:

Use the file Exercise C.step from the "Exercise C\Input File" directory in the class directory or in the copy of the solutions folders on your computer. Perform a midplane mesh using an absolute mesh size of 0.2 inch for all parts. Use the automatically calculated midplane mesh thickness for all parts.


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Chapter 4: Midplane Meshing and Plate Elements Loading:

20 psi internal pressure throughout assembly

Constraints:

Fully constrained at inlet and outlet edges (as shown on diagram)

Element:

Plate

Material:

Stainless Steel (AISI 302) Cold-rolled



~37,198

0.0178

* * * Hints:

• • •

The coordinate origin is in the exact center of the square header The centerline of the rectangular inlet is at Z = 6.75" The centerlines of the round outlets are at Y = +/- 4.5" and Z • -5"

A completed archive of this model (Exercise C.ach) is available in the "Exercise C\Results Archive" folder in the class directory or in the copy of the solutions folders on your computer.

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Chapter

5

Meshing Chapter Objectives • • • •

Learn how to refine the mesh in specific areas of a model Learn how to add joints to a model Learn how to create bolted connections Learn how to perform mesh convergence tests

Refinement Options Automatic Refinement Points For models that contain small features, it is often necessary to use a relatively fine mesh to adequately capture the geometry. However, if the entire model is meshed at the fine mesh size, an unnecessarily large number of elements will be created. Refinement points can be added to the model to create a fine mesh in a local region and a coarser mesh for the rest of the model. There are two methods that can be used to create refinement points. Automatic Once a surface mesh has been generated on the model, you can have refinement points automatically applied to the model by accessing the "Mesh" tab and selecting the "Automatic" button from the "Refinement Points" panel. The "Automatic Refinement Points" dialog will appear. This dialog will contain a "Density of refinement points" slider. You can move this slider to the "Coarse" or "Fine" setting to determine the level of refinement that you want to achieve. When you press the "Generate" button, the small features of the model will be identified and refinement points will be created. When the number of refinement points created is reported, press the "Close" button. You will now notice many black dots on the model. These symbolize the refinement points. If you mesh the model again, the refinement points will be used. You can repeat this process as many times as necessary. Specify If you want to create a refinement point with specific parameters at a specific point in the model, you can access the "Mesh" tab and select the "Specify" button from the "Refinement Points" panel. This can be done before or after a mesh has been generated. The "Refinement Point Browser" dialog shown in Figure 5.1 will appear. To define a refinement point, press the "Add" button. The model must be meshed again following the creation of refinement points in order for the refinement to take effect. Autodesk® Simulation Mechanical 2012 – Part 1 – Seminar Notes

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Figure 5.1: Refinement Point Browser Dialog X: Define the X coordinate of the refinement point in this column. If you selected a vertex on the model, this column will already be defined. Y: Define the Y coordinate of the refinement point in this column. If you selected a vertex on the model, this column will already be defined. Z: Define the Z coordinate of the refinement point in this column. If you selected a vertex on the model, this column will already be defined. Radius: Specify the radius, around the refinement point, within which you want the refinement to occur. A spherical zone centered at the refinement point and having this radius will be defined, though only a point will be displayed. The mesh lying within this spherical zone will be refined. Mode: This drop-down box has two options. The "Size" option will require you to specify the mesh size desired within the spherical refinement zone. The "Divide" option will require you to specify a divisor by which the mesh size within the refinement zone is to be divided. Mesh size: If the "Size" option is specified in the "Mode" column, define the mesh size that will be applied within the specified spherical radius of the refinement point. Divide factor: If the "Divide" option is specified in the "Mode" column, define the divide factor that will be applied to the mesh size within the spherical radius of the refinement point. For example, a factor of 2.5 would result in a mesh size of 40% of the original size (L/2.5 = 0.4L). If a mesh has already been generated, you can select a vertex or vertices on the model and then select the "Add to Selected Nodes" button from the "Refinement Points" panel, within the "Mesh" tab. This will access the "Create Refinement Point" dialog, which will allow you to define the radius and either the mesh size or the divide factor. These options correspond to the columns in the "Refinement Point Browser" dialog. If you right-click and select the "Add: Refinement Point…" command while no vertex is selected; the X, Y, and Z coordinates may be typed into the provided data fields. This is an alternative to using the Refinement Point Browser.

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Global Refinement Options Global refinement can be created by selecting the"3D Mesh Settings" button from the "Mesh" panel. By pressing the "Options…" button on the "Model Mesh Settings" dialog and selecting the "Model" icon on the left, the dialog shown in Figure 5.2 will appear.

5.2: Model Mesh Settings Screen with the Model Icon Active With the exception of the two items discussed below, the options within the "Model" section of the mesh settings dialog are beyond the scope of this introductory level course. Please consult the help files for further information. The appropriate help file section may be accessed by pressing the "Help" button within the model mesh setting dialog. Default meshing options: Use automatic geometry-based mesh size function: By default, the mesh size is made finer around curved features and in areas of localized close proximity of features (such as where a hole or a corner is closely located to another edge of the same part). Beyond the areas of geometry-based mesh size adjustment, a relatively larger mesh size is used. If this option is disabled, the resultant mesh size will typically be smaller on average and more uniform. The element count will also typically increase, though the mesh size at curved features will generally be coarser. Perform solid meshing at time of analysis: By default, solid meshing is postponed until the first time a model is checked or analyzed. The mesh engine stops after verification of the surface mesh integrity. This is advantageous since it is a waste of time to solid mesh a model if you haven't yet approved the surface mesh. In other words, you may want to make the mesh finer, coarser, or locally refined. By deactivating this option, you will force the mesh engine to immediately proceed with solid meshing. In order to see additional options within the dialog to be discussed next, deactivate the "Use automatic geometry-based mesh size function" checkbox. We can restore the setting later, if desired. Select the "Surface" icon at the top left corner of the Model Mesh Settings Screen (Options dialog). This is the icon that will be selected by default when you first press the "Options…" button on the "Model Mesh Settings" dialog. Selecting the "Options" tab within this screen will bring up the dialog shown in Figure 5.3.


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5.3: Options Tab of the Model Mesh Settings Screen with the Surface Icon Active NOTE: The fields within the Surface settings "Options" tab will not appear unless the Model option, "Use automatic geometry-based mesh size function" is disabled (see previous page). Instead, the following message will appear… "Automatic surface mesh refinement is in effect from the model-level setting's "General" tab on the "Model Mesh Settings" dialog. Surface meshing options are not available when this is in effect." Edge curve refinement section: Mode: The options in this drop-down box allow you to control how elements are created along the curves of a model. With the exception of the "None" option, which performs no edge curve refinement, all of the options use the value in the "Angle (1-90 degrees)" field to place elements along the curves. The default option of "Curvature of edge curve" will use the Angle value as the average angle between the elements along the edge only. The restriction is not imposed for the elements along the adjacent curved surface. This is often adequate. The "Minimum adjacent surface curvature" option will use the Angle value as the minimum angle between two surface elements (i.e. the restriction is not limited to the edge curve). This will normally result in a greater number of elements than the "Curvature of edge curve" option but fewer than the fourth option. The "Maximum adjacent surface curvature" option will use the Angle value as the largest allowable angle between two elements. This will usually result in larger numbers of elements along curved surfaces. Splitting quadrangles into triangles section: The options in this section will allow you to control the quality of the elements formed in your surface mesh. In a quadrilateral element, it is possible for one node to not lie in the plane defined by the remaining three nodes (let's call this Plane 1). The off-plane node and the two nearest nodes form another plane (we'll call this one Plane 2) that is not parallel to Plane 1. If the angle between these two planes is greater than the value specified in the "Fold angle is greater than" field, the quadrilateral element will be split into two triangular elements. Triangular elements, by definition, are planar. If the internal angle between two sides of an element is larger than the value in the "Node angle is greater than" field, that element will be split into two triangular elements. These options will result in the creation of better solid elements by the solid mesh engine.

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Creating Joints A convenient method that can be used to create beam or truss geometry to simulate pin joints is the joint utility. This is only available for models originating from CAD solid models. First, select all of the surfaces that you want included in the joint. You can either click on the surfaces on the model (be sure to hold down the key to select multiple surfaces) or select the headings for those surfaces in the tree view (again be sure to hold down the key to select multiple surfaces). You must have preselected "Point" button from the "Shape" panel and "Surfaces" from the "Select" panel within the "Selection" tab, in order to select surfaces by clicking on them in the model. To create a joint, select the "Joint" button from "CAD Additions" panel from within the "Mesh" tab. The "Create Joint" dialog shown in Figure 5.4 will appear to allow you to enter the specifications for this joint.

Figure 5.4: Create Joint Dialog If surfaces were selected in the display area when the command was selected, they will be listed in the "Participating surfaces" section. Surfaces can be added to this section by selecting them in the display area and pressing the "Add" button. Joint type: Select the type of joint that you want to create in this drop-down box. Pin joint (lines to axis endpoints): This option will create a classic pin joint where the nodes at each end of the surfaces included in the joint are connected to the opposite end of the joint axis. This type of joint will allow the model to rotate around the axis. Universal joint (lines to axis midpoint): This option will create a classic universal joint. The nodes at either end of the model will be connected to the midpoint of the axis. This type of joint will allow the model to rotate about the axis as well as swivel about the center point of the axis. Each type of joint is shown in Table 5.1


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Chapter 5: Meshing Table 5.1: Joint Types – Pin Joint versus Universal Joint Pin Joint

Universal Joint

(two points on axis of rotation)

(single point at center)

Automatic detection of axis/center-point: If you want the joint creator to decide where the axis of rotation will be, based on the geometry of the surfaces involved in the joint, select this radio button. Manual axis/center-point specification: If you want to specify the axis of rotation, select this radio button and then enter the X, Y and Z coordinates. If your joint is a pin joint, you will have to enter the coordinates for the two end points of the axis. If your joint is a universal joint, you will have to enter the coordinate for the center point. When you press the "Mesh model" button in the "Model Mesh Settings" dialog, the surface mesh will be created as usual and then the joint application program will create the lines that will be the truss or beam elements. These lines will be placed in the next part available in numerical order. If you defined multiple joints, each joint will be placed in its own part.

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Creating Bolts A convenient method that can be used to model screws, rivets, and bolted connections using beam and truss elements is the bolt wizard. Like the joint utility, this tool is only available for FEA models originating from CAD solid models. To create a bolted connection select the "Bolt" button from "CAD Additions" panel from within the "Mesh" tab. The "Generate Bolted Connection" dialog shown in Figure 5.5 will appear to allow you to enter the necessary specifications.

Figure 5.5: Create Bolted Connection Dialog The "Part Number" field will default to the first available non-CAD number. You may change the target part number if desired. Bolts with differing parameters should be created using unique part numbers. Bolts with identical parameters may be defined using a common part number. A pull-down list is provided for the selection of the "Type of Bolt." Table 5.2 describes the three available types. For simplicity, the type of fastener will be called a "bolt" although the approach can represent any similar fastener. The top row of figures shows the physical joint. Autodesk® Simulation Mechanical 2012 – Part 1 – Seminar Notes

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Chapter 5: Meshing The bottom row shows the FEA equivalent construction; where the heavy line segments represent the beam elements created by the bolt wizard: Table 5.2: Type of Bolts Created by the Generate Bolted Connection Dialog

"Bolt With Nut"

"Bolt Without Nut"

"Grounded Bolt"

The bolt is threaded (tight fit) into the bottom part (extra beam elements connect the fastener to the hole).

The bolt is threaded into the foundation or other rigid item that is not modeled. A boundary condition is placed on the end of the bolt.

Enter, within the provided fields, the desired "Bolt Diameter," "Head Diameter," "Nut Diameter," and the "Number of Spokes" to be used to represent the head and nut. Assign the appropriate head contact, nut contact and bolt hole surfaces using the "Add" buttons after having selected each set of surfaces. Surfaces can be removed from any of the three lists by pressing the "Remove" buttons. For each surface added to the interior hole surface(s) list, there will be a checkbox labeled "Tight Fit." Check this box for surfaces where the fastener is to be tightly fit (such as for tapped holes, body-bound bolts, expanded rivets, etc.). Additional beam elements will be introduced as shown in the middle figure above. To preload the bolt, select either the "Axial Force" or "Torque" radio button. If a torque is entered, it will be converted to an axial force based on one of the following equations: With a nut:

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F=

T K *D


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Chapter 5: Meshing Without a nut:

F=

T 1.2 * K * D

where T is the torque magnitude, K is the friction factor, and D is the bolt diameter. At the outer end of each spoke that represents a bolt head or nut, a construction vertex will be created. If the model has been meshed prior to the definition of the bolts, it will have to be remeshed. During meshing of the adjacent CAD parts, element nodes will be created at these construction vertices to ensure proper connectivity of the CAD and parts.

Mesh Convergence Testing As mentioned previously, the stress results will depend on the density of the mesh. It is therefore recommended that you perform an analysis with a few different mesh sizes to see the effect on the results. Once you change the mesh size to a smaller value and the results do not change significantly, the results can be considered to have converged. The Results environment has a tool that can assist in this process. Access the RESULTS menu and select the "von Mises Precision" button from the "Stress" panel drop down menu, within the "Results Contours" tab. The model will be displayed with the Stress von Mises Precision contour. Stress is calculated at each node in each element. Thus, multiple elements that meet at a common node provide independent stress calculations at that node. The Results environment normally displays the average of these independent stresses. For example,

Figure 5.6: Precision Example Element Number 1 2 3 4

Node Number 5 5 5 5

von Mises Stress 20,000 15,000 19,000 10,000

Average (smoothed) Stress = 16,000 Highest von Mises in model = 25,000 (node 9) Precision =

(max stress @ node – min stress @ node)/2 Max stress in model


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Precision =

(20,000 - 10,000)/2 = 0.20 25,000

Note that the precision values will range between 0 (best) and 0.5 (worst). The precision result is a plus or minus fraction of the largest stress in the model. Consider the preceding example. At the subject node, there is a stress value variation of 10,000 (or +/5,000 relative to the median stress). A range of +/- 5,000 is +/- 20 percent of 25,000 (the highest stress in the model). Hence, the precision result of 0.2 indicates that the stress variability at that node is +/- 20 percent of the maximum stress. It can also be helpful to look at a color contour plot showing the actual range of stress variation at a node. This can be done by selecting the "Results Contours: Settings: Smoothing Options" command. Select the "Range" option in the "Smoothing function:" drop-down. Do this while viewing a stress result (such as von Mises, one of the Principal stresses, or one of the Stress Tensors), not while viewing the Precision of von Mises Stress result.

Performing a Mesh Study A mesh study wizard is included with the Autodesk® Simulation software. This wizard automates the process of checking multiple mesh sizes to achieve good convergence of the stress results. Automated mesh studies may be performed only for CAD-based models and for the analysis type "Static Stress with Linear Material Models." To access this feature, go to the command "Mesh Study Wizard," found within the "Tools" subfolder of the Start menu's Autodesk® Simulation 2012 program group. For more information regarding how to set up and run a mesh study, go to the "Getting Started" tab and then select "In-product Help" button from "Help" panel. Expand the top-level "Autodesk Simulation" branch, if it is not already expanded. Then, expand the "Mesh Models" branch and then "Mesh Overview" sub-branch in the tree view. Next, expand the "Meshing CAD Solid Models" sub-branch. Finally, select the topic "Perform Mesh Studies."

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Exercise D Yoke and Clevis Assembly Brick Elements Concepts that will be illustrated: • • •

Using refinement points Adding a joint to a model Using the Bolt Wizard to create a bolted connection

Objective:

If you review the results of the yoke analysis performed in Chapter 1, you will notice that the stress results are not perfectly symmetrical, as would be expected. Perform the analysis again using the refinement options. Also, add a pin joint to the large hole and specify a bolted connection at the small hole. Apply the load to the center of the joint.

Geometry:

Use the file Exercise D.step in the "Exercise D\Input File" folder of the class directory or in the copy of the solutions folders on your computer.

Meshing:

After meshing initially using a mesh size setting of 85 percent, apply refinement points using the "Refinement Points: Automatic" command. Adjust the slider towards the right until approximately 45 refinement points are created. Then, regenerate the surface mesh. Create the pin joint and the bolt after the refined mesh has been finalized. Regenerate the mesh one more time after specifying the bolt so that the head and nut will be properly connected to the sides of the clevis.

Loading:

800 lbf total (400 lbf per node) in the –X direction at the center of the pin joint in the large hole.


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Chapter 5: Meshing Constraints:

Fully constrain the four edges of the clevis base. This will simulate the behavior of a full perimeter weld. Do not fix the entire base surface. Constrain Ty at the center of the large hole's joint. This will prevent rotation of the yoke about the center of the small hole and ensure symmetrical behavior of the top and bottom halves of the yoke.

Element:

Brick (Yoke), Beam (Bolt), and Truss (Joint, 0.1 in2 cross-sectional area)

Material:

Steel (ASTM-A36) – Yoke and Clevis Steel (AISI 4130) – Joint and Bolt

Bolt Specifications: Bolt Diameter = 0.75" Head and Nut Diameter = 1.125" Number of Spokes = 12 Specify a "Tight Fit" for all bolt hole surfaces Axial Force (Preload) = 500 lbf Results: Description

Maximum von Mises Stress (psi)


Yoke (Part 1)

~1,595

0.00059

Clevis (Part 2)

~2,306

0.000150

A completed archive with results (Exercise D.ach) is located in the "Exercise D\Results Archive" folder in the class directory or in the copy of the solutions folders on your computer.

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Chapter

6

Introduction to Contact Chapter Objectives • •

Learn the types of contact available Learn how to use contact in an analysis

Uses for Contact Often in assemblies, some parts are not in bonded contact with adjacent parts. For example, the mating surfaces of two parts that are bolted together are not bonded. These surfaces are in contact and would be free to slide relative to each other or to separate from each other except as constrained by the bolts. If the meshes on both parts were to be bonded, the analysis might not represent the correct conditions or behavior of the assembly. Another example would be a shaft in a hole. When a load is applied to the shaft, it will cause the shaft to bear on only one side of the hole. As the hole and shaft deform the surfaces on the unloaded side will typically slide or separate somewhat. Contact is also necessary to properly model interference fits, which occur when an inner part undergoes expansion within an outer part or when the outer part experiences shrinkage.

Contact Options Setting up Contact Pairs Autodesk® Simulation has the ability to model contact between parts. This can be set up before or after creating the mesh. First, you must specify the 2 surfaces or parts that will be involved in each contact pair. Select these surfaces or parts either in the tree view or in the display area. Once a pair is selected, right-click and select the "Contact" pull-out menu. Select the command for the type of contact desired, as explained below. A new heading will appear under the "Contact (Default: Bonded)" heading in the tree view listing the surfaces involved in this pair. Any number of contact pairs may be added. You may also change the default contact setting by right-clicking on the "Contact (Default: Bonded)" heading and selecting the desired type of contact globally. Any individual contact pairs that are defined will override the global default setting for those particular pairs. The default setting should represent the most prevalent type of contact that exists within the assembly in order to minimize the number of overrides that must be defined. When the default setting is changed, a detailed list of all of the detected contact pairs within the assembly will automatically be generated and will appear beneath the "Contact (Default: …)" heading. Contact pair definitions can automatically be generated for all contacting surfaces between two or more parts. To use this feature, select two or more parts, right-click and choose the "Create Contact Between Parts…" command. In addition, there is a global parameter that Autodesk® Simulation Mechanical 2012 – Part 1 – Seminar Notes

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Chapter 6: Introduction to Contact can be found by clicking the "Global CAD Import Options" button within the "Application Menu: Options: CAD Import" dialog. To make generation of all contact pairs fully automatic whenever importing a CAD model, activate the "Yes" radio button to the right of "Automatically generate contact pairs:" heading.

Types of Contact There are seven types of contact available for a Static Stress with Linear Material Models analysis. When the nodes lying along two contact surfaces are within the distance specified via the "Tolerance value" field under the "Mesh matching" heading in the "Model Mesh Settings: Options: Model" dialog, the meshes will be matched. The contact pair behavior will depend upon which type of contact is specified. When surfaces do not belong to an explicitly defined contact pair, the contact will follow the settings in the "Contact (Default: Bonded)" heading in the tree view. NOTE: The default may be changed from Bonded to any other type of contact described below by right-clicking on the heading and selecting the desired command. All contact pairs that are explicitly defined by the user will appear in the tree view, identified by a heading showing the type of contact and the part/surface numbers belonging to the pair. The settings can be changed for each pair by right-clicking on the heading for that pair and selecting the desired command. Bonded If the "Bonded" command is selected, an attempt will be made to match the nodes on the two surfaces of the contact pair. When matched and bonded, the two surfaces will be in perfect contact throughout the analysis. When a node on one surface deflects, the node on the adjoining surface will deflect the same amount and in the same direction. In fact, as far as the processor is concerned, only one node exists at each point where the mesh vertices meet. If the two surfaces are coincident but at least one pair of adjacent nodes are not within the mesh matching tolerance, and, if "Smart bonded/welded contact" is enabled; then, the nodes will be bonded using multipoint constraint equations (MPCs) rather than via mesh matching. See Element Connectivity – "Smart Bonding" (page 8) for additional information regarding this feature. Welded If the "Welded" command is selected, an attempt will be made to match the nodes along the edges of the contact surfaces. These nodes will act the same as if the "Bonded" command were selected. The nodes along the interior of these surfaces will not be bonded. These nodes will be free to move relative to each other, including the possibility of passing through each other. In the same manner as for Bonded contact, MPCs will be used to connect the edge nodes of a Welded contact pair if "Smart bonded/welded contact" is enabled and at least one pair of nodes falls outside of the mesh matching tolerance. Free/No Contact If the "Free/No Contact" command is selected, the nodes on the two surfaces in the contact pair may or may not be matched, depending on the geometry and other mesh settings. However, in any case, the nodes belonging to each part will not interact with each other and will move independently.

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Chapter 6: Introduction to Contact Surface Contact If the "Surface Contact" command is selected, the nodes on the two surfaces in this contact pair will be matched. The difference between this command and the "Bonded" command is that these nodes will be free to move away from each other. If the nodes move towards each other, stiffness will be applied to resist this movement. Imagine a very small line created between the nodes on these surfaces. If that line becomes longer during the analysis, it will have no effect on the model. If that line becomes shorter, it will act as a spring with a stiffness value that will resist this motion. If the "Surface Contact" command is selected, the analysis will involve an iterative process. This process will be used to determine if the deflection due to the loading will cause each pair of nodes on these surfaces to be in contact or not. Sliding/No Separation If the "Sliding/No Separation" command is selected, the nodes on the two surfaces in the contact pair may or may not be matched, depending on the geometry and other mesh settings The difference between this command and the "Bonded" command is that these nodes will be free to slide on the contact surface Separation/No Sliding If the "Separation/No Sliding" command is selected, the nodes on the two surfaces in the contact pair may or may not be matched, depending on the geometry and other mesh settings The difference between this command and the "Bonded" command is that these nodes will be free to move away from each other

Edge Contact If the "Edge Contact" command is selected, the nodes along the edges of the contact surfaces will be matched. These nodes will act the same as if the "Surface Contact" command were selected. The nodes along the interior of these surfaces will not be matched together. These nodes will be free to move relative to the nodes on the other surface. Even if the physical locations of the interior surface nodes happen to be coincident, they will still function independently. If the nodes along the edges move towards each other, a stiffness will be applied to resist this movement. Imagine a very small line created between the nodes on these edges. If that line becomes longer during the analysis, it will have no effect on the model. If that line becomes shorter, it will act as a spring with a stiffness value that will resist this motion. If the "Edge Contact" command is selected, the analysis will involve an iterative process. This process will be used to determine if the deflection due to the loading will cause each pair of nodes on these surfaces to be in contact or not.


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Chapter 6: Introduction to Contact

Friction If either the "Surface Contact" or "Edge Contact" option is selected for a contact pair, then friction may be included if desired. Right-click on a contact pair heading or on the "Contact (Default)" heading and choose the "Settings…" command. A "Contact Options" dialog will appear. If the contact type is "Surface Contact," then the dialog shown in Figure 6.1 will appear.

Figure 6.1: Contact Options Dialog for Surface Contact Pairs If the contact type is "Edge Contact," then the dialog shown in Figure 6.2 will appear.

Figure 6.2: Contact Options Dialog for Edge Contact Pairs Include friction: If this checkbox is active, you will be able to specify a static friction coefficient in the "Static friction coefficient" field. This value will affect how much force is necessary to cause the two surfaces to move relative to each other when a contact reaction is present. Friction occurs for movement perpendicular to the direction of contact and is zero where the contact force is zero. The larger the coefficient, the larger the necessary force to cause movement between the surfaces.

Surface Contact Direction Refer once again to the "Contact Options" dialog for surface contact pairs (preceding Figure 6.1). For surface contact pairs, the default option for determining the contact direction is "Calculate by matching directions." This option will calculate the contact direction by averaging the individual normal directions of the element faces at each node. This is the recommended method. If a meshed surface is curved, some of the element faces may not be flat (that is, the fourth node may not be coplanar with the other three, resulting in face warpage). This is especially true if the mesh is coarse. Also, if the mesh is imperfectly matched (that is, not all of the nodes are snapped together within the contact region), then the adjacent element faces will not be coincident. In such cases, the default method may produce incompatible contact directions. Contact elements will only be created at nodes that are matched and for which the calculated contact directions are within the specified tolerance 112


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Chapter 6: Introduction to Contact angle, which is 20 degrees by default. In order to achieve compatible directions, you can increase the value in the "Direction tolerance angle" field. Another situation that may lead to incompatible contact directions and dropped contact elements is when two surfaces that are not parallel meet at one edge, such as when the edge of an inclined cutting tool acts against a flat object. The element faces adjacent to the contact line are not parallel for the two parts and the angle of the faces may differ considerably. If the direction tolerance angle is increased sufficiently, the contact elements will be created and will act along a direction that is the average of the normal vectors for the two surfaces contacting at the edge. It may, however, be desirable to have the contact force act normal to one of the parts. In such cases, choose either the "Normal to the first part/surface" or "Normal to the second part/surface" option in the "Surface contact direction" drop-down box. For example, if you want the contact reaction to act normal to the cutting tool and this is the second part listed in the contact pair heading, then you would choose the "Normal to the second part/surface" option. If gravity (that is, part weight) is the source of the contact force, then choose the normal direction based on which surface has a normal vector that is closest to the vertical direction (that is, closest to the direction of gravitational acceleration). For the contact direction options, an explicitly defined contact pair is required, since there is no specific order to the parts/surfaces when the contact type is "Default." These direction options are not implemented for global surface contact.


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Contact Example How to Model Shrink Fits: The type of connection used between the parts will define whether they are assumed to be locked together due to friction or to slip in the plane of contact between the two parts. Choose between the following two cases: Case 1: If the two parts are assumed to be bonded together, shear forces will be developed at the interface between the two parts as they cool. This is because cooled parts will contract in both the radial and axial directions. However, they will not be permitted to freely contract at the interface with the mating (that is, bonded) part. Bonding two parts together, when each is experiencing different thermal expansion or contraction rates, may result in the development of shear forces in excess of those that are physically possible. In reality, the shear force cannot exceed the maximum available friction force (which is the normal contact force times the friction coefficient). Use bonded contact when you do not expect axial slippage or are not concerned about axial slippage nor the effect this has on the resultant stresses. Case 2: If shear forces between the parts are expected to be great enough to cause axial slippage, then surface contact should be used. If friction is not included, the shear force will be zero and the objects will freely slide relative to each other, though normal contact forces will still be developed due to the interference. To most accurately model the shrink fit, include friction. The friction force will resist slippage, preventing it from occurring until the shear force exceeds the available friction force. Even if slippage occurs, the friction force, which is also the shear force, may affect the stress results. Directions on how to model a shrink fit: 1.

Model as two different parts.

2.

Define a uniform temperature in the "Analysis Parameters" dialog in the "Thermal\Electrical" tab.

3.

Apply a load case multiplier for the thermal effects in the "Load Case" tab of the "Analysis Parameters" dialog.

4.

Define a thermal coefficient of expansion and the stress free reference temperature for each part. The change in temperature (delta T) is the difference between the stress free reference temperature and the default nodal temperature defined within the analysis parameters screen. This delta T causes the part growth or shrinkage that produces the interference. For a part to shrink, the stress free reference temperature needs to be higher than the default nodal temperature. Setting the stress free reference temperature to be lower than the default nodal temperature will cause the part to expand. NOTE: You may also apply a part-based temperature to a part or apply temperature results from a prior thermal analysis. Any applied or imported temperature will override the default nodal temperature setting.

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Shrink Fit Example The model shown in Figure 6.3 is a one-eighth symmetry model of a disk which will be shrink fit onto a hub.

Figure 6.3: Cold Model Geometry 1.

First model the disk in the heated-up configuration using the equations to adjust the dimensions. Note that at this point the interference can be a perfect zero or can be chosen to include a "gap" between the parts. A gap should only be included if the contact (gap) elements will be created manually.

2.

Define a stress free reference temperature for the disk (outer part) so that the assigned default nodal temperature will cause the disk to contract.

3.

The stress free reference temperature of the hub (inner part) and the default nodal temperature should be the same. Therefore, the hub will not move due to thermal effects.


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Controlling Equations: dT = Tref – Tdefault = [Radial Interference / (Ri + Radial Interference)] / α Ro' = Ro / (1-α *dT) Ri' = Ri / (1-α *dT) t' = t / (1-α *dT) where: Tref is the stress free reference temperature Tdefault is the default temperature assigned to the parts (basis of FEA solution) α is the coefficient of expansion of the disk Ri, Ro and t are the cold dimensions of the disk Ri', Ro' and t' are the hot dimensions of the disk The inner part is drawn with the cold dimensions because it will experience no thermal expansion. The outer part is drawn with the hot dimensions. Then the thermal expansion will contract the outer part and create the interference. Given: α = 6.5e-6 Ri = 2.997" Ro = 10.000" t = 2.000" Radial Interference = 0.003" (= 0.006" Diametral Interference) Tdefault = 0 °F

116

Hot Disk Geometry:

Case 1

Case 2

Tref (°F) Ro' (inch) t' (inch) Ri' (inch)

153.85 °F 10.010" 2.002" 3.000"

153.85 °F 10.010" 2.002" 3.000"

Model Setup:

Case 1

Case 2

Elements E (psi) ν alpha (1/F°) Tref (°F) Tref (°F) Tdefault (°F) Load case Friction

Brick 30e6 psi 0.3 10e-6 153.85 °F for outer ring 0 °F for inner ring 0 °F turn on thermal effect Bonded surfaces

Brick 30e6 psi 0.3 10e-6 153.85 °F for outer ring 0 °F for inner ring 0 °F turn on thermal effect 0.3


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Figure 6.4: Heated Model Geometry For this example, we will use the CAD solid model file Shrink.stp located in the "Chapter 6 Example Model\Input File" directory in the class directory or in the copy of the solutions folders on your computer.

Case 1 "Start: All Programs: Autodesk: Autodesk Algor Simulation 2012: Autodesk Simulation 2012"

Press the Windows "Start" button and access the "All Programs" pull-out menu. Select the "Autodesk" folder and then the "Autodesk Algor Simulation 2012" pull-out menu. Choose the "Autodesk Simulation 2012 software" command.

"Open"

Click on the "Open" icon at the left side of the dialog.

"STEP (*.stp, *.ste, *.step)" "Shrink.stp" "Open"

Select the " STEP (*.stp, *.ste, *.step)" option in the CAD Files section of the "Files of type:" drop-down box. Select the file "Shrink.stp" in the "Chapter 6 Example Model\Input File" directory. Press the "Open" button.

Mouse "Part…" Mouse "40%"

Choose the option to "Use STEP file units" if it is not already selected and click the "OK" button. The original STEP file length unit is inches. A dialog will appear asking you to choose the analysis type for the model. From the pull-out menu, choose "Linear: Static Stress with Linear Material Models" and press the "OK" button. Right-click on the "CAD Mesh Options" heading under Part 2 in the tree view and select the "Part…" command. Move the "Mesh size" slider to the right to decrease the size to "40%" for this part only.

"OK"


"Mesh: Mesh: Generate 3D Mesh"

Select the "Mesh" tab. Click on the "Generate 3D Mesh" button in the "Mesh" panel.



"Use STEP file units" "OK" "Linear: Static Stress with Linear Material Models" "OK"


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"Setup: Constraints: General Constraint"

Click and drag using the middle mouse button to rotate the model viewpoint so that all three symmetry planes can be clearly seen and selected. Referring to Figure 6.5, click on one of the surfaces that is to have X symmetry. Holding down the key, click on the other surface that has X symmetry. Select the "Setup" tab. Click on the "General Constraint" button in the "Constraints" panel.

"X Symmetry"

Press the "X Symmetry" button.

"OK"

Press the "OK" button to apply these boundary conditions.

Mouse Mouse Mouse


Referring to Figure 6.5, click on one of the surfaces that has Y symmetry. Holding down the key, click on the other surface that has Y symmetry. Click on the "General Constraint" button in the "Constraints" panel.

"Y Symmetry"

Press the "Y Symmetry" button.

"OK"


Mouse Mouse


Referring to Figure 6.5, click on one of the surfaces that have Z symmetry. Holding down the key, click on the other surface that has Z symmetry. Select the "Setup" tab. Click on the "General Constraint" button in the "Constraints" panel.

"Z Symmetry"

Press the "Z Symmetry" button.

"OK"


Mouse Mouse

Figure 6.5: Symmetry Constraints

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Chapter 6: Introduction to Contact Assigning the Parameters Once the model has been constructed and the loads and constraints have been applied, use the FEA Editor environment to specify material properties. Mouse

Right-click on the "Element Definition" heading for Part 2.

"Edit Element Definition…"

Select the "Edit Element Definition…" command.

Mouse

Click on the "Thermal" tab.

153.85

Type "153.85" in the "Stress free reference temperature" field.

"OK"


Mouse

Click on the "Material" heading for Part 1.

Mouse

Holding down the key, click on the "Material" heading for Part 2 in the tree view.

Mouse


"Edit Material…"

Select the "Edit Material…" command. The "Element Material Selection" dialog will appear.

"Edit Properties"

Press the "Edit Properties" button.

30e6

Type "30e6" in the "Modulus of Elasticity" field.

0.3

Type "0.3" in the "Poisson's Ratio" field.

"Setup: Model Setup: Parameters"

Type "6.5e-6" in the "Thermal Coefficient of Expansion" field. Press the "OK" button to exit the "Element Material Specification" dialog. Press the "OK" button to accept the information entered into the "Element Material Selection" dialog for Parts 1 and 2. Select the "Setup" tab. Click on the "Parameters" button in the "Model Setup" panel.

1

Type "1" in the first row of the "Thermal" column.

6.5e-6 "OK" "OK"

"OK" "Analysis: Analysis: Check Model" "Tools: Environments: FEA Editor"

Press the "OK" button to accept the information entered in the "Analysis Parameters" dialog. Select the "Analysis" tab. Click on the "Check Model" button in the "Analysis" panel. Select the "Tools" tab. Press the "FEA Editor" button in the "Environments" panel.


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Chapter 6: Introduction to Contact Analyzing the Model "Analysis: Analysis: Run Simulation"

Select the "Analysis" tab. Click on the "Run Simulation" button in the "Analysis" panel.

Reviewing the Results "View: Appearance: Visual Style

Select the "View" tab. Click on the options button to the bottom of "Visual Style" button in the "Appearance" panel. Select "Shaded with Mesh" from the pull-out menu.

If you look closely at the disk/hub interface, you can see that the nodes on each part move together due to the bonded contact. You may want to increase the displaced model "Scale Factor" to exaggerate the deformation more ("Results Options: Displaced Model Options"). The disk is trying to shrink in both diameter and thickness. However, because of the bonded contact, the thickness of the disk at its ID can only shrink as much as the hub compresses axially. We will compare this behavior, and the resultant stresses, to a second version of the model. This time, frictional surface contact will be used between the parts. A second design scenario will be created so that the results of each version may both be retained. * * *

Case 2 "Tools: Environments: FEA Editor" Mouse "Copy"

120

Select the "Tools" tab. Press the "FEA Editor" button in the "Environments" panel. Right-click on the "Design Scenario 1" heading at the top of the tree view and select the "Copy" command. Design Scenario 2 will be created and will be the active scenario.

Mouse

Right-click on the "Contact (Default: Bonded)" heading.

"Surface Contact"

Select the "Surface Contact" command.

Mouse

Right-click on the "Contact (Default: Surface)" heading.

"Settings …"

Select the "Settings…" command. The "Contact Options" dialog will appear.

Mouse

Activate the "Include Friction" checkbox.

0.3

Type "0.3" in the "Static Friction Coefficient" field.

"OK"



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Chapter 6: Introduction to Contact Analyzing the Model "Analysis: Analysis: Run Simulation"


If you once again closely examine the disk/hub interface with the mesh displayed, this time you'll see that the nodes of the disk shifted axially along the length of the hub. The thickness was able to decrease due to thermal shrinkage despite the friction in the interface. Animating the on-screen image will make the effect more apparent. You should also see a significant reduction in the maximum von Mises stress value (approximately 33,000 psi versus 43,300 psi). Figure 6.6 (next page) shows a comparison of the results for the bonded and frictional surface contact versions of the model.

Result Options The total contact force can be determined for each contact pair in a model in the Results environment. Right-click on the heading in the tree view for the contact pair and select the "Contact Force" command. A "Contact Force" dialog will appear with the total contact force for that pair. The contact distribution can be seen by using the "Results: Element Forces and Moments: 1) Axial Force" command. This will display the contact force in the individual contact elements. An archive containing both design scenarios, with results, is available in the "Chapter 6 Example Models\Results Archive" folder in the class directory or in the copy of the solutions folders on your computer.


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Figure 6.6: Comparison of Stress and Deformed Shape (Front View)

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Exercise E Yoke Model with Contact Brick Elements Concepts that will be Illustrated: •

Applying surface contact between parts in an assembly.

Objective:

Analyze the yoke model again, but include the pins in the CAD solid model. The loads and constraints will be applied to the pins and contact will be defined between the pins and the yoke.

Geometry:

Use the file Exercise E.step in the "Exercise E\Input File" folder of the class directory or in the copy of the solutions folders on your computer. Mesh the model at 90% of the default mesh size.

Loading:

Apply a total of 800 lbf in traction to the end faces of the pin in the large hole.

Constraints:

Fully constrain the end faces of the pin in the small hole. Constrain the Z translation of the shaft in the large hole.

Element:

Brick

Material:

Steel (ASTM-A36) for all parts

Questions:

Are the specified constraints adequate to ensure a statically stable model and to prevent unwanted motion of the parts? If not, add the necessary constraints. As always, constrain the model in a way that will provide the necessary stability but will not impede the expected natural deformation of the parts. How do the results compare to the previous results? How do the runtimes compare?


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Chapter 6: Introduction to Contact Results: Part Description


Yoke (Part 1)

3,429

Small Pin (Part 2)

3,591

Large Pin (Part 3)

425


Full Assembly

0.00047

A completed archive with results (Exercise E.ach) is located in the "Exercise E\Results Archive" folder in the class directory or in the copy of the solutions folders on your computer.

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Chapter

7

Introduction to Linear Dynamics Chapter Objectives • • • • • •

Learn about the analysis parameters setup for a modal analysis Learn about lumped masses Learn about the analysis parameters setup for a modal analysis with load stiffening Learn about the analysis parameters setup for a critical buckling analysis Perform a natural frequency (modal) analysis Perform a critical buckling analysis

Modal Analysis A modal analysis is performed using the "Natural Frequency (Modal)" analysis option. Most of the element types available for a static stress analysis are also available for a modal analysis. The one exception is the gap element. Also, surface and edge contact will not be considered during a modal analysis. The only factors that affect a modal analysis are the geometry, constraints, and mass. Therefore, no loads will be used in the analysis. No constraints are required for a modal analysis to run successfully. However, if a part will be constrained during its use, apply the proper constraints to the FEA model. This is important to receive accurate modal results because the constraints can have a very significant effect on the natural frequencies. The majority of the setup for a modal analysis is done in the "Analysis Parameters" dialog. This dialog is shown in Figure 7.1.

Figure 7.1: Natural Frequency (Modal) Analysis Parameters Dialog


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Chapter 7: Introduction to Linear Dynamics The "General" tab will be used to specify all of the necessary information. The most important piece of information that must be specified is the "Number of frequencies/modes to calculate". This control can be used in conjunction with the "Lower cut-off frequency" and "Upper cut-off frequency" fields. If a value is entered in the "Lower cut-off frequency" field, the processor will find the first natural frequency above the specified frequency. The subsequent natural frequencies will be calculated until the number specified in the "Number of frequencies/modes to calculate" field is reached. If a value is entered in the "Upper cut-off frequency" field, the processor will stop after it has calculated a frequency above this value regardless of the value in the "Number of frequencies/modes to calculate" field. If a model is not fully constrained, activate the "Rigid body modes are expected" checkbox. This will notify the processor that rigid or free body motion may be present in the model. Examples of a fully or partially unconstrained model would be a floating buoy or a communication satellite in orbit. Typically, the first several vibration modes of a model that is not fully constrained will be true rigid body modes and the results will not be meaningful. In other words, there will be motion (translation and/or rotation) of the entire body but no distortion of the body's shape. To see valid vibration modes you may have to ignore the first several mode shapes, reflecting rigid body modes. Therefore, computation of additional modes should be requested. Alternately, a lower cut-off frequency may be specified in the analysis parameters to filter out the typically very low frequency rigid body modes.

Lumped Masses One load that can be applied to models in a modal analysis is a nodal lumped mass. This is a concentrated mass or weight that will be applied to a node in the model. The mass can be defined to be effective for specific translational and/or rotational DOFs. To apply translational mass effects, only the mass/weight needs to be defined. It can act uniformly in all directions or have different effective magnitudes in the three global directions. For example, a mass mounted in a pendulum fashion would exhibit little mass effect in the direction tangent to the bottom of its arc of travel. You could move the object it's attached to easily in this direction because the mass is free to pivot on its mountings. Moving the structure side-to-side would require more effort. For most situations, a mass that is uniform in all three translational directions will be appropriate. For rotational DOFs, a mass moment of inertia must be entered for all applicable axes of rotation. This is essentially, the rotational inertia of the object for rotation about the three global axis directions. The values for X, Y, and Z rotation will differ for everything except a spherical object due to the differing radii of gyration, though the mass is constant. The lumped masses may be defined in units of either mass or force. To apply a nodal lumped mass, select the node, or nodes, which you want to, apply it to and right-click in the display area. Select the "Add: Nodal Lumped Mass…" command. The dialog shown in Figure 7.2 will appear.

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Chapter 7: Introduction to Linear Dynamics

Figure 7.2: Nodal Lumped Mass Object Dialog In the "Mass Input" section, specify if the nodal lumped mass will be defined as a mass ("Units of mass") or a weight ("Units of force"). If the nodal lumped mass is to be applied equally against all of the translational DOFs of that node, activate the "Uniform" checkbox and specify the magnitude in the "X Direction" field in the "Mass/Weight" section. If the nodal lumped mass is to be applied against only one or two of the translations DOFs of that node, or if it will be applied to all of the translational DOFs non-uniformly, deactivate the "Uniform" checkbox and specify the appropriate magnitudes in the "X Direction", "Y Direction" and "Z Direction" fields. If the nodal lumped mass is to be applied as a mass moment of inertia against any of the rotational DOFs, specify the appropriate magnitudes in the "X Direction", "Y Direction" and "Z Direction" fields in the "Mass Moment of Inertia" section.

Load Stiffening As explained previously, standard modal analysis does not account for the loads on the model. In some situations, however, the loads will affect the natural frequencies. An example would be a guitar string. Applying tension will change the frequency. Loads that produce membrane stresses will affect the natural frequency of the object. Tensile membrane stresses will increase the natural frequencies and compressive membrane stresses will lower them. Pure bending stresses will not affect the natural frequency. To account for the loads in a modal analysis, you must select the "Natural Frequency (Modal) with Load Stiffening" analysis type. Apply the loads and constraints that the subject part or assembly would experience during its use.


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Chapter 7: Introduction to Linear Dynamics All of the element types available for a regular modal analysis are available for this analysis type with the exception of truss and membrane elements. The "Analysis Parameters" dialog for a load stiffening analysis is shown in Figure 7.3.

Figure 7.3: Natural Frequency (Modal) with Load Stiffening Analysis Parameters Dialog As can be seen, the "Analysis Parameters" dialog is basically a combination of the dialogs for modal and static stress analyses. Load multipliers, gravity loads, temperature loads and centrifugal loads can be applied to a model in the same manner as a static stress analysis.

Example of Natural Frequency (Modal) Analysis This example is an introduction to Autodesk® Simulation's natural frequency (modal) analysis capabilities. The example will give step-by-step instructions to create a mesh and analyze a three-dimensional (3-D) model of a tuning fork. There are three sections: Setting up the model – Open the model in the user interface and create a mesh on the model. Then, use the FEA Editor environment to add the necessary loads and define the model parameters. Visually check the model for errors with the Results environment. Analyzing the model – Analyze the model using the natural frequency (modal) processor. View the processor log file. Reviewing the results – View the frequencies and mode shapes graphically using the Results environment. Use the 3-D solid model, TuningFork.step, located in the class directory (or in the "Chapter 7 Example Model\Input File" folder copied to your computer) to create a simple model of the tuning fork (see Figure 7.4). The cylindrical surfaces of the tuning fork will be completely 128


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Chapter 7: Introduction to Linear Dynamics constrained. The material for this part is steel (AISI 4130) with a mass density of 0.000732 lbf*s2/in/in3 and a modulus of elasticity of 30e6 lb/in2. Analyze the model to determine the first five natural frequencies and their mode shapes. We will use 50% of the default mesh size.

Figure 7.4: Tuning Fork Model

Meshing the Model "Start: All Programs: Autodesk: Autodesk Algor Simulation 2012: Autodesk Simulation 2012" "Getting Started: Launch: Open" "STEP (*.stp, *.ste, *.step)" "TurningFork.step" "Open" "Use STEP file units" "OK" Mouse "Linear: Natural Frequency (Modal)" "OK"

Press the Windows "Start" button and access the "All Programs" pull-out menu. Select the "Autodesk" folder and then the "Autodesk Algor Simulation 2012" pull-out menu. Choose the "Autodesk Simulation 2012 software" command. Click on the "Open" button in the Launch panel. Alternatively you select “Open” from the quick access toolbar or Application Menu. Select the "STEP (*.stp, *.ste, *.step)" option in the CAD Files section of the "Files of type:" drop-down box. Navigate to the location of the "TurningFork.step" file on your computer and highlight it. Press the "Open" button. Choose the option to "Use STEP file units" if it is not already selected and click the "OK" button. The original STEP file length unit is inches. If the desired analysis type is not already set, press the menu button to the right of the analysis type field. Select the "Linear" pull-out menu, and choose the " Linear: Natural Frequency (Modal)"" option. Press the "OK" button.

The model will now appear in the FEA Editor environment.


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Chapter 7: Introduction to Linear Dynamics "Mesh: Mesh: 3D Mesh Settings" Mouse "Mesh model" Mouse

Select the "Mesh" tab. Click on the "3D Mesh Settings" button in the "Mesh" panel. Move the slider towards the right to change the mesh size to "50%." Press the "Mesh model" button in the "Model Mesh Settings" dialog. Use the mouse, to rotate, pan and zoom, to inspect the mesh

Adding Constraints "View: Navigate: TopView"

Select the "View" tab. Click on the options button to the bottom of "Orientation" button in the "Navigate" panel. Select "Top View" from the pull-out menu.






Click on one of the cylindrical surfaces at the end of the tuning fork. Holding down the key, click on the other cylindrical surface at the end of the tuning fork. Select the "Setup" tab. Click on the "General Constraint" button in the "Constraints" panel.

"Fixed"

Press the "Fixed" button.

"OK"


Mouse Mouse

Defining the Materials Mouse

Right-click on the "Material" heading for Part 1 in the tree view.

"Modify Material…"


"Steel (AISI 4130)"

Expand the Steel folder and then expand the AISI folder. Select "Steel (AISI 4130)" within the Autodesk Simulation Material Library.

"OK"


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"View: Orientation: Isometric View"

Select the "View" tab. Click on the options button to the bottom of "Orientation" button in the "Navigate" panel. Select "Isometric View" from the pull-out menu.




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Reviewing the Results We want to view the mode shapes and frequencies for the part. "Results Contours: Load Case Options: Next" "Results Contours: Load Case Options: Set" 2

Click on the "Next" button in the "Load Case Options" panel. Select the options button below the "Next" button. Click on the "Set" button. Type a "2" in the "Enter load case" field and press to specify that you would like to review load case number 2. The model should appear as shown in Figure 7.5.

NOTE: If your displaced shape for mode 2 is not as shown in Figure 7.5, it is likely that your computer has calculated the same vibration mode but is showing it 180 º out-of-phases from the point in the vibration cycle captured in the image below. Click the "Start Animation" button in the "Captures" panel and you should see the structure go through the pictured shape during the vibration cycle. Click the "Stop Animation" button in the "Captures" panel when you are finished examining the vibration mode.

Figure 7.5: Mode Shape 2 of the Tuning Fork Results:

Mode

Frequency (Hz)

1 2 3 4 5

249.78 312.657 424.896 891.359 931.95

Note that the natural frequency results will be sensitive to mesh density and to mesh quality. This is especially true for models comprised of brick elements and having thin cross-sections that undergo bending during vibration. As in stress analysis, a minimum of three or four brick elements though the thickness is recommended to accurately capture flexural effects. Alternately, two elements may be sufficient if the optional midside nodes are enabled. Autodesk® Simulation Mechanical 2012 – Part 1 – Seminar Notes

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An archive, with results, is available in the "Chapter 7 Example Model\Results Archive" folder in the class directory or in the copy of the solutions folders on your computer.

Critical Buckling Analysis In the normal use of most products, buckling can be catastrophic if it occurs. The failure is not one of stress, but of geometric instability. Once the geometry of the part starts to deform, it can no longer support even a fraction of the initially applied force. The worst part about buckling for engineers is that buckling usually occurs at relatively low stress values compared to what the material can withstand. So a separate check must be performed to see if a product or section is acceptable with respect to buckling. Buckling almost always involves compression. In civil engineering, buckling is to be avoided when designing support columns, load bearing walls and sections of bridges which may flex under load. For example, an I-beam may be perfectly "safe" when considering only the maximum stress, but fail disastrously if just one local spot of a flange should buckle. In engineering, designs involving thin parts in flexible structures, like airplanes and automobiles, are susceptible to buckling. Even if the stresses are very low, buckling of local areas can cause the whole structure to collapse by a rapid progression of propagated buckling. Sometimes, buckling is used as a characteristic part of a design. You may have seen or used the type of oil can where you pump the oil out by pressing on the bottom of the oil can. If you press a little, nothing happens. If you press harder, the bottom suddenly "snaps through", pumping out a small amount of oil. Then it snaps back when you release your thumb. This phenomena is known as "snap-through" or "oil-can" buckling. For situations involving linear materials, such as steel or glass, and small deflections or deformations prior to buckling; a straightforward solution is available. This is the solution used in the Autodesk Simulation software. It is important to be aware of the fact that three types of buckling are possible—fully elastic, partially plastic, and fully plastic. The linear critical buckling solver determines the buckling load based on fully elastic buckling assumptions. In other words, it is assumed that all materials are below yield regardless of the magnitude of the buckling load. If, in reality, the stresses have to exceed yield prior to the structure becoming unstable, then the buckling phenomena is nonlinear. Short structures with large cross-sections may only fail by crushing, which is a fully plastic failure mode. For nonlinear situations, buckling can be determined as part of a nonlinear stress analysis using the Mechanical Event Simulation analysis type. A high critical buckling safety factor does not necessarily mean that a structure is safe. It only means that it is not susceptible to elastic buckling. A separate, traditional stress analysis is also necessary to see if objectionable stresses are produced by operating loads. It is possible for a very highly stressed structure to pass linear buckling criteria just like it's possible for a lowly stressed structure to fail buckling criteria.

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Setting Up a Critical Buckling Analysis To set up a buckling analysis, select the "Critical Buckling Load" analysis type. After you apply the loads and constraints and define the element and material properties, right-click on the "Analysis Parameters" heading and select the "Edit Analysis Parameters…" command. The dialog shown in Figure 7.6 will appear.

Figure 7.6: Critical Buckling Load Analysis Parameters Dialog The setup for a buckling analysis is similar to that for a static stress analysis. Assign the multipliers for the pressure, acceleration, displacement and temperature effects in the "Multipliers" tab and set up the gravity in the "Gravity" tab. In the "Sparse Solver" section of the "Solution" tab, you can specify how many buckling modes that you want to calculate. Once a buckling analysis is completed, the "Results Options: Show Displaced Model" command can be used to view the buckled shapes of the model. How the buckling load is determined is explained in the "Result Options" section (next page).


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Result Options Modal: When a natural frequency (modal) analysis is performed and the model is displayed in the Results environment, each mode will be presented as a separate load case. The frequency value for each mode will be displayed as an annotation in the lower left corner of the display area. The displaced shape for each mode can be shown using the "Results Options: Show Displaced " command, which is enabled by default. Note that displacement results are an available result for modal analyses (with or without load stiffening). However, these are not scaled to any actual load or structural excitation and are therefore only meaningful as a means of demonstrating the mode shapes. A restart analysis, such as random vibration or transient stress, is needed in order to obtain meaningful stress and displacement results. Buckling: For a critical buckling load analysis, the result will be presented as a buckling multiplier in the annotation at the lower left corner of the display area. There will be a different multiplier provided for each of the calculated buckling modes. Note that the buckling mode shapes are not necessarily the same as the natural frequency mode shapes. In fact, they are typically different except for very simple columns. The buckling load multiplier is the factor by which the applied loads would need to be multiplied in order to produce buckling. For example, if a load of 500 lbf had been applied to a model and the buckling multiplier is 1.5, that means that buckling will occur at 750 lbf (1.5 * 500). A multiplier that is less than 1.0 indicates that buckling occurs at less than the applied load. Finally, a negative buckling multiplier indicates that buckling occurs for a load acting in the opposite direction. For example, a column in tension won't buckle but one in compression will.

Other Linear Dynamics Analyses In addition to the three analyses discussed previously in this chapter, there are a number of other linear dynamics analysis types that may be performed using the Autodesk® Simulation package. Most of these are known as restart analyses because they require a modal or modal with load stiffening analysis to be completed prior to performing the subsequent analysis type. The modal results are then scaled to obtain actual stresses and deflections produced by a known structural excitation. The exception is transient stress (direct integration), which, like the critical buckling load analysis, does not require a prior modal analysis of the structure. Here is a list of the other linear dynamics analyses: •

Frequency Response

•

Random Vibration

•

Response Spectrum

•

Transient Stress (Direct Integration)

•

Transient Stress (Modal Superposition)

•

Dynamic Design Analysis Method (DDAM) – Autodesk® Simulation Professional package is required for this analysis type.

There is a brief summary of each analysis type within "Appendix B – Analysis Types in Autodesk® Simulation."

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Exercise F Concrete Platform Brick Elements Concepts that will be Illustrated: • •

Setting up, running, and reviewing a modal analysis Setting up, running, and reviewing a critical buckling analysis

Objective:

Determine the first six (6) natural frequencies and their mode shapes for the concrete platform. Then, in a second design scenario, perform a critical buckling analysis. Solve for the first five (5) critical buckling modes (default setting).

Geometry:

Use the file Exercise F.SAT in the "Exercise F\Input File" folder of the class directory or in the copy of the solutions folders on your computer. Specify an absolute mesh size of 3 inches.

Constraints:

Fully fixed the bottom surface at each of the four legs.

Loading (for Critical Buckling Analysis): Standard gravity (-Z direction) 100,000 lbf normal force acting on top surface Element:

Brick

Material:

Concrete (High Strength)


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Chapter 7: Introduction to Linear Dynamics Modal Results: Mode Number

Frequency (Hz)

1

10.8

2

12.0

3

17.6

4

20.8

5

36.7

6

42.8

Mode Number

Buckling Load Multiplier

1

170

2

200

3

229

4

236

5

293

Buckling Results:

Note:

The buckling safety factor is very high, indicating that this structure is clearly not susceptible to buckling due to geometric instability. Nonetheless, a linear static stress analysis would show that the applied load already produces tensile stresses exceeding the strength of non-reinforced concrete, which is typically less than 500 psi. So the structure would collapse due to material failure. This is stated to emphasize the importance of checking a design with regard to both static stress and buckling criteria.

A completed archive with results (Exercise F.ach) is located in the "Exercise F\Results Archive" folder in the class directory or in the copy of the solutions folders on your computer. The results archive includes a third design scenario (static stress analysis) showing tensile stresses in excess of the strength of nonreinforced concrete.

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Chapter

8

Steady-State Heat Transfer Chapter Objectives • • • • • •

Perform an example of a steady-state heat transfer analysis Overview of thermal contact settings Overview of element options for thermal analyses Overview of loading options (part, surface, and nodal loads) Overview of results options Complete a steady-state heat transfer exercise CAD model importing, meshing, and the application of loads and constraints in heat transfer analysis is similar to the respective processes associated with linear static stress analysis, covered previously in this manual. We will begin this section with a walk-through of a simple steady-state heat transfer analysis, after which topics specific to thermal analysis will be discussed in greater detail.

3-D Radiator Example This example is an introduction to Autodesk® Simulation's steady-state heat transfer analysis capabilities. The example will give step-by-step instructions to create a mesh and analyze a three-dimensional (3-D) model of a radiator. There are three sections: Setting up the model – Open the model in the FEA Editor environment and create a mesh on the model. Add the necessary loads and define the model parameters. Visually check the model for errors with the Results environment. Analyzing the model – Analyze the model using the steady-state heat transfer processor. View the processor log file. Reviewing the results – View the temperatures and heat fluxes graphically using the Results environment. Use the archive file, Radiator.ach, located in the "Chapter 8 Example Model\Input File" folder to create a simple model of the radiator (see Figure 8.1). This file may be copied to your computer from the class directory or the Solutions CD. The fluid at the left end of the model is 120°F. The tube and the ends of the radiator are insulated. The fins are convecting to an ambient temperature of 70°F with a coefficient of 0.04

in ⋅ lbs . All of the in ⋅ sec ⋅ °F 2

solid parts are made of Steel (ASTM-A36). The thermal conductivity of the fluid is 600

in ⋅ lbs . Analyze the model to determine the temperature profile of the fluid. sec ⋅ in ⋅ °F


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Chapter 8: Steady-State Heat Transfer

Figure 8.1: Radiator Model

Meshing the Model "Start: All Programs: Autodesk: Autodesk Algor Simulation 2012: Autodesk Simulation 2012" "Getting Started: Launch: Open" "Autodesk Simulation Archive (*.ach)" "Radiator.ach" "OK"

Press the Windows "Start" button and access the "All Programs" pull-out menu. Select the "Autodesk" folder and then the "Autodesk Algor Simulation 2012" pull-out menu. Choose the "Autodesk Simulation 2012 software" command. Click on the "Open" button in the Launch panel. Alternatively you select “Open” from the quick access toolbar or Application Menu. Select the "Autodesk Simulation Archive (*.ach)" option in the "Files of type:" drop-down box. Select the file Radiator.ach in the "Chapter 8 Example Model\Input File" directory. Select the location on your hard drive where you want the model to be extracted and press the "OK" button.

The model will now appear in the FEA Editor environment. The analysis type will have already been set as "Steady-State Heat Transfer" and the units system set to "English (in.)". "Mesh: Mesh: 3D Mesh Settings" "Mesh model"

"View: Navigate: Orbit"

138

Select the "Mesh" tab. Click on the "3D Mesh Settings" button in the "Mesh" panel. Press the "Mesh model" button to create a mesh using the default options. Select the "View" tab. Click on the "Orbit" button in the "Navigate" panel. Now inspect the mesh, rotating the model around by pressing the left mouse button and dragging the cursor across the screen. Press the key to cancel the command.


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Setting up the Model Since you have created a solid mesh, the "Element Type" heading in the tree view has already set to "Brick" and the default "Element Definition" parameters have been applied. Adding Loads

"View: Navigate: Back View"

Select the "View" tab. Click on the options button to the bottom of "Orientation" button in the "Navigate" panel. Select "Back View" from the pull-out menu.

Mouse

Click on the heading for Part 1 in the tree view.

Mouse

Holding down the key, click on the heading for Part 2 in the tree view.

Mouse


"Visibility"

Select "Visibility" to hide the parts.

"Selection: Shape: Rectangle"

Select the "Selection" tab. Click on the "Rectangle" button in the "Shape" panel.



Mouse

Mouse

Click and drag a selection rectangle that fully encloses all of the fins but does not enclose the pipe fittings. Holding down the key, click and drag a selection rectangle that fully encloses all four holes in the fins but does NOT fully enclose any of the remaining fin surfaces. This will remove the inner surfaces of each hole from the selection set. These surfaces will not have the thermal load applied.

"Setup: Thermal Loads: Convection"

Select the "Setup" tab. Click on the "Convection” button in the "Thermal Loads" panel.

0.04

Type "0.04" in the "Temperature Independent Convection Coefficient" field.

70

Type "70" in the "Temperature" field.

"OK"


Mouse "Visibility of all Parts"

Right-click on the "Parts" heading at the top of the parts list in the tree view. Select "Visibility of all Parts ". You may need to select it again to see all parts.

Mouse

Right-click on the heading for Part 17 in the tree view.

"Visibility"

Select "Visibility" to hide the parts.

"View: Navigate: Top View" Mouse

Select the "View" tab. Click on the options button to the bottom of "Orientation" button in the "Navigate" panel. Select "Top View" from the pull-out menu. Draw a box enclosing the far left edge of the model (-X end, where the fitting has been hidden).

"Setup: Thermal Loads: Controlled Temperature"

Select the "Setup" tab. Click on the "Controlled Temperature” button in the "Thermal Loads" panel.

120


"OK"



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Chapter 8: Steady-State Heat Transfer Mouse


" Visibility "

Select the "Visibility " command.

Defining the Materials Mouse "M" Mouse Mouse Mouse "Edit: Material…" "Steel (ASTM-A36)"

Click on the heading for Part 1 in the tree view. Holding the and keys, press the keyboard’s "M" key. This will collapse the parts list in the tree view. Holding down the key, click on the heading for Part 18 in the tree view. All parts should now be selected. Holding down the key, click on the heading for Part 2 in the tree view to deselect it. Right-click on one of the selected headings. Select the "Edit" pull-out menu and select the "Material…" command. Expand the Steel folder and then expand the ASTM folder. Select "Steel (ASTM-A36)" within the Autodesk Simulation Material Library.

"OK"


Mouse

Right-click on the heading for Part 2 tree view.

"Edit: Material…"

Select the "Edit" pull-out menu and select the "Material…" command.

"Edit Properties"


600

Type "600" in the "Thermal conductivity" field.

"OK"


"OK"



Select the "Analysis" tab. Click on the "Check Model" button in the "Analysis" panel. Click on the "Details >>" button to see the solid meshing progress log. This process will take some time to complete for all eighteen parts. The dialog will automatically close after solid meshing has been completed. Select the "Tools" tab. Press the "FEA Editor" button in the "Environments" panel.

"Details >> " "Tools: Environments: FEA Editor"

Analyzing the Model

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Reviewing the Results We want to view the temperature profile of the fluid part. In order to do this, we should hide the other parts. "Results Options: View: Load and Constraint"

Click on the "Load and Constraint" button in the "View" panel with the "Results Options" tab to hide the load and constraint symbols.

Mouse


Mouse Mouse

Holding down the key, click on the heading for Part 18 in the tree view. Holding down the key, click on the heading for Part 2 in the tree view to deselect it.

Mouse


"Visibility"

Select the "Visibility" command. The temperature profile for the fluid should appear as shown in Figure 8.2.

Figure 8.2: Temperature Profile of the Fluid A completed archive with results (Radiator.ach) is located in the "Chapter 8 Example Model\Results Archive" folder in the class directory or in the copy of the solutions folders on your computer.


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Meshing Options All of the basic meshing options in the FEA Editor environment are available for a steady-state heat transfer analysis. For more information on these options, refer to Chapter 5, Meshing.

Thermal Contact One meshing option that is unique to thermal analysis of assembly models is thermal contact. This can be applied in the FEA Editor environment. Thermal contact is used to represent imperfect contact between two parts. You will be able to define a resistance value for each contact pair in the assembly. This feature can also be used to model the effects of small parts without physically including them in the model. For example, a thin epoxy film can be represented by thermal contact between the parts that it connects. If this part were to be included in the analysis, it would result in a large number of elements because of its size relative to the rest of the model and the small elements that would be needed to mesh it. There are four types of thermal contact available. These can be set up for individual pairs of parts or surfaces by selecting the appropriate headings in the tree view or display area and right-clicking. Select the "Contact" pull-out menu and select the appropriate contact type as described below. If you want certain contact parameters to be applied to every contact pair in the model, right-click on the "Contact" heading in the tree view and select the appropriate command for the default contact type desired. Bonded If the "Bonded" command is selected, the nodes on the surfaces in this contact pair will be matched. Heat will flow freely from one part to the other through the bonded surfaces and it will flow without resistance. Welded If the "Welded" command is selected, the nodes along the edges of the contact surfaces will be matched. These nodes will act the same as if the "Bonded" command were selected. The nodes along the interior of these surfaces will not be matched together. No heat will be transferred between these nodes. Free/No Contact If the "Free" command is selected, the nodes on the surfaces in this contact pair will not be matched. No heat will be transferred between these nodes. Surface Contact If the "Surface Contact" command is selected, the nodes on the surfaces in this contact pair will be matched. The difference between this command and the "Bonded" command is that you will be able to define a thermal contact resistance between the surfaces. This can be done by right-clicking on the heading for the contact pair and selecting the "Settings…" command. You will be able to specify the total combined resistance in all of the surfaces involved in the selected contact pairs ("Total Resistance") or the amount of resistance per unit area ("Distributed Resistance") in the "Type:" drop-down box. Enter the appropriate value in the "Value:" field.

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Chapter 8: Steady-State Heat Transfer NOTE: If thermal results will subsequently be used as a load in a structural analysis in which surface contact is to be used, then this should be anticipated prior to running the heat transfer analysis. Thermal contact should be specified wherever surface contact is to be used later, even if no thermal resistance is to be imposed. This will ensure that the node numbering will be consistent between the two models or two design scenarios. Where two parts having surface or thermal contact meet, there will be sets of two nodes at each point where the meshes are matched. These will have the same coordinates and will be connected by zero-length gap elements (for structural analysis) or thermal contact elements (for heat transfer analysis). Otherwise, with bonded contact, the nodes for each part will be merged and only one node will exist at each point where the meshes are matched.

Element Options There are five types of elements available for a steady-state heat transfer analysis. All of the element types share the same basic loading options that will be discussed later in this chapter.

Rod Elements Rod elements are line elements that consist of 2 nodes. These elements can be created in the FEA Editor environment. Rod elements are used to represent parts that have a constant cross-section that is small relative to the length. These elements can be used to represent wires. Since the cross-section is small, it is assumed that the entire cross-section at a specific point along the length is at a uniform temperature. The cross-sectional area and perimeter will be required. The perimeter will be used to calculate the surface area for convection and radiation to the environment. Rod elements cannot be used in an enclosure for body-to-body radiation. Rod elements have two material models available. The first material model is the "Isotropic" material model. This material model is used for a material that has material properties that are constant with regards to the temperature. The second material model is the "Temperature Dependent Isotropic" material model. This material model is used for a material that has different material properties at different temperatures. The material properties for each temperature will be entered into a spreadsheet. The temperatures that the model will experience must be between the low and high values of the spreadsheet.

2-D Elements 2-D elements are planar elements that are drawn in the Y-Z plane. Each element consists of an area enclosed by three or four lines. These elements are generally created by building and meshing Y-Z sketches in the FEA Editor environment. There are two geometry types available for 2-D elements—planar and axisymmetric. The planar geometry is used to model parts of a constant thickness that can be represented by a cross-section. The axisymmetric geometry is used to model parts that have a continuous cross-section that is revolved about a center axis. In Autodesk® Simulation, this axis of revolution must be the global Z axis and the cross-section must be drawn in the +Y half of the Y-Z plane. 2-D elements have four available material models. The first is "Isotropic." This model is used for materials that have identical thermal properties in all directions and at all temperatures. The second material model is "Orthotropic." This model is used for materials that have different thermal properties in different directions but the properties are assumed not to vary as the temperature changes. The third and fourth material models are Autodesk® Simulation Mechanical 2012 – Part 1 – Seminar Notes

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Chapter 8: Steady-State Heat Transfer "Temperature Dependent Isotropic" and "Temperature Dependent Orthotropic." As the names imply, these are temperature dependent variants of the Isotropic and Orthotropic material models. Either one allows you to model materials that have different thermal conductivity or specific heat values at different temperatures. The material properties for each temperature will be entered into a spreadsheet within the "Element Material Specification" dialog. The temperatures that the FEA model will experience during the analysis must fall between the low and high values of the spreadsheet. For an orthotropic material model, you will need to define two orthogonal material axes. The "Principal Axis Transformation Angle" field on the "General" tab of the "Element Definition" dialog is used to accomplish this. The value in this field is measured counterclockwise from the positive Y axis and defines the direction of the principal material axis (also referred to as the "n" axis or the "r" axis). The "s" axis will be based on the same transformation angle but measured counterclockwise from the positive Z axis. The third material axis will always be the X axis for 2-D elements. Please note that the letters "n" and "r" are used interchangeably when referring to the first material axis. For example, the conductivity in this direction may be referred to as "Thermal conductivity, Local Axis n" or as "Kr."

Plate Elements Plate elements are 3-D area elements that consist of an area enclosed by three or four lines. These elements can be created from CAD solid parts or assemblies by using the "Midplane" mesh setting. They can also be manually created in the FEA Editor environment. Lastly, plate elements can be generated from CAD surface models (i.e. those models consisting of zero-thickness surface geometry, rather than solids). To do this, choose the "Plate/Shell" mesh option. These elements are used to represent parts that are thin relative to the other dimensions. Since these parts are thin, it is assumed that both the top and bottom of the plates are the same temperature. No temperature distribution will exist through the thickness. In the "General Controls and Parameters" section of the "General" tab of the "Element Definition" dialog, you will be able to define a point in space (the "Element Normal" point) that will be used to define the top of the plate elements in this part. The top of the plate will face away from this point. The orientation of the plate is only used when considering the side of a plate involved in an enclosure for body-to-body radiation. As is true for the 2-D elements discussed previously, plate elements have four available material models. The first is "Isotropic," used for materials that have identical thermal properties in all directions and at all temperatures. The second material model is "Orthotropic," used when materials have different thermal properties in different directions but the properties are assumed not to vary with the temperature. The third and fourth material models are "Temperature Dependent Isotropic" and "Temperature Dependent Orthotropic." As the names imply, these are temperature dependent variants of the Isotropic and Orthotropic material models. Either one allows you to model materials that have different thermal conductivity or specific heat values at different temperatures. The material properties for each temperature will be entered into a spreadsheet within the "Element Material Specification" dialog. The temperatures that the FEA model will experience during the analysis must fall between the low and high values of the spreadsheet. For an orthotropic material model, you will need to define the orientation of the three orthogonal material axes, "n," "s," and "t" (or "r," "s," and "t"). This is done in the "Orientation" tab of the "Element Definition" dialog, which is shown in Figure 8.3. Please note that the letters "n" and "r" are used interchangeably when referring to the first material axis. For example, the conductivity in this direction may be referred to as "Thermal conductivity, Local Axis n" or as "Kr." 144


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Figure 8.3: Orientation Tab of the Element Definition – Thermal Plate Dialog There are four options available for defining the n, s and t axes. These are found in the "Material axis direction specified using" drop-down box. If the "Global X-direction" option is selected, the n axis will be the global X axis, the s axis will be the global Y axis and the t axis will be the global Z axis. If the "Global Y-direction" option is selected, the n axis will be the global Y axis, the s axis will be the global Z axis and the t axis will be the global X axis. If the "Global Z-direction" option is selected, the n axis will be the global Z axis, the s axis will be the global X axis and the t axis will be the global Y axis. If any of these three options are selected, the material axes can be rotated counterclockwise about the n axis by the value specified in the "Material Axis Rotation Angle" field. If the "Spatial Points" option is selected, you will need to enter the coordinates of at least three points in the "Spatial point coordinates" table. Once the spatial points are defined, you can select the appropriate spatial points in the "Index of spatial point 1", "Index of spatial point 2" and "Index of spatial point 3" drop-down boxes. The n axis will be a vector going from "Index of spatial point 1" to "Index of spatial point 2". The s axis will be normal to the n axis and will travel through "Index of spatial point 3". The t axis will be calculated as the cross product of n and s.

Brick and Tetrahedral Elements Brick and tetrahedral elements are 3-D solid elements. Tetrahedral elements consist of 4 triangular faces and 4 corner nodes. Brick elements consist of 4, 5, or 6 triangular and/or quadrilateral faces and 4, 5, 6 or 8 corner nodes. These elements can be created in the FEA Editor environment. Valid forms are the same as those used for structural analysis and are shown in Table 2.1 (page 34). As is true for the previously discussed 2-D and plate elements, both brick and tetrahedral elements have four available material models. The first is "Isotropic," used for materials that have identical thermal properties in all directions and at all temperatures. The second material model is "Orthotropic," used when materials have different thermal properties in different directions but the properties are assumed not to vary with the temperature. The third and fourth material models are "Temperature Dependent Isotropic" and "Temperature Dependent Orthotropic." As the names imply, these are temperature dependent variants of Autodesk® Simulation Mechanical 2012 – Part 1 – Seminar Notes

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Chapter 8: Steady-State Heat Transfer the Isotropic and Orthotropic material models. Either one allows you to model materials that have different thermal conductivity or specific heat values at different temperatures. The material properties for each temperature will be entered into a spreadsheet within the "Element Material Specification" dialog. The temperatures that the FEA model will experience during the analysis must fall between the low and high values of the spreadsheet. For an orthotropic material model, you will need to define the orientation of the three orthogonal material axes, "n," "s," and "t" (or "r," "s," and "t"). This is done by defining three points in the "Orientation" tab of the "Element Definition" dialog. Please note that the letters "n" and "r" are used interchangeably when referring to the first material axis. For example, the conductivity in this direction may be referred to as "Thermal conductivity, Local Axis n" or as "Kr." You must know the node numbers of three vertices in order to define the axes. To determine the node numbers, use the "Analysis: Check Model" command to load the model into the Results environment. You can determine the number of a node in two ways. The first way is to select the node on the model and use the "Inquire: Results…" command. The node number will be displayed in the resulting dialog. The second method is to zoom in on the node and select the "Display Options: Show Node Numbers" command. The latter method should be avoided when two different nodes exist at the same coordinates (such as where two parts are connected via surface contact), because the overlapping numbers will likely be misread. The "Orientation" tab of the "Element Definition" dialog is shown in Figure 8.4.

Figure 8.4: Orientation Tab of the Element Definition – Thermal Brick Dialog The three nodes numbers acquired from the Results environment will be entered into the "Orientation Node 1", "Orientation Node 2" and "Orientation Node 3" fields. The n axis will be a vector going from "Orientation Node 1" to "Orientation Node 2". The s axis will be normal to the n axis and will travel through "Orientation Node 3". The t axis will be calculated as the cross product of the n and s axes. If no nodes are specified in this tab, the n axis will be the global X-axis, the s axis will be the global Y-axis and the t axis will be the global Z-axis. This is the same as the "Global X-direction" orientation option available for plate elements.

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Loading Options Each element type in a steady-state heat transfer analysis can have eight types of loads applied. These eight loads can be split into three categories: nodal loads, surface loads and element loads. All of the loads will be set up identically for all of the element types. The one exception is that plate elements will have an additional option for surface loads. Surface loads on plate elements can be applied to one or both sides. This can be specified by checking the "Apply load to both sides" checkbox in the "Plate Options" section within the load definition dialog. Since there is no conduction through the thickness of a plate element, applying a load on both sides is the equivalent of doubling the load.

Nodal Loads Nodal Initial Temperature Initial temperatures can be applied to any node on the model. To add an initial temperature, first click on the desired selection method in the "Shape" panel and then click on "Vertices" button in the "Select" panel. Then select the "Setup" tab and click on the "Initial Temperature" button in the "Thermal Loads" panel. Now click on the vertex or vertices to which you want to apply the load too and then press "Enter". The dialog shown in Figure 8.5 will appear if 1 node was selected before accessing this command. Initial temperatures are used to define the initial temperature of a node. This node will not be held at this temperature throughout the analysis.

Figure 8.5: Nodal Temperature Object Dialog Magnitude: Enter the desired magnitude of the nodal temperature in this field. The node will begin the analysis at this temperature. Description: This field allows you to apply a name for this set of nodal temperatures. This description will be used to name each temperature in the tree view. Nodal Controlled Temperatures Nodal controlled temperatures can be applied to any node on the model. To add a controlled temperature, first click on the desired selection method in the "Shape" panel and then click on "Vertices" button in the "Select" panel. Then select the "Setup" tab and click on the "Controlled Temperature" button in the "Thermal Loads" panel. Now click on the vertex or vertices to which you want to apply the load too and then press "Enter". . The dialog shown in Figure 8.6 will appear if 1 node was selected before accessing this command.


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Chapter 8: Steady-State Heat Transfer Controlled temperature will hold the temperature of a node at a certain value. temperature will be conducted through the part.

This

For a nodal controlled temperature to be used properly during the analysis, a "Boundary temperature multiplier" must be assigned in the "Multipliers" tab of the "Analysis Parameters" dialog. The "Boundary temperature multiplier" adjusts the temperature. Setting the multiplier to 0 does not disable the nodal controlled temperature; it changes the magnitude to 0.

Figure 8.6: Nodal Applied Temperature Object Dialog Magnitude: Enter the desired magnitude of the nodal controlled temperature in this field. This temperature will be conducted through the part. Stiffness: A nodal controlled temperature is used to fix a node to a certain temperature throughout the analysis. This is done using a thermal boundary element. The heat is transferred from the new node to the node on the model through an element with a thermal stiffness specified in the "Stiffness" field. The heat flow will be equal to the product of the stiffness and the difference of the magnitude of the nodal applied temperature and the calculated temperature for that node. The temperature of the node on the model will depend on the stiffness value. A high stiffness value will cause the node on the model to be very close to the magnitude of the applied nodal temperature. A low stiffness means that the temperature of the node on the model could be significantly lower than the magnitude of the applied nodal temperature. Description: This field allows you to apply a name for this set of nodal temperatures. This description will be used to name each temperature in the tree view.

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Surface Loads Surface Initial Temperatures An initial temperature can be applied to any surface on a model. To add a initial temperature, first click on the desired selection method in the "Shape" panel and then click on "Surfaces" button in the "Select" panel. Then select the "Setup" tab and click on the "Initial Temperature" button in the "Thermal Loads" panel. Now click on the surface or surfaces to which you want to apply the load too and then press "Enter". A nodal temperature will be applied to every node on the selected surface/s. If any of the lines meeting at a certain node are in the selected surfaces, a nodal temperature will be applied to that node. Refer to the section about nodal temperatures for the definitions of the commands on this dialog. Surface Controlled Temperatures A controlled temperature can be applied to any surface on a model. To add a controlled temperature, first click on the desired selection method in the "Shape" panel and then click on "Surfaces" button in the "Select" panel. Then select the "Setup" tab and click on the "Controlled Temperature" button in the "Thermal Loads" panel. Now click on the surface or surfaces to which you want to apply the load too and then press "Enter". A nodal controlled temperature will be applied to every node on the selected surface/s. If any of the lines meeting at a certain node are in the selected surfaces, a nodal applied temperature will be applied to that node. Refer to the section about nodal applied temperatures for the definitions of the commands on this dialog. For a surface controlled temperature to be used properly during the analysis, a "Boundary temperature multiplier" must be assigned in the "Multipliers" tab of the "Analysis Parameters" dialog. The "Boundary temperature multiplier" adjusts the temperature. Setting the multiplier to 0 does not disable the surface applied temperature; it changes the magnitude to 0. Surface Convection Load Convection can be applied to any surface in the model. To apply convection first click on the desired selection method in the "Shape" panel and then click on "Surfaces" button in the "Select" panel. Then select the "Setup" tab and click on the "Convection" button in the "Thermal Loads" panel. Now click on the surface or surfaces to which you want to apply the load too and then press "Enter". The dialog shown in Figure 8.7 will appear.


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Figure 8.7: Surface Convection Object Properties Dialog In general, a convection load is defined by two parameters: a convection coefficient and an ambient temperature. The ambient temperature is the temperature of the environment surrounding the surface. Enter this value in the "Ambient Temperature" field. Two types of convection coefficients may be defined: Constant Convection Coefficient For a surface that will have the same convection coefficient for all of the nodes, a constant convection coefficient can be used. To set up this type of convection coefficient, specify a value in the "Temperature Independent Convection Coefficient" field. This value can be derived from experimental data. If no experimental data is available, the user interface provides a library of pre-defined convection coefficients for air and water (for buoyant or forced flow) or can calculate a value based on various user-input parameters. To use a predefined value, press the "Read from Library…" button and select the condition that most closely matches the parameters of the model being analyzed. To calculate a convection coefficient, press the "Calculate…" button. You will be requested to enter flow, geometry and material properties about the model and the ambient fluid in three tabs. After the necessary data is specified, press the "Calculate film/convection coefficient" button. A value will be calculated for the convection coefficient. When you leave this dialog, you will have the option to have this value automatically assigned to the "Convection Coefficient" field. For information on the equations used for the convection coefficient calculations, refer to the In-Product Help or Online Wiki Help. From the "Contents" tab, navigate to "Setting Up and Performing the Analysis: Thermal: Loads and Constraints: Convection: Film/Convection Coefficient Calculator."

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Chapter 8: Steady-State Heat Transfer Temperature-Dependent Convection Coefficient For a surface that will have a different convection coefficient at nodes with different temperatures, a temperature-dependent convection coefficient can be used. To set up this type of convection coefficient, activate the "Temperature Dependent Curve" checkbox. Press the "View/Edit Curve" button. The "Temperature Dependent Data" dialog shown in Figure 8.8 will appear.

Figure 8.8: Temperature Dependent Data Dialog The convection coefficient can be dependent on two temperature values. Select the "Lookup based on surface temperature" radio button if you want the value of the nodes to be used to calculate the corresponding convection coefficient. Select the "Lookup based on average temperature (surface and ambient)" radio button if you want the average of the temperature at the node and the ambient temperature to be used to calculate the corresponding convection coefficient. Type a descriptive name of the curve in the "Name" field. In the "Convection Coefficient as a Function of Temperature" table, enter the convection coefficient for each temperature value. The temperature range must enclose the expected range of temperatures during the analysis. You can import data from a comma separated value (*.csv) file using the "Import…" button. When the curve is completed, press the "OK" button. Select the appropriate curve in the "Temperature Dependent Curve" dropdown box. If you need to change values in an existing curve, select that curve and press the "Modify" button. For convection to be used properly during the analysis, a "Convection multiplier" must be assigned in the "Multipliers" tab of the "Analysis Parameters" dialog. The "Convection multiplier" scales the convection coefficient.


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Chapter 8: Steady-State Heat Transfer Surface Radiation Load Radiation can be applied to any surface in the model. To apply radiation, first click on the desired selection method in the "Shape" panel and then click on "Surfaces" button in the "Select" panel. Then select the "Setup" tab and click on the "Radiation" button in the "Thermal Loads" panel. Now click on the surface or surfaces to which you want to apply the load too and then press "Enter". The dialog shown in Figure 8.9 will appear.

Figure 8.9: Surface Radiation Object Dialog The radiation defined in this dialog is to the ambient conditions. For example, a hot plate on a table exchanging heat with the surroundings. This radiation will not take into account the exchange of heat from another body. In order to account for this type of heat transfer, you must set up body-to-body radiation, which is discussed later in this chapter. Radiation is defined by two parameters: an ambient temperature and a radiation function. Ambient Temperature: Specify the temperature of the environment surrounding the surface in this field. Radiation Function: The radiation function, Frad, adjusts the amount of heat transferred by radiation to account for absorptivity (α) of the cold surface, emissivity (ε) of the hot surface, and the view factor (Vm-s) between the model (m) and the surroundings (s). Absorptivity and emissivity are properties of the two objects. At equilibrium, α = ε. The view factor is dependent on the geometry between the model and the surroundings and can be obtained from heat transfer textbooks. The radiation function is defined as Frad = ε * Vm-s = α * Vm-s, since equilibrium is assumed. For radiation to be used properly during the analysis, a "Radiation multiplier" must be assigned in the "Multipliers" tab of the "Analysis Parameters" dialog. The "Radiation multiplier" adjusts the radiation function.

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Chapter 8: Steady-State Heat Transfer Surface Heat Source A surface heat source can be applied to any surface in the model. To apply a surface heat source, first click on the desired selection method in the "Shape" panel and then click on "Surfaces" button in the "Select" panel. Then select the "Setup" tab and click on the "Heat Source" button in the "Thermal Loads" panel. Now click on the surface or surfaces to which you want to apply the load too and then press "Enter". The dialog shown in Figure 8.10 will appear.

Figure 8.10: Surface Heat Flux Object Dialog Heat Source: Define the magnitude of the heat source per unit area in this field. A positive value will represent a heat source and a negative value will represent a heat sink. For a surface heat source to be used properly during the analysis, a "Convection multiplier" must be assigned in the "Multipliers" tab of the "Analysis Parameters" dialog. The "Convection multiplier" adjusts the heat source magnitude.

Element Loads Internal Heat Generation Internal heat generation can be applied to any part in a model. To apply internal heat generation to a model, first click on the desired selection method in the "Shape" panel and then click on "Parts" button in the "Select" panel. Then select the "Setup" tab and click on the "Internal Heat Generation" button in the "Thermal Loads" panel. Now click on any part or parts to which you want to apply the load too and then press "Enter". The dialog shown in Figure 8.11 will appear.


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Figure 8.11: Heat Generation Object Dialog There are two types of internal heat generation available in the program: Constant Internal Heat Generation If the magnitude of the internal heat generation in a part will be constant throughout the part regardless of the temperature in that area, a constant internal heat generation can be applied. To apply a constant internal heat generation, enter the magnitude of the internal heat generation per unit volume in the "Internal Heat Generation" field. Temperature-Dependent Internal Heat Generation If the magnitude of the internal heat generation in a part will vary throughout the part based on the temperature in that area, a temperature-dependent internal heat generation can be applied. To set up this type of internal heat generation activate the "Temperature Dependent" checkbox. Press the "Curve…" button and the dialog shown in Figure 8.12 will appear.

Figure 8.12: Temperature Dependent Data Dialog

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Chapter 8: Steady-State Heat Transfer In the table at the left side of the dialog, enter the temperature values and corresponding heat generation rate for each. Click the "Add Row" button as needed for each additional data point you wish to enter. The temperature values must be in ascending order. If the data is entered out of sequence, or if additional temperature values are added later, clicking the "Sort" button will automatically reorder the list. The temperature range must enclose the expected range of temperatures that will occur during the analysis. You can import data from a comma separated value (*.csv) file using the "Import CSV…" command. You may also export a curve for later use in another analysis by clicking the "Export CSV…" command. The table or graph may be printed using the "Print Table…" or the "Print Plot…" command. When the curve is completed, press the "OK" button. Select the appropriate curve in the "Temperature Dependent Curve" drop-down box. If you need to change values in an existing curve, select that curve and press the "Modify" button. An "Equation Editor.." command is also provided. This opens a dialog, as shown in Figure 8.13, that list various mathematical functions from which complex curves may be created. The Equation Editor automatically fills in the heat generation versus temperature data table based on user-specified start, end, and interval values. The "Overwrite Nodes" option causes the Equation Editor data to replace any previously entered data points in the heat generation versus temperature table.

Figure 8.13: Equation Editor Dialog For internal heat generation to be used properly during the analysis, a "Heat generation multiplier" must be assigned in the "Multipliers" tab of the "Analysis Parameters" dialog. The "Heat generation multiplier" adjusts the magnitude of the internal heat generation.

Body-to-Body Radiation Body-to-body radiation is a type of load that is applied to part of or all of a model. Body-tobody radiation accounts for heat transfer between parts of a model due to radiation. As mentioned before, the radiation applied to a surface only transfer’s heat to the surroundings. To set up body-to-body radiation, click on the "Body-to-Body Radiation" button in the "Thermal Loads" panel. The dialog shown in Figure 8.14 will appear.


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Figure 8.14: Body-to-Body Radiation Dialog The first thing to do when setting up body-to-body radiation is to determine the type of emissivity that will be used in the model. If the emissivity on all of the surfaces will be constant regardless of the temperature on the surface, you can proceed to the next step. If the emissivity on any of the surfaces will vary with the temperature of the surface, press the "Emissivity curves…" button. The dialog shown in Figure 8.15 will appear.

Figure 8.15: Body-to-Body Radiation Temperature Dependent Emissivity Dialog Enter a descriptive name for the emissivity curve in the "Description" field. Then enter the emissivity values at each temperature in the "Temperature Dependent Emissivity" table. The temperature range must include all of the temperatures that the surface will experience.

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Chapter 8: Steady-State Heat Transfer Press the "Add curve…" button to define multiple curves. Press the "OK" button when you have defined all of the emissivity curves. The next step for the body-to-body radiation setup is to define surfaces. To define a surface, press the "Define Surfaces…" button in the "Surface Parameters" section. The dialog shown in Figure 8.16 will appear.

Figure 8.16: Body-to-Body Radiation Surfaces Dialog Press the "Add surface" button. A dialog will appear which will allow you to select a specific surface on a part to include in this surface or all of the surfaces on a part. If a part consists of plate elements, you will also need to specify the side of the plate elements that will be included in the surface. Pressing the "OK" button will return you to the previous dialog. The information that you specified will appear in the "Definition of Surface" section. If you define multiple surfaces, you can select the desired surface in the "Surface number" dropdown box. If the emissivity of the selected surface does not vary with temperature, select the "Temperature independent" option in the "Type of emissivity" drop-down box and enter the constant emissivity value in the "Temperature independent emissivity" field. If the emissivity of the selected surface varies with temperature, select the "Temperature dependent" option in the "Type of emissivity" drop-down box and select the appropriate curve in the "Temperature dependent emissivity curve" field. To do this, emissivity curves must first be defined by clicking the "Emissivity curves…" button and providing the necessary data, which consists of a table of emissivity versus temperature values. When you have defined the emissivity for each surface, press the "OK" button. The next step is to define the enclosures. An enclosure is comprised of one or more of the surfaces that were defined in the previous step. The surfaces in an enclosure will exchange heat with each other through radiation. A surface can only be included in one enclosure. Select the enclosure that you want to define in the "Enclosure number" drop-down box and press the "Add" button in the "Surfaces" section. A dialog will appear that will allow you to select the surfaces that will be included in this enclosure. Once you select a surface, press the "OK" button. Press the "Add" button again to add another surface. If you want to include shadowing in this enclosure, select the "Included" option in the "Shadowing" dropdown box. Shadowing indicates that one body blocks the direct line of sight between surfaces of another body. An example is nested cylinders as shown in Figure 8.17. The inside of the large cylinder could radiate across the diameter, passing right through the small cylinder. To avoid this situation, shadowing should be included. Only surfaces defined in the enclosure will have a shadowing effect.


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Figure 8.17: Example of Shadowing If the surfaces in the enclosure will also radiate to the environment, select the "Timeindependent" or "Time-dependent" option in the "Ambient temperature" drop-down box and specify the ambient temperature in the "Ambient temperature value" field. Timedependent ambient temperature is only supported for transient thermal analyses (see next chapter). If the "Time-dependent" option is selected, specify the load curve that the ambient temperature will follow in the "Ambient temperature load curve" field. After defining the parameters for all of the enclosures, press the "OK" button. The body-tobody radiation setup is now complete. The "Radiation multiplier" on the "Multipliers" tab of the "Analysis Parameters" dialog and the "Radiation" tab will be used for body-to-body radiation in the same way as they were used for radiation to the ambient surroundings. Element Definition Options for Body-to-Body Radiation The Element Definition dialog for thermal brick or 2-D elements includes an option to specify the part as transparent or non-transparent for body-to-body radiation. The dialog for thermal bricks is shown in Figure 8.18.

Figure 8.18: General Tab of the Element Definition – Thermal Brick Dialog (with the Advanced Settings Option Enabled) If a body is specified as "Transparent," body-to-body radiation will pass through it without producing any shadowing effect. Otherwise, as the default "Non-transparent" type of part,

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Chapter 8: Steady-State Heat Transfer it will participate in body-to-body radiation by absorbing or emitting radiant heat and/or by shadowing radiation between other parts.

Controlling Nonlinear Iterations There are a few options that can be included in a steady-state heat transfer analysis that will cause the solution process to be nonlinear. These include radiation, temperature-dependent material models and temperature-dependent loads. When any of these options are included in an analysis, an iterative process must be performed. The iterative process is controlled by the options on the "Advanced" tab of the "Analysis Parameters" dialog. This dialog is shown in Figure 8.19.

Figure 8.19: Advanced Tab of the Analysis Parameters Dialog If any of the conditions listed above exist in your model, activate the "Perform" checkbox (this option is off by default). You can control how many times the processor can iterate on the solution using the "Maximum number of iterations" field. The solution after this many iterations will be used as the analysis result. In some cases, an adequate solution will be converged upon before the maximum number of iterations. There are two values that are calculated to determine the quality of the convergence. The first value is the corrective norm. The corrective norm is calculated as:

∑ (T n

i =1

i old Ti new

)2

n Where n is the total number of nodes in the model.


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Chapter 8: Steady-State Heat Transfer The second value is the relative norm. This is calculated as:

∑ (T n

i =1

i old

− Ti new

∑ (Ti )2 n

i =1

)2 .

old

Where n is the total number of nodes in the model. The "Corrective tolerance" field can be used to define the maximum value for the corrective norm. The "Relative tolerance" field can be used to define the maximum value for the relative norm. The temperature of a node after an iteration, Tcur, could be higher or lower than the final converged value. The value in the "Relaxation parameter" field can be used to minimize the oscillations. This value will be multiplied by the difference of the new and old temperatures for this node. The product will be added to the old temperature. This value will be used as Tcur. A relaxation parameter between 0.8 and 1 will provide the best results. There are five options to decide to stop the iterative process. These can be selected in the "Criteria" drop-down box. If the "Do all N iterations" option is selected, all of the iterations specified in the "Maximum number of iterations" field will be performed. If the "Stop when corrective norm < E1 (case 1)" option is selected, the iterations will stop when the corrective norm is less than the value in the "Corrective tolerance" field. If the "Stop when relative norm < E2 (case 2)" option is selected, the iterations will stop when the relative norm is less than the value in the "Relative tolerance" field. If the "Stop when either case 1 or 2" option is selected, the iterations will stop when either the corrective norm is less than the value in the "Corrective tolerance" field or the relative norm is less than the value in the "Relative tolerance" field. If the "Stop when both case 1 and 2" option is selected, the iterations will stop when the corrective norm is less than the value in the "Corrective tolerance" field and the relative norm is less than the value in the "Relative tolerance" field.

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Result Options The Results environment is used to view the results of a steady-state heat transfer analysis. For information on the options available for results presentation, refer to Chapter 3. The following result options are available in the RESULTS pull-down menu: Temperature: If this command is selected, the display will be based on the temperatures from the steady-state analysis. Heat Flux: If one of the commands in this pull-out menu is selected, the display will be based on the flux value at the element centroid. Heat Rate of Face: If this command is selected, the display will be based on the heat rate normal to the associated face. Precision of Heat Flux Magnitude: Precision is a measure of the adequacy of the mesh and indicates regions requiring mesh refinement. A low numerical value of this measure is desirable. It may be used to refine the grid for improved (lower numerical value) accuracy where the numerical value of precision is high. The precision is based on the discontinuous (across element boundaries) heat flux magnitude from element to element. It is calculated as follows:

 q i'' − q i'' max  Pi =  2 q ' ' MAX  0

min

if q ' ' if q ' '

MAX

MAX

 ≠ 0    = 0 

where: Pi is the precision at node i,

q ''i

max

is the maximum heat flux magnitude at node i, obtained by finding the maximum

over its neighboring elements,

q ''i

min

is the minimum heat flux magnitude at node i, obtained by finding the minimum

over its neighboring elements,

q ''

MAX

is the global maximum of the heat flux magnitude.

Calculating the Total Flow: It is often important to know the total amount of heat flowing through a surface of a model. This can be done in the Results environment. First, access the RESULTS pull-down menu and select the "Heat Rate of Face" command. Note: In order to inquire about and to sum the heat rate of element faces or model surfaces, smoothing of the results must be disabled. To do this, go to the "Results Options" pull down menu and deselect the "Smooth Results" command. Select the element faces or model surface through which you want to know the total heat flow. Access the INQUIRE pull-down menu and select the "Results" command. The


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Chapter 8: Steady-State Heat Transfer "Inquire: Results" dialog will appear as shown in Figure 8.20. Select the "Sum" option in the "Summary:" drop-down box.

Figure 8.20: Inquire: Results Dialog

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Exercise G Infrared Detector Model Brick Elements Concepts that will be Illustrated: • • •

Defining internal heat generation Specifying a surface radiation load Running a steady-state heat transfer analysis

Objective:

Determine the temperature of an infrared detector that is submerged in liquid nitrogen and has a specified amount of heat generated by an electrical heater.

Geometry:

Use the file Exercise G.ach in the "Exercise G\Input File" folder copied to your computer from the class directory or Solutions CD. Mesh the model using an absolute mesh size of 0.5 mm.

The cold finger has been built as two parts. One part represents the portion that is submerged in the liquid nitrogen. Loading:

The bottom 25 mm of the finger has a surface applied temperatures of -196°C. The top surface of the detector radiates to an ambient temperature of 27°C with a radiation function of 0.9. The heat generated by the electrical heater is 0.025 J/(mm3*s).

Element:

Brick


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Chapter 8: Steady-State Heat Transfer Materials:

Electrical heater and detector: Thermal conductivity = 1.00 J/(s*mm*°C) Cold finger: Thermal conductivity = 0.01 J/(s*mm*°C)

Results: Maximum Temperature 55.9 °C

A completed archive with results (Exercise G.ach) is located in the "Exercise G\Results Archive" folder in the class directory or in the copy of the solutions folders on your computer.

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Chapter

9

Transient Heat Transfer Chapter Objectives • • • •

Discussion of when to use a transient heat transfer analysis Overview of loading options unique to transient thermal analyses Overview of results options unique to transient thermal analyses Complete a transient heat transfer exercise

When to Use Transient Heat Transfer A transient heat transfer analysis will determine how the temperature distribution in a model changes over time. The magnitudes of the thermal loads can also vary throughout the analysis. This type of analysis is useful for models that will experience different loads during a typical application. A transient heat transfer analysis will require the mass density and specific heat properties for each material in the model. The results are output at each time step. In the "Analysis Parameters" dialog, there are three parameters in the "Event" section. The "Number of time steps" field controls how often the results are calculated. The "Time-step size" field determines the size of each time step. Equal time steps will be used throughout the analysis. The "Output interval" field controls how often the calculated results are output to the result files. It is recommended that this value be kept at 1.

Element Options All of the element types available in a steady-state heat transfer analysis are also available in a transient heat transfer analysis.

Loading Options All of the loading options discussed in Chapter 8 are available for a transient heat transfer analysis. Two loading features that are exclusive to a transient heat transfer analysis are discussed under the heading, "Important Note Regarding Load Curve Factors," that follows the "Load Curves" discussion (next page). One detail that should be noted is that the thermal stiffness matrix may change during the analysis if certain loads or material models are used. If any temperature-dependent materials or loads are present in the model, the matrix should be recalculated to assure accurate results. Also, if convection or radiation loads are present, the matrix must be recalculated to include the updated surface temperature. To reduce analysis time, you can control how often the matrix is reformulated. This is done in the "Advanced" tab of the "Analysis Parameters" dialog. Specify how often you want to reformulate the matrix in the "Number of time steps between matrix reformulation" field. A large number will have less accurate results, but a faster analysis time.


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Chapter 9: Transient Heat Transfer

Load Curves Loads in a transient heat transfer analysis follow load curves. The load curves are used to change the magnitudes of the loads throughout the analysis. Multiple load curves can be defined in a model and multiple loads can follow a single load curve. A load can be assigned to a load curve by selecting the appropriate load curve in the "Load Curve" drop-down box. Load Curve 0 is the default value for most loads. This load curve will keep the load at the specified magnitude throughout the analysis. The load curves are set up in the "Analysis Parameters" dialog by pressing the "Load Curves…" button. The dialog shown in Figure 9.1 will appear.

Figure 9.1 Load Curve Input Dialog You will define the curve by entering values in the "Time" and "Factor" columns. Each load curve must start at time 0 and must go to time equal to or greater than the duration of the event. The value in the "Factor" column will affect the loads assigned to this load curve. Important Note Regarding Load Curve Factors: For most loads, the value in the "Factor" column will be multiplied by the magnitude of the load. One exception to this is a load curve applied to the ambient temperature of a convection or radiation load. In this case, the value in the "Factor" column will be added to the magnitude of the temperature. Another exception is when a load curve is used to control a surface-applied or nodal-applied temperature. In this case, the value in the "Factor" column is part of an expression including also the applied load’s "Stiffness" and "Scale" values. The result of this expression is added to the applied temperature (see "Controlling Nodal and Surface Applied Temperatures" on page 168). In any case, the values used throughout the analysis event are linearly interpolated between the values entered into the "Time" and "Factor" columns whenever the time of the current calculation iteration doesn’t correspond exactly with a given load curve data point.

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Nodal Heat Source In addition to the loading options available for steady-state heat transfer analyses, a nodal heat source can be applied to a transient heat transfer analysis. The magnitude of a nodal heat source can vary during the analysis. Nodal heat sources can be applied to any node on the model. To add a nodal heat source, first click on the desired selection method in the "Shape" panel and then click on "Vertices" button in the "Select" panel. Then select the "Setup" tab and click on the "Heat Source" button in the "Thermal Loads" panel. Now click on the vertex or vertices to which you want to apply a nodal heat. The dialog shown in Figure 9.2 will appear if 1 node was selected before accessing this command.

Figure 9.2: Nodal Heat Source Object Dialog Magnitude: Enter the desired magnitude of the nodal heat source in this field. A positive magnitude represents heat flowing into the node. A negative magnitude represents heat flowing out of the node. Load Case / Load Curve: Specify the load curve that will control the magnitude of the nodal heat source throughout the analysis. The load curve must be defined in the "Analysis Parameters" dialog. Activation Time: If you want the nodal heat source to start during the analysis, specify that time in this field. The "Factor" of the specified load curve at time 0 will be applied at this time in the analysis. The load curve will continue from this point. For example, if you have a load curve defined for 10 seconds and apply it to a nodal heat source with an activation time of 2 seconds, the factor at 0 seconds on the load curve will be applied 2 seconds into the analysis. The factor at 5 seconds on the load curve will be applied 7 seconds into the analysis. Description: This field allows you to apply a name for this set of nodal heat sources. This description will be used to name each heat source in the tree view.


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Controlling Nodal and Surface Applied Temperatures For a transient heat transfer analysis, the magnitudes of nodal and surface applied temperatures can vary during the analysis. To control the magnitude of an applied temperature, add the applied temperature to the model and specify the magnitude and stiffness as explained in Chapter 8. It is recommended that the applied temperature have a large stiffness value. Next, activate the "Varies with Time" checkbox. Specify the load curve that will control the magnitude of the applied temperature throughout the analysis. The load curve must be defined in the "Analysis Parameters" dialog. Specify a scale factor to be applied to the load curve in the "Scale" field. The magnitude of the applied temperature will be calculated at each time step using the following equation:

 Factor * Scale   + Tapplied temperature Tnode =  Stiffness   Tnode is the value of the applied temperature at a specific time. Tapplied temperature is the magnitude of the applied temperature defined in the FEA Editor environment. Factor refers to the factor of the load curve specified in the "Load Case / Load Curve" field. Scale refers to the value in the "Scale" field. Stiffness refers to the stiffness of the applied temperature. The easiest and most intuitive way to control the temperature of nodes or surfaces is to do the following. Specify an applied temperature "Magnitude" of zero (0). Set both the "Stiffness" and "Scale" fields to the same high value. By default, both of these fields will have a value of 1e11. Define a load curve with the values in the factor column equal to the exact temperatures that you want for each time listed in the load curve table. Substituting these values into the above equation, it can be seen that the Scale and Stiffness values will cancel each other out and, since Tapplied temperature = 0, the resultant Tnode value will be equal to the Factor throughout the analysis. In other words, the load curve will show actual temperature versus time values when this technique is employed.

Result Options All of the result options available for a steady-state heat transfer analysis are also available for a transient heat transfer analysis. These results are calculated at each time step of the analysis. Each time step can be viewed in the Results environment as a separate load case. The "next/previous" buttons in the "Load Case Options" panel within the "Results Contours" tab can be used to toggle forward and backward through the load cases. An animation of a result through all of the time steps can be created using the "Save As AVI" button in the "Captures" panel. In addition to viewing the results in the display area, you can also create a graph of the results at one or multiple nodes at each time step of an analysis. This can be done by selecting the nodes and right-clicking in the display area. Select either the "Graph Value(s)" or the Embed Graph" command, depending upon whether you want a separate graph window or a graph embedded within the current presentation plot. A graph will appear plotting the currently displayed value throughout the analysis duration.

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Exercise H Transistor Case Model Brick Elements Concepts that will be Illustrated: • • •

Defining internal heat generation Specifying surface convection load Setting up and running a transient heat transfer analysis

Objective:

Perform a transient heat transfer analysis to determine the cooling effect of air blown over a transistor case.

Geometry:

Use the file, Exercise H.ach, in the "Exercise H\Input File" folder copied to your computer from the class directory or Solutions CD. Use the default mesh size.

Loading:

The free ends of the wires are 150°C. Apply convection to these surfaces at an ambient temperature of 150°C with a convection coefficient of 100 J/(s*°C*mm2). 25°C air is blown across the top surface of the case. At the beginning of the analysis, the convection coefficient is 2.5E-7 J/(s*°C*mm2). After 10 minutes, the convection coefficient is 2.5E-3 J/(s*°C*mm2).

Element:

Brick

Material:

Wires: Mass density = 8.933E-9 N*s2/mm/mm3 Thermal conductivity = 0.005 J/(s*mm*°C) Specific heat = 385,000 J/(N*s2/mm*°C) Case:

Mass density = 2.65E-10 N*s2/mm/mm3 Thermal conductivity = 0.0104 J/(s*mm*°C) Specific heat = 745,000 J/(N*s2/mm*°C)


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Chapter 9: Transient Heat Transfer Analysis Parameters:

Number of time steps = 20 Duration = 600 s

Load Curve: Time (s)

Factor

0

1

600

10000

Results:

Minimum Temperature at 10 Minutes 27.5 °C A completed archive with results (Exercise H.ach) is located in the "Exercise H\Results Archive" folder in the class directory or in the copy of the solutions folders on your computer.

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Chapter

10 Thermal Stress Chapter Objectives • •

Learn how to perform a thermal stress multiphysics analysis Complete a thermal stress exercise

Multiphysics Overview When two or more different analysis types are combined for the same model, it is referred to as a multiphysics analysis. These analyses are categorized as either coupled or uncoupled, with the majority of scenarios fitting the latter description. An uncoupled multiphysics scheme consists of running an analysis one time and then using the obtained results as a load in a different type of analysis, for which the solution is also run only once. This is also referred to as one-way coupling because the results of the first analysis affect the results of the second one. However, the results of the second analysis have no effect on the results of the first one. Conversely, in a fully coupled analysis (two-way coupling), two different types of solutions are executed concurrently and iteratively until both converge. This method is used when the results of each analysis are interdependent, such as in fluid thermal analyses – where natural buoyancy due to the temperature distribution drives a significant portion of the fluid flow. The temperature profile affects the fluid flow and the flow, in turn, affects the temperature profile. With the products included in the Autodesk® Simulation Mechanical package, it is possible to perform thermal stress analyses based on linear and non linear material models. For coupled multiphysics analyses or any uncoupled analyses involving fluid flow and electrostatics, the Multiphysics version is required. Depending upon the type of load being applied from a prior analysis to a subsequent analysis, and also, depending upon the type of elements in the model, the meshes for each phase of the multiphysics analysis may or may not have to be identical. Specifically, identical geometry is required for multiphysics analyses involving line elements (such as trusses and beams) and area elements (such as plates and membranes). For volume elements (such as bricks and tetrahedra), the meshes do not have to be matched, assuming the involved loads also support differing meshes. Node mapping is supported for nodal-based results that are available for selection within the Analysis Parameter dialog. For other types of loads, identical meshes are required. Node mapping uses a combination of interpolation and projection to map the nodal results from one analysis to a differing mesh in a subsequent analysis. Though the meshes may differ, parts with nodal results being applied to a subsequent analysis must also exist, and have the same part number, in the subsequent analysis. In other words, even if the geometry differs, the part numbering must be identical. For example, Part 3 in analysis B receives its load from Part 3 in analysis A. Autodesk® Simulation Mechanical 2012 – Part 1 – Seminar Notes

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Chapter 10: Thermal Stress

Parts that are not required for or have no effect on a particular phase of a multiphysics analysis may be deactivated when running that phase of the analysis. An example of this would be the air between conductors in an electrostatic analysis. It is needed to calculate electrical field strength but has no effect on the stresses in a structural analysis. Another example would be the pipes carrying fluid in an uncoupled fluid/thermal analysis. The pipes are deactivated for the fluid flow analysis but activated for the thermal analysis.

Performing a Thermal Stress Analysis The temperature profile from a steady-state or transient heat transfer analysis can be applied to a static stress or Mechanical Event Simulation (MES) analysis. The temperature values at each node will be compared to a stress free reference temperature for each part and the difference will be multiplied by the thermal expansion coefficient to calculate thermal strain and the resulting stresses. The geometry in both models may be identical but do not have to be identical for this multiphysics analysis. We will outline the procedure for completing a thermal stress analysis. Then, there is an exercise in which the results of a specific time step from a transient heat transfer analysis will be used as a thermal load in a subsequent linear static stress analysis.

To set up a thermal stress analysis, perform the following steps: 1.

Set up and run the steady-state or transient heat transfer analysis.

2.

Change the analysis type to either "Static Stress with Linear Material Models" or "MES with Nonlinear Material Models". When prompted, choose "Yes" to create a new design scenario rather than changing the initial design scenario’s analysis type.

3.

Load and constrain the model appropriately.

4.

In the "Element Definition" dialog for each part, enter a value in the "Stress Free Reference Temperature" field.

5.

Make sure that there is a value in the "Thermal Coefficient of Expansion" field in the "Element Material Specification" dialog for each part.

6.

Access the "Parameters" button from the "Model Setup" panel.

7.

For a static stress analysis with linear material models, type "1" in the "Thermal" column for each load case in which the thermal stress will be included. Note that the load case multiplier does not directly multiply the nodal temperatures. Rather, it multiplies the thermal load, which is based on the difference between the stress free reference temperature and the nodal temperature. For example, say the nodal temperature is 150F and the stress free temperature is 70F. This is a stress-

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Chapter 10: Thermal Stress from heat transfer analysis" drop-down box. If you select the "Specified" option, enter the desired time step in the "Time step" field. 8.

For an MES analysis, if you are using the results from a transient heat transfer analysis, set the "Duration" and "Capture rate" equivalent to those used in the transient heat transfer analysis. If the results of a steady-state heat transfer analysis are to be used as the source of nodal temperatures, define a load curve that will be used to control the temperature magnitude throughout the analysis. For temperatures from transient heat transfer analyses, the load curve multiplier will be ignored. The temperatures will be read-in as-is and applied without modification by the load curve. In the "Multiphysics" tab, change the "Source of nodal temperatures" drop-down box to either the "Steady-state analysis" or "Transient analysis" option. Specify the load curve that will be used to multiply the temperatures in the "Nodal temperature load curve index" drop-down box. Press the "Browse…" button next to the "Temperature data in file" field. Navigate to the results file from the heat transfer analysis and press the "Open" button.

9.

Run the analysis.

NOTE: When the preceding method is used to import nodal temperatures into a stress analysis, the nodal temperature transfer is done via node mapping. So, the heat transfer and stress analysis meshes need not be identical. Nonetheless, it is often appropriate and convenient to match the meshes. The best way to ensure identical geometry is to run, or at least solid mesh, the heat transfer model and then copies it to a new design scenario for the stress analysis phase. There is an alternate method of importing temperature data. It is based on the nodal coordinates, but without the interpolation and projection capabilities of the node mapping process. For a node to receive a load, it must be located at the same coordinates as a node with results in the prior analysis. Otherwise, a default nodal temperature will be applied. For this alternate method, use the "Loads from File…" command. This command is accessed from the context menu obtained by right-clicking in the display area of the FEA Editor with nothing selected. Other types of loads can also be applied using this command (such as electrostatic reaction forces and fluid boundary reaction forces). This alternate method has the disadvantage of not being able to apply differing results at the same sets of coordinates—for example, where two parts meet that are connected via surface or edge contact. Let us suppose that thermal resistance is specified between the contact surfaces. At such places, there will be two or more nodes existing at identical coordinates (one for each part) and their temperatures will likely be different. The user cannot control which nodal temperature gets applied at the matching coordinates in the subsequent analysis. Whereas, in the outlined procedure, if three parts meet at a common nodal location and each has a different temperature, all three temperatures will be applied to the subsequent analysis. In other words, the unique temperatures of each part are maintained where they meet.


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Chapter 10: Thermal Stress For more information regarding the alternate temperature application method, refer to the program help files. Go to the "Help: Contents" and, from there; navigate to one of the following sections: •

"Autodesk Simulation: Setting Up and Performing the Analysis: Set Up Analyses: Linear: Loads and Constraints: Temperatures"

•

"Autodesk Simulation: Setting Up and Performing the Analysis: Setting Up Part 2: Nonlinear: Loads and Constraints: Temperatures."

The pertinent information appears below the "Method 2" heading under the "Applying a Temperature Profile from a Thermal Analysis" topic. For more information concerning capabilities and/or limitations for other loads, consult the specific sections of the help files dealing with each load type of interest.

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Exercise I Disk Brake Rotor Heat-up and Stress Brick Elements Concepts that will be Illustrated: •

Applying a surface heat flux load

•

Using the temperature results from a transient heat transfer analysis as a thermal load in a linear static stress analysis

Objective:

Perform a transient heat transfer analysis to determine the temperature profile of the rotor during braking. Choose the time step with the maximum temperature differential and use these temperatures to determine the thermal stress via a second design scenario. Use mirror planes to observe a full-model representation.

Geometry:

Use the one-eight symmetry model file, Exercise I.step, in the "Exercise I\ Input File" folder copied to your computer from the Solutions CD. Use 50% of the default mesh size.

Thermal Loading:

Define a constant applied temperature of 100° F at the hub bore surface. Specify a heat flux of 4000 in.lbf/(s*in2). The heat flux will decrease linearly from the full magnitude to zero during the duration of the simulation event.

Constraints (Stress Analysis):

Apply the appropriate symmetry boundary conditions to each of the model's three planes of symmetry.


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Element:

Brick

Material:

Thermal Analysis:

Mass density = 6.9e-4 lbf*s2/in/in3 Thermal conductivity = 6 in*lbf/(s*in*°F) Specific heat = 500,000 in*lbf/(lbf*s2/in*°F)

Stress Analysis:

Mass density = 6.9e-4 lbf*s2/in/in3 Modulus of Elasticity = 18e6 psi Poisson's Ratio 0.265 Thermal Coef. of Expansion = 7.2e-6 /° F

Thermal Analysis Parameters:

Duration = 20 s Number of Steps = 10 Default Nodal Temperature = 100° F

Thermal Load Curve:

Element Data (Stress Analysis):

Time (s)

Factor

0

1

20

0

Stress Free Reference Temperature = 80° F

Results:

Maximum Temperature at 12 Seconds

Maximum von Mises Stress

~321 °F

~23,316 psi

A completed archive with results (Exercise I.ach) is located in the "Exercise I\Results Archive" folder in the class directory or in the copy of the solutions folders on your computer.

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Appendix A – Finite Element Method Using Hand Calculations


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Model Description and Governing Equations In this appendix, we will illustrate how FEA calculations on the truss structure shown below can be performed by hand. Figure A.1 shows the model to be analyzed.

Figure A.1: System of Trusses to be Solved by Hand Given: F = 10,000 lbs — force L = 120 in — length A = 2 in 2— area E = 30x106 psi — modulus of elasticity θ = 45° Hand Calculations: First, we know that the sum of the forces in the X and Y directions must be 0 at Node 1.

∑F ∑F

x

=F13 cos θ − F14 = 0

(1)

y

=F12 + F13 sin θ − 10,000 = 0

(2)

Since we will assume small deflections, we can ignore the rotation of the trusses. Consider the elongation of each member as the deflection along the original position.


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Figure A.2: Forces and Deflections of Each Member

F12 L12 ≈ ∆y AE F L δ14 = 14 14 ≈ ∆x AE F13L13 δ13 = ≈ ∆y sin θ − ∆x cos θ AE δ12 =

Substituting for ∆x and ∆y gives

F13L13 F12 L12 F L = sin θ − 14 14 cos θ AE AE AE

(3)

Solving equations 1, 2 and 3 for the three unknown forces gives F12=7,929 F13=2,929 F14=-2,071 σ12=3,965 σ13=1,465 σ14=−1,036 ∆x=0.00414 ∆y=-0.01586 F = 10,000 lbs — force L = 120 in — length A = 2 in 2— area E = 30x106 psi — modulus of elasticity θ = 45°

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Hand-Calculation of the Finite Element Solution To see how a hand-calculation would be performed using the finite element method, we will now present the construction of the stiffness matrix for each element. For the element from point 1 to point 2:

0 0  AE 0 1 k= L 0 0  0 − 1

0 0 0 − 1 (2 ) 30 x10 6 = 0 0 120  0 1

(

)

0 0 0 1  0 0  0 − 1

0 0 0 − 1 0 0  0 1

For the element from point 1 to point 3:

0.5 − 0.5 − 0.5  0.5  0.5 0.5 − 0.5 − 0.5 (2 ) 30 x10 6 AE  k= = 0.5  L 2 − 0.5 − 0.5 0.5 120 2   0.5  − 0.5 − 0.5 0.5

(

)

0.5 − 0.5 − 0.5  0.5  0.5 0.5 − 0.5 − 0.5  − 0.5 − 0.5 0.5 0.5    0.5  − 0.5 − 0.5 0.5

For the element from point 1 to point 4:

1  AE  0 k= L − 1  0

0 −1 0 0 0 1 0 0

0 0 (2 ) 30 x10 6 = 0 120  0

(

)

1 0  − 1  0

0 −1 0 0 0 1 0 0

0 0 0  0

Combine the individual matrices to create the total stiffness matrix: 0.354  1.354  0.354 1.354   0 0  0 −1 k = (500,000 ) − 0.354 − 0.354  − 0.354 − 0.354  −1 0  0  0

0 0 − 0.354 − 0.354 − 1 0 − 1 − 0.354 − 0.354 0 0 0 0 0 0 0 1 0 0 0 0 0 0.354 0.354 0 0 0 0.354 0.354 0 0 0 0 0 1 0

0

0

0

0

0 0 0  0 0  0 0  0

The force vector can be constructed. The horizontal and vertical forces at point 1 are known.

 0  − 10,000    F2 x  F =   F2 y   F3 x     F3 y 


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Appendix A – Finite Element Method Using Hand Calculations The displacement vector can also be constructed. The only two unknowns are the horizontal and vertical displacements of point 1. All other displacements are 0.  D1x  D   1y   0  D=   0   0     0 

Now we can invert the stiffness matrix and solve the equation:

{D} = [K ]−1 {F } After solving the above equation, the displacement results are:

D1x = 0.414 x10 −2 in D1 y = −1.59 x10 − 2 in The stresses can be calculated by dividing the axial forces by the cross-sectional area.

σ 1 = 3965 psi

σ 2 = 1471 psi

σ 3 = −1035 psi

®

Autodesk Simulation Example Figure A.3 below shows the truss system as modeled in the user interface. It is loaded and constrained as illustrated previously in Figure A.1 (page 179).

Figure A.3: Truss System Model

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Appendix A – Finite Element Method Using Hand Calculations Figure A.4 shows the results of the analysis. The X and Y components of the displacement are shown. Table A.1 shows a comparison of the program results to the hand calculation results. An archive of the model including the results (Truss Example.ach) is available in the "Appendix A Example\Results Archive" folder of the class directory or in the copy of the solutions folders on your computer.

Figure A.4: Displacements in the X and Y directions ®

Table A.1: Comparison of Autodesk Simulation Results to the Hand Calculations

∆1x ∆1y σ12 σ13 σ14

Hand Calculations

Autodesk Simulation

0.00414 in -0.0159 in 3965 psi 1465 psi -1036 psi

0.00414 in -0.0159 in 3964 psi 1464 psi -1036 psi


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Appendix B – Analysis Types in Autodesk® Simulation


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Appendix B – Analysis Types in Autodesk® Algor® Simulation

Background on the Different Analysis Types Static Stress with Linear Material Models Static stress analysis with linear material models is the most common type of FEA used today. Industrial products, manufacturing, consumer products, civil engineering, medical research, power transmission and electronic design are just a few of the areas in which static stress analysis is often performed. The simplest of all analysis types, the static stress analysis with linear material models, should only be used in cases where all applied loads are static and all material strains are expected to be in the linear elastic range. Whenever any of the strains produced are expected to be in the nonlinear range of the materials used, a nonlinear analysis type should be specified. Static stress analysis with linear material models enables the study of stress, strain, displacement and shear and axial forces that result from static loading. This analysis type is often sufficient for situations in which loads are known and the time of peak stress is evident. When performing a static stress analysis with linear material models, engineers apply static loads such as forces, pressures or known "imposed" displacements to a finite element model. Then, they add elastic material data, boundary conditions and other information such as the direction of gravity. Static forces are assumed to be constant for an infinite period of time, while resulting strain, movement and deformation are small. Engineers assume that the material will not deform beyond its elastic limit and any resulting dynamic effects from the loading are insignificant. Natural Frequency (Modal) Engineers have to design things to withstand vibration when it cannot be avoided. For example, tires and shock absorbers ("dampers" in technical terms) help reduce vibration in cars and trucks. Similarly, flexible couplings help isolate vibrations produced by the engines. Vibration is about frequencies. By its very nature, vibration involves repetitive motion. Each occurrence of a complete motion sequence is called a cycle. Frequency is defined as so many cycles in a given time period. Individual parts have, what engineers call, natural frequencies. For example, a violin string at a certain tension will vibrate only at a set number of frequencies, which is why you can produce specific musical tones. There is a base frequency in which the entire string is going back and forth in a simple bow shape. Harmonics and overtones occur because individual sections of the string can vibrate independently within the larger vibration. These various shapes are called modes. The base frequency is said to vibrate in the first mode, and so on up the ladder. Each mode shape will have an associated frequency. Higher mode shapes have higher frequencies. The most disastrous consequences occur when a power-driven device, such as a motor for example, produces a frequency at which an attached structure naturally vibrates. This event is called resonance. If sufficient power is applied, the attached structure will be destroyed. When vibration causes resonance in an object, destruction will result unless it has been designed to withstand the stress. The wine glass, for example, is not sound enough to withstand the resonance caused by the frequencies produced by the opera singer.


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Appendix B – Analysis Types in Autodesk® Simulation Note that ancient armies, which normally marched in step, were taken out of step when crossing bridges. Should the beat of the marching feet align with a natural frequency of the bridge, it could fall down. Engineers must design so that resonance does not occur during regular operation of machines. This is a major purpose of modal analysis. Ideally, the first mode has a frequency higher than any potential driving frequency. Frequently, resonance cannot be avoided, especially for short periods of time. For example, when a motor comes up to speed it produces a variety of frequencies. So it may pass through a resonant frequency. Other vibration processes, such as time history, response spectrum, random vibration, etc., are used in addition to modal analysis to deal with this type of more complex situation. These are called transient natural frequency processors. Transient Stress (Direct Integration) When you strike a guitar string or a tuning fork, it goes from a state of inactivity into vibration to make a musical tone. This tone seems loudest at first, then gradually dies out. Conditions are changing from the first moment the note is struck. When an electric motor is started up, it eventually reaches a steady-state of operation. But to get there, it starts from zero rpm and passes through an infinite number of speeds until it attains the operating speed. Every time you rev the motor in your car, you are creating transient vibration. When things vibrate, internal stresses are created by the vibration. These stresses can be devastating if resonance occurs between a device producing vibration and a structure responding to vibration. A bridge may vibrate in the wind or when cars and trucks go across it. Very complex vibration patterns can occur. Because things are constantly changing, engineers must know what the frequencies and stresses are at all moments in time. Sometimes transient vibrations are extremely violent and short-lived. Imagine a torpedo striking the side of a ship and exploding, or a car slamming into a concrete abutment, or dropping a coffeepot on a hard floor. Such vibrations are called shocks, which is just what you would imagine. In real life, shock is rarely a good thing and almost always unplanned. But shocks occur regardless. Because of vibration, shock is always more devastating than if the same force were applied gradually. The direct integration process works best when the time is relatively short and conditions are violent, such as conditions of shock. Transient Stress (Modal Superposition) The transient stress (modal superposition) analysis uses mode shapes and natural frequencies calculated through a linear natural frequency analysis to solve for time-varying loads at low frequencies. Engineers can produce the dynamic response of a structure subjected to forces, moments, temperatures or boundary accelerations. Furthermore, ground acceleration components can be added in any or all three of the global directions to determine dynamic responses such as deflection, velocity, acceleration and stress versus time.

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Appendix B – Analysis Types in Autodesk® Algor® Simulation Modal superposition excludes the effects of high frequency modes; thus, it uses only low frequency modes of vibration and requires fewer calculations. This type of analysis is used for fluid flow, structural vibration and load testing. For example, the effects of impulsive wind loading on towers or sinusoidal loading on air purification equipment can be determined. The transient stress (modal superposition) analysis uses the time history processor. The time history processor uses the mode shapes and natural frequencies calculated by the linear mode shapes and natural frequencies processor to perform a modal superposition solution for timevarying forcing functions. The dynamic response can be produced for two general types of input: 1. 2.

Ground acceleration input in any (or all) of the three global (X,Y,Z) directions. Time-varying loads (forces/moments) applied to any (or all) nodal degrees-offreedom.

Response Spectrum Engineers use this type of analysis to find out how a device or structure responds to sudden forces or shocks. It is assumed that these shocks or forces occur at boundary points which are normally fixed. An example would be a building, dam or nuclear reactor when an earthquake strikes. During an earthquake, violent shaking occurs. This shaking transmits into the structure or device at the points where they are attached to the ground (boundary points). Response spectrum analysis is used extensively by civil engineers who must design structures in earthquake-prone areas. The quantities describing many of the great earthquakes of the recent past have been captured with instruments and can now be fed into a response spectrum program to determine how a structure would react to a past real-world earthquake. Mechanical engineers who design components for nuclear power plants must use response spectrum analysis as well. Such components might include nuclear reactor parts, pumps, valves, piping, condensers, etc. When an engineer uses response spectrum analysis, he/she is looking for the maximum acceleration, velocity and displacements that occur after the shock. These in turn lead to maximum stresses. Autodesk® Simulation's response spectrum analysis utilizes formulas recommended by the U. S. Nuclear Regulatory Commission (NRC). Random Vibration Engineers use this type of analysis to find out how a device or structure responds to steady shaking of the kind you would feel riding in a truck, rail car, rocket (when the motor is on) and so on. Also, things that are riding in the vehicle, such as on-board electronics or cargo of any kind, may need random vibration analysis. The vibration generated in vehicles from the motors, road conditions, etc. is a combination of a great many frequencies from a variety of sources and has a certain "random" nature. Random vibration analysis is used by engineers who design various kinds of transportation equipment. Engineers provide input to the processor in the form of a power spectral density (PSD), which is a representation of the vibration frequencies and energy in a statistical form.


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Appendix B – Analysis Types in Autodesk® Simulation When an engineer uses random vibration analysis, they are looking to determine the maximum stresses resulting from the vibration. These stresses are important in determining the lifetime of a structure of a transportation vehicle. Also, it would be important to know if things being transported in vehicles will survive until they reach the destination. Frequency Response Suppose an electric motor is to drive a conveyer system to move grain from the storage area to the area where it will be processed into cereal. When the motor is switched on, the system starts up, going through a number of transient conditions, possibly with occasional rumbling and buzzing, finally reaching a steady-state condition for smooth, normal operation. Analyzing the parts of the conveyer system throughout this time and during the final running state can be done with a random vibration analysis. But this type of analysis may provide much more information than is actually needed if the engineers only want to study the normal running operation. Further, defining the input information to include the final condition would involve a large amount of data. Frequency response analysis was invented to analyze only the steady-state operation of the system. The inputs and output are very simple and the analysis works quickly. The engineers run one modal analysis followed by all the steady-state scenarios they desire. This type of analysis is recommended whenever the transient phase of operation is either very short in relation to the total operating time or is of no interest. Critical Buckling Load If you press down on an empty soft drink can with your hand, not much will seem to happen. If you put the can on the floor and gradually increase the force by stepping down on it with your foot, at some point it will suddenly squash. This sudden scrunching is known as buckling. In the normal use of most products, buckling can be catastrophic if it occurs. The failure is not one of stress, but of geometric stability. Once the geometry of the part starts to deform, it can no longer support even a fraction of the force initially applied. The worst part about buckling for engineers is that buckling usually occurs at relatively low stress values compared to what the material can withstand. So a separate check must be performed to see if a product or section is acceptable with respect to buckling. Buckling almost always involves compression. In civil engineering, buckling is to be avoided when designing support columns, load bearing walls and sections of bridges which may flex under load. For example an I-beam may be perfectly "safe" when considering only the maximum stress, but fail disastrously if just one local spot of a flange should buckle. In engineering, designs involving thin parts in flexible structures like airplanes and automobiles are susceptible to buckling. Even if the stress is very low, buckling of local areas can cause the whole structure to collapse by a rapid progression of propagated buckling. Sometimes, buckling is used as a characteristic part of a design. You may have seen or used the type of oilcan where you pump the oil out by pressing on the bottom of the oilcan. If you press a little, nothing happens. If you press harder, the bottom suddenly "snaps through", pumping out a small amount of oil. Then it snaps back when you release your thumb. This phenomenon is known as "snap through" or "oil can" buckling.

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Appendix B – Analysis Types in Autodesk® Algor® Simulation For situations involving linear materials such as steel or glass and small deflections or deformations prior to buckling, a straightforward solution is available – Autodesk ® Simulation’s Critical Buckling analysis type. For nonlinear situations, buckling can be determined as part of a nonlinear stress analysis using the Mechanical Event Simulation (MES) analysis type. Natural Frequency (Modal) with Load Stiffening The natural frequency (modal) with load stiffening analysis is very similar to natural frequency (modal) analysis. However, it can handle a situation when a part is under compression or tension at the same time that vibration is induced. Think of a violin or guitar string. If you tighten or loosen the screw, nothing is done to the string to change its mass or length, but the tone changes anyway. This effect makes music possible and engineers call it load stiffening. Dynamic Design Analysis Method (DDAM) The Dynamic Design Analysis Method (DDAM) enables engineers to analyze models using U.S. Navy procedures for shock design. All mission-essential equipment onboard surface ships and submarines must be qualified for shock loads, such as from depth charges, mines, missiles and torpedoes. This analysis can determine the characteristics of underwater explosion phenomena including the effects of shock waves, surface ship or submarine body response to shock loading and application of shock spectra to component design. Engineers can use DDAM to analyze the shock response at the mountings of shipboard equipment such as masts, propulsion shafts, rudders, exhaust uptakes and other critical structures. MES with Nonlinear Material Models Engineers often need to check a design while it is moving in a dynamic event such as buckling, swinging, rotation or oscillation. MES combines kinematic, rigid- and flexiblebody dynamics and nonlinear stress analysis capabilities. As a result, MES can simultaneously analyze mechanical events involving large deformations, nonlinear material properties, kinematic motion and forces caused by that motion and then predict the resulting stresses. One of the main advantages of MES is the need to make fewer assumptions. With MES, there is no need for elaborate hand calculations, interpretation of results or experiments to determine equivalent loading. The fewer the assumptions that need to be made, the lesser the chance for errors will be. Static Stress with Nonlinear Material Models Like MES, this analysis type supports nonlinear material behavior. However, the inertial and damping effects included in a full, dynamic analysis are excluded. Therefore, all parts must be statically stable. However, geometric nonlinearity is accounted for in Static/NLM analyses. So, the results will correctly reflect changes in load location, load orientation, and part cross-section that occur as the structure deforms. Riks Buckling Analysis A Riks analysis is specifically intended to capture post-buckling and collapse events. An example of post-buckling behavior is the snap-through action of the bottom of an old style oil Autodesk® Simulation Mechanical 2012 – Part 1 – Seminar Notes

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Appendix B – Analysis Types in Autodesk® Simulation can, where the structure becomes unstable, buckles inward, and then becomes stable once again. Like Static/NLM analyses, a Riks model must be statically stable, since inertial and damping effects are not supported. In addition, surface and element based loads are not supported. However, nodal forces and moments are supported. Natural Frequency (Modal) with Nonlinear Material Models The natural frequency (modal) with nonlinear material models analysis calculates the natural frequencies of a system. It is a very similar to the linear modes shapes and natural frequencies processor except that it also considers the effects of nonlinear materials such as rubber and many kinds of plastics and composite materials. Steady-State Heat Transfer Steady-state heat transfer analysis is used to determine the steady-state temperature distribution and heat flow. This type of analysis can be performed when the temperature at every point within the model, including the surfaces, is independent of time. Transient Heat Transfer Transient heat transfer analysis is used to determine the temperature distribution and heat flow within an object having time-dependent temperature conditions. The specific heat constant and the density of the material are required to perform a transient analysis. Steady Fluid Flow Steady fluid flow analysis provides for the simulation of incompressible, viscous flows as governed by the Navier-Stokes equations. It can be used to analyze flows that have reached a steady condition. Turbulence capabilities enable the prediction of turbulent flow (large changes in velocity over small distances) and laminar flow (smooth, gradual changes in velocity distribution) at the same time in the same model. Unsteady Fluid Flow Unsteady fluid flow analysis provides for the simulation of incompressible, viscous flows as governed by the Navier-Stokes equations. It can be used to analyze flows that have not yet reached a steady condition. Turbulence capabilities enable the prediction of turbulent flow (large changes in velocity over small distances) and laminar flow (smooth, gradual changes in velocity distribution) at the same time in the same model. Flow Through Porous Media The flow through porous media analysis will analyze fluid flow through a fully saturated porous medium. The flow must be steady, incompressible and isothermal and must maintain its dimensional integrity. The permeability of the medium can be independent of direction or can vary in orthogonal directions. This processor can calculate the flow in a 2-D planar, 2-D axisymmetric or 3-D configuration. Each part can have an individual permeability. A part can also be used to model unrestrained flow as the fluid moves between porous media.

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Appendix B – Analysis Types in Autodesk® Algor® Simulation The flow can be generated by pressures and velocities. At least one pressure load must be applied to the model so that a reference is established. Any surface without a velocity or pressure applied will be considered impermeable. Open Channel Flow Open channel flows involve the existence of a free surface between the flowing fluid and a gas above it. In such flows, the liquid and the gas are clearly separated, not interpenetrating (mixing), and the density ratio between them is quite large. Flow is generally governed by the force of gravity and inertia. An example of this is the flow within a manometer when pressure is applied or removed. The liquid lies in the bottom of the U-tube and air is above the liquid. Due to a low density and negligible viscosity, both the inertia and the viscous force of the gas are negligible, and the only influence of the gas is the pressure acted on the interface. Hence, the region of gas need not be analyzed, and the free surface is calculated as a boundary with constant pressure (for example, zero pressure by totally ignoring the air effect). Electrostatic Current and Voltage Electrostatic current and voltage analysis predicts the outcome when an electric potential is applied to a conductive material, which results in a voltage and current distribution over the surface or throughout the volume of an object and its surroundings. This enables engineers to study an assembly’s electric conduction properties. The input consists of electrical conductivity, voltage at boundaries and current loadings. The output consists of voltage at nodes, current flux density (vectors) at element centroids and current flow through element faces. Electrostatic Field Strength and Voltage Electrostatic field strength and voltage analysis is used to study electric fields around objects. It can also analyze dielectrics, which are non-conducting (insulating) materials polarized by electric fields. Analysts can use electrostatic field strength and voltage analysis to ensure that an electric field does not exceed the dielectric strength of a capacitor or a surrounding medium. Unlike electrostatic current and voltage analysis, electrostatic field strength and voltage analysis requires engineers to model the area around a conducting object. Engineers typically specify voltage, permittivity values or charge density as inputs for electric field analyses. The output consists of voltage at nodes and electric and displacement fields (vectors) at element centroids. Transient Mass Transfer Mass transfer refers to mass in transit due to gradients in the concentration of species within a mixture, and the transfer is due to random molecular motion. “Species transport” is an analogous name for mass transfer. The solution of mass transfer is to determine the species concentration distribution and corresponding species flux over a time interval. As implemented in Autodesk® Simulation, the mass transfer occurs via Poisson mode, which considers diffusion mass transfer balance only. There are no convective terms included, and the species do not interact with each other. (Consequently, one model with ten species will give the same results as ten individual models with one specie each.) Poisson mode can be applied for both fluid and solid phases. A typical application example is chemical species migrating through a membrane. Multiple species may be involved in each part of the model.


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Appendix B – Analysis Types in Autodesk® Simulation Steady Coupled Fluid Flow and Thermal This multiphysics analysis will combine the heat transfer analysis with fluid flow analysis, based on steady state conditions. The heat transfer due to the flow of the fluid over a surface will be accounted for as well as the natural convection (buoyancy) in the fluid due to the temperatures. All of the options available for a steady fluid flow analysis and a steady-state heat transfer analysis are available. Transient Coupled Fluid Flow and Thermal This multiphysics analysis will combine the heat transfer analysis with fluid flow analysis, based on transient (unsteady) conditions. The heat transfer due to the flow of the fluid over a surface will be accounted for as well as the natural convection (buoyancy) in the fluid due to the temperatures. All of the options available for an unsteady fluid flow analysis and a transient heat transfer analysis are available.

Choosing the Right Analysis Type for Your Application Below are some basic guidelines that you can follow to choose the correct analysis type for your situation. The example applications listed are by no means comprehensive. They are provided only as a general indication of the type of analysis that can be performed with each analysis type. Static Stress with Linear Material Models: •

Use when you want to calculate the displacements and stresses due to static loads.

•

The magnitude or direction of the loading will not change over time.

•

No inertial effects. (The mass of the model may be used to determine loads, such as gravity and centrifugal forces.)

•

Although contact is a nonlinear effect, it can be included in a static stress analysis; the solution becomes iterative.

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Examples: Structures (buildings, car frames, truss systems, etc.), bodies (valve bodies, ship hulls, housings, support brackets, pressure vessels, etc.), and press-fits.

Natural Frequency (Modal): •

Use when you want to calculate the natural frequencies and mode shapes of the model due to purely geometric and material properties.

•

Examples: Structures (buildings, bridges, towers, etc), shafts, bodies (housings, support brackets, etc.).

Natural Frequency (Modal) with Load Stiffening:

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Use when you want to calculate the natural frequencies and mode shapes of the model due to purely geometric and material properties.

•

Axial compressive or tensile loads affect the frequency of the system.

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Examples: Structures (buildings, bridges, towers, etc), shafts, bodies (housings, support brackets, etc.).


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Appendix B – Analysis Types in Autodesk® Algor® Simulation Response Spectrum: •

Use when you want to calculate the maximum displacements and stresses due to a spectrum-type load.

•

Examples: Structures subjected to earthquakes, blast and shock loads, etc.

Random Vibration: •

Use when you want to calculate the statistical response of a system (displacements and stresses) due to a random vibration, white noise, or a power spectrum density.

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Examples: Suspension systems, aerospace components, fans and pumps.

Frequency Response: •

Use when you want to calculate the steady state response (displacements and stresses) due to a harmonic or sinusoidal load or acceleration.

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Examples: Structures with rotating imbalance, frequency sweeps, fans and pumps.

Transient Stress (Direct Integration or Modal Superposition): •

Use when you want to calculate the displacements and stresses over time due to loads that will vary in a known fashion.

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Inertial effects are included.

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Examples: Structures subjected to transient events (buildings, bridges, towers, etc), bodies (housings, support brackets, etc.), and rotating imbalance.

Critical Buckling Load: •

Use when you want to calculate the load that will cause your model to buckle due to geometric instability.

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No inertial effects. (The mass of the model may be used to determine loads, such as gravity and centrifugal forces.)

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Examples: Column designs, structures (buildings, bridges, towers, etc.).

Dynamic Design Analysis Method (DDAM): •

Use when you want to calculate the maximum displacements and stresses due to a spectrum-type load.

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Use when designing naval equipment or vessels.

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Examples: exhaust uptakes, masts, propulsion shafts

MES (Mechanical Event Simulation) with Nonlinear Material Models: •

Use when you want to calculate the displacements, velocities, accelerations, and stresses over time due to dynamic loads.

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The loads can be constant, vary over time, or vary based on calculated results.

•


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Examples: Linkages, mechanisms, press-fit, snap-fits, multiple body contact, impact, forming and extruding processes, rubber and foam components (bellows and seats).


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Static Stress with Nonlinear Material Models: •

Use when you want to calculate the displacements and stresses due to static loads.

•

The loads can be constant, vary between "time steps" or load cases, or vary based on calculated results.

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Inertial effects are ignored. (The mass of the model may be used to determine loads, such as gravity and centrifugal forces.)

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Examples: Press-fit, multiple body contact, forming and extruding processes, rubber and foam components (bellows and seats).

Natural Frequency (Modal) with Nonlinear Material Models: •

Use when you want to calculate the natural frequencies and mode shapes of the model.

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The change in frequency due to displacements or changing material properties is not included.

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Loads do not affect the frequencies.

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Boundary conditions are fixed.

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Examples: Structures (buildings, bridges, towers, etc.), shafts, bodies (housings, support brackets, etc.).

Riks Buckling Analysis: •

Use when you want to calculate the displacements and stresses before and after the model has buckled or collapsed.

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Inertial effects are ignored.

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Examples: Columns, components with snap-through behavior.

Steady State Heat Transfer: •

Use when you want to calculate temperature and heat fluxes after an infinite period of time (steady-state conditions).

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The thermal loads are constant over time.

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Examples: structures (furnaces, insulating walls, etc), electrical components

Transient Heat Transfer:

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Use when you want to calculate the temperature and heat fluxes over time due to the thermal loads.

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The thermal loads can be constant or change over time.

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The material can change states between a solid and liquid.

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Examples: Structures (furnaces, insulating walls, brake systems, etc.), electrical components, and annealing processes.


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Appendix B – Analysis Types in Autodesk® Algor® Simulation Steady Fluid Flow: •

Use when you want to calculate the velocity and pressure distribution due to the motion of a fluid.

•

The fluid has reached a steady-state solution at each "time step" or load case.

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•

Examples: Valves, rotating equipment (fans, mixers, etc.), wind and drag force analysis, and flow measuring devices.

Unsteady Fluid Flow: •

Use when you want to calculate the velocity and pressure distribution due to the motion of a fluid.

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The fluid is undergoing acceleration during the analysis or changes over time.

•


•

Examples: Valves, rotating equipment (fans, mixers, etc.), wind and drag force analysis, and flow measuring devices.

Flow through Porous Media: •

Use when you want to calculate the velocity and pressure distribution of a fluid passing through a series of filtering layers.

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The flow is through (or dominated by) a fully saturated porous medium.

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The fluid has reached a steady-state solution after an infinite period of time.

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•

Examples: Aquifers, catalyst beds, filters, and sedimentary studies.

Electrostatic Current and Voltage: •

Use when you want to calculate the current and voltage distribution after an infinite period of time (steady-state conditions) due to induced voltages and current sources.

•

Examples: Electrical components (circuit breakers, circuit boards, batteries, etc.) and piezoelectric devices.

Electrostatic Field Strength and Voltage: •

Use when you want to calculate the electric field and voltage distribution after an infinite period of time (steady-state conditions) in an insulator due to induced voltages and charges.

•

Examples: Insulators and micro electromechanical systems (MEMS)

Transient Mass Transfer: •

Use when you want to calculate the concentration over time of multiple species

•

The transport of the species is due to random molecular motion.

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Examples: Chemical species through a membrane (drug delivery, etc.).


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Appendix B – Analysis Types in Autodesk® Simulation Steady Coupled Fluid Flow and Thermal: •

Use when you want to calculate the temperatures, heat fluxes, velocities, and pressure distribution in a fluid or a model with fluid and solid parts.

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The fluid has reached a steady-state solution at each "time step" or load case.

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The thermal results have reached a steady-state solution at each "time step" or load case.

•


•

Examples: Heat exchangers, circuit boards, cooling/heating system design, and HVAC systems.

Transient Coupled Fluid Flow and Thermal: •

Use when you want to calculate the temperatures, heat fluxes, velocities, and pressure distribution in a fluid or a model with fluid and solid parts.

•

All of the results can vary over time.

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The fluid is undergoing acceleration during the analysis or changing over time.

•


•

The thermal loads can be constant or change over time.

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Examples: Heat exchangers, circuit boards, cooling/heating system design, and HVAC systems.

Combining Analysis Types for Multiphysics Real-world mechanical behavior is often the result of several physical factors acting simultaneously. Multiphysics options enable engineers to simulate a product's behavior when those multiple physical factors interact. The following are types of multiphysics analysis combinations that can be completed in addition to the two coupled fluid thermal analysis types previously discussed.

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Thermal, fluid flow, electrostatic and structural

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Thermal, fluid flow and structural

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Fluid flow and thermal

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Fluid flow and structural

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Thermal and structural

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Electrostatic and thermal

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Electrostatic and structural (commonly used for Micro Electromechanical Systems – MEMS)


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Appendix C – Linear Loads and Constraints


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Nodal Loading Nodal Forces Forces can be applied to any node on the model. To add a force, first select the "Selection" tab and then click on "Vertices" button in the "Select" panel. Also select "Point" in the "Shape" panel. Then select the "Setup" tab. Click on the "Force" button in the "Loads" panel. Click on the vertex or vertices to which you want to apply a force and then press "Enter". The following dialogue appears. This dialogue will appear if 1 node was selected before accessing this command.

Figure C.1: Nodal Force Object Dialog Magnitude: Enter the desired magnitude of the nodal forces in this field. Place a "-" before the value if you want this force applied in the negative direction of the vector chosen. If you have selected multiple nodes, a force of this magnitude will be applied to each node. Direction section: If you select the "X", "Y" or "Z" radio buttons, the "X", "Y" and "Z" fields will be filled in to represent a unit vector along that direction. If you select the "Custom" radio button, you will be able to define a unit vector in the "X", "Y" and "Z" fields. If you press the "Vector Selector…" button, you will be able to define a vector by clicking on two nodes in the model. Load Case / Load Curve: The number in this field will control the load case to which this force is applied. If you want a force to be present in multiple load cases, you must apply two forces to the node and change this value. Time-dependent curves are disabled for linear static analyses. For nonlinear analyses, click the "Curve…" button to define a load curve. Description: This field allows you to apply a name for this set of nodal forces. This description will be used to name each force in the tree view.


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Appendix C – Linear Loads and Constraints Nodal Lumped Masses Lumped masses can be used to resist the translation or rotation of nodes, assuming the element type to which they're attached support rotational DOFs. Otherwise, only translation will be resisted. With nodes selected right-click in the display area and select the "Add" pull-out menu. Select the "Nodal Lumped Mass..." command. The dialog box shown in Figure C.2 will appear.

Figure C.2: Nodal Lumped Mass Object Dialog Select the appropriate radio button in the "Mass Input" section to determine if the lumped mass input values will be defined in units of force or mass (=weight/gravity). If the lumped mass will be equally effective in all translational directions, activate the "Uniform" checkbox and specify the magnitude of the mass in the "X Direction" field of the "Mass/Weight" section. If the lumped mass has different effective magnitudes along the three translational directions, deactivate the "Uniform" checkbox and specify the appropriate values in the "X Direction", "Y Direction" and "Z Direction" fields in the "Mass/Weight" section. If the lumped mass will be effective in rotational directions, specify the appropriate values in the "X Direction", "Y Direction" and "Z Direction" fields in the "Mass Moment of Inertia" section. Nodal Moments Moments can be applied to any node on the model that is on an element type that has a rotational DOF (i.e. beams and plates). To add a moment, first select the "Selection" tab and then click on "Vertices" button in the "Select" panel. Also select "Point" in the "Shape" panel. Then select the "Setup" tab. Click on the "Moment button in the "Loads" panel. Click on the vertex or vertices to which you want to apply a force and then press "Enter". The following dialogue appears. This dialogue will appear if 1 node was selected before 202


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Appendix C – Linear Loads and Constraints accessing this command.. Since the nodes on brick elements only have the translational DOFs, a moment cannot be applied directly to a brick element part.

Figure C.3: Nodal Moment Object Dialog Magnitude: Enter the desired magnitude of the nodal moments in this field. A positive value will be applied counterclockwise according to the right-hand rule. Place a "-" before the value if you want this moment applied in the clockwise direction. If you have selected multiple nodes, a moment of this magnitude will be applied to each node. Direction section: If you select the "X", "Y" or "Z" radio buttons, the "X", "Y" and "Z" fields will be filled in to represent a unit vector along that direction. If you select the "Custom" radio button, you will be able to define a unit vector in the "X", "Y" and "Z" fields. If you press the "Vector Selector…" button, you will be able to define a vector by clicking on two nodes in the model. Load Case / Load Curve: The number in this field will control which load case this moment is applied to. If you want a moment to be present in multiple load cases, you must apply two moments to the node and change this value. Time-dependent curves are disabled for linear static analyses. For nonlinear analyses, click the "Curve…" button to define a load curve. Description: This field allows you to apply a name for this set of nodal moments. This description will be used to name each moment in the tree view. Nodal Prescribed Displacement Nodal Prescribed Displacement can be applied to any node on the model. A node to which a displacement boundary element is added will translate or rotate by the specified magnitude in the specified direction. To add a Nodal Prescribed Displacement, first select the "Selection" tab and then click on "Vertices" button in the "Select" panel. Also select "Point" in the "Shape" panel. Click on the vertex or vertices and then click on "Prescribed Displacement" button in the "Constraints" panel. The dialog shown in Figure C.4 will appear if 1 node was selected before accessing this command.


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Figure C.4: Nodal Displacement Boundary Element Object Dialog Type section: In this section, select the "Translation" or "Rotation" radio button to specify the type of displacement boundary element that will be applied. The value in the "Magnitude" field will control how much the displacement boundary element will translate or rotate. Rotational displacement boundary elements should only be applied to nodes on elements that have a rotational degree of freedom in that direction. Magnitude: Enter the desired magnitude of the nodal displacement boundary element in this field. If the "Translation" radio button in the "Type" section is selected, place a "-" before the value if you want this displacement applied in the negative direction of the vector chosen. If the "Rotation" radio button in the "Type" section is selected, a positive value will be applied counterclockwise according to the right-hand rule. Place a "-" before the value if you want this rotation displacement boundary element to be applied in the clockwise direction. If you have selected multiple nodes, a displacement boundary element of this type and magnitude will be applied to each node. Direction section: If you select the "X", "Y" or "Z" radio buttons, the "X", "Y" and "Z" fields will be filled in to represent a unit vector along that direction. If you select the "Custom" radio button, you will be able to define a unit vector in the "X", "Y" and "Z" fields. If you press the "Vector Selector…" button, you will be able to define a vector by clicking on two nodes in the model. Stiffness: During the analysis, an element will be generated between the selected node and a new node located an arbitrary distance from the selected node in the specified direction. This element will be a line connecting the two nodes. The translation or rotation will be applied to the new node. The value in this field will control how much of the translation or rotation gets transferred to the selected node. A large stiffness (~1e8) will cause more of the translation or rotation to be applied to the selected node. This is useful for modeling springs or other supports in a model.

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Appendix C – Linear Loads and Constraints Description: This field allows you to apply a name for this set of nodal displacement boundary elements. This description will be used to name each displacement boundary element in the tree view. Nodal Temperatures Nodal temperatures can be applied to any node on the model. To add a nodal temperature, first select the "Selection" tab and then click on "Vertices" button in the "Select" panel. Also select "Point" in the "Shape" panel. Then Select the "Setup" tab. Click on the "Temperature" button in the "Loads" panel. Click on the vertex or vertices to which you want to apply a temperature and then press "Enter". The following dialogue appears. The dialog shown in Figure C.5 will appear if 1 node was selected before accessing this command.

Figure C.5: Nodal Temperature Object Dialog Magnitude: Enter the desired magnitude of the nodal temperature in this field. The difference between this value and the value in the "Stress Free Reference Temperature" in the "Parameters and Controls" section of the "General" tab in the "Element Definition" dialog will be used to calculate the thermal stress. Description: This field allows you to apply a name for this set of nodal temperatures. This description will be used to name each temperature in the tree view. Nodal Voltages Nodal voltages can be applied to any node on the model. To add a nodal voltage, first select the "Selection" tab and then click on "Vertices" button in the "Select" panel. Also select "Point" in the "Shape" panel. Then select the "Setup" tab and then expand the options in the "Loads" panel and then click on the "Voltage" button. Click on the vertex or vertices to which you want to apply a temperature and then press "Enter". The following dialogue appears. The dialog shown in Figure C.6 will appear if 1 node was selected before accessing this command.


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Figure C.6: Nodal Voltage Object Dialog Magnitude: Enter the desired magnitude of the nodal voltage in this field. Description: This field allows you to apply a name for this set of nodal voltages. This description will be used to name each voltage in the tree view.

Edge Loading Edge Forces Edge forces can be applied to any edge on a model that originated from a CAD solid model. To add an edge force, first select the "Selection" tab and then click on "Edges" button in the "Select" panel. Also select "Point" in the "Shape" panel. Then select the "Setup" tab. Click on the "Force" button in the "Loads" panel. Click on the edge or edges to which you want to apply a force and then press "Enter". A magnitude will be defined for the edge force. Nodal forces will be applied to the nodes on that edge so that the combined magnitude will equal the defined magnitude. The total force will be evenly distributed over the edge. Edge Prescribed Displacement Edge prescribed displacement can be applied to any edge on a model that originated from a CAD solid model. To add edge displacement boundary elements, first select the "Selection" tab and then click on "Edges" button in the "Select" panel. Also select "Point" in the "Shape" panel. Then click on the edge or edges and then click on "Prescribed Displacement" button in the "Constraints" panel. A magnitude will be defined for the edge displacement boundary in the same manner as a nodal displacement boundary element. Nodal displacement boundary elements will be applied to the nodes on that edge.

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Surface Loading Surface Force Surface forces can be applied to any surface on a brick, tetrahedral or plate part. To add a surface force, first select the "Selection" tab and then click on "Surfaces" button in the "Select" panel. Also select "Point" in the "Shape" panel. Then Select the "Setup" tab. Click on the "Force" button in the "Loads" panel. Click on the surface to which you want to apply a force and then press "Enter". The following dialogue appears. Multiple surfaces can be selected by holding down the key. The dialog shown in Figure C.7 will appear if 1 surface was selected before accessing this command.

Figure C.7: Surface Force Object Dialog Magnitude: Enter the magnitude of the force that will be distributed over each selected surface in this field. A force of this magnitude will be applied to each surface that is selected. The area of each surface will be calculated from the CAD model and the magnitude will be divided by this value. A pressure or traction with the resulting magnitude will be applied to each surface. Direction section: If you select the "Normal" radio button, the force will be applied normal to the face of each element on the surface. If a positive value was entered in the "Magnitude" field, the force will be directed into the element. If a negative value was entered in the "Magnitude" field, the force will be directed away from the element. If you select the "X", "Y" or "Z" radio buttons, the "X", "Y" and "Z" fields will be filled in to represent a unit vector along that direction. If you select the "Custom" radio button, you will be able to define a unit vector in the "X", "Y" and "Z" fields. If you press the "Vector Selector…" button, you will be able to define a vector by clicking on two nodes in the model. Description: This field allows you to apply a name for this set of surface forces. This description will be used to name each surface force in the tree view.


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Appendix C – Linear Loads and Constraints Pressure/Traction Pressures and tractions can be applied to any surface on the model. To add a pressure or traction, first select the "Selection" tab and then click on "Surfaces" button in the "Select" panel. Also select "Point" in the "Shape" panel. Then Select the "Setup" tab. Click on the "Pressure" button in the "Loads" panel. Click on the surface to which you want to apply a pressure or traction and then press "Enter". Multiple surfaces can be selected by holding down the key. The dialog shown in Figure C.8 will appear.

Figure C.8: Surface Pressure/Traction Object Dialog Magnitude section: Pressure: If you want to apply a normal pressure, select the "Pressure" radio button and specify the magnitude of the pressure to be applied to each surface in the "Magnitude" field. A positive pressure will be directed into the element. A negative pressure will be directed away from the element. The units are force/area. Traction: If you want to apply a pressure along a specific direction, select the "Traction" radio button and specify the X, Y and Z components of the traction in the "X Magnitude", "Y Magnitude" and "Z Magnitude" fields. Hydrostatic Pressure Hydrostatic pressure can be applied to any surface on the model. To add a hydrostatic pressure, first select the "Selection" tab and then click on "Surfaces" button in the "Select" panel. Also select "Point" in the "Shape" panel and then select the "Setup" tab. Select the options button in the "Loads" panel and then click on the "Hydrostatic Pressure" button. Click on the surface to which you want to apply a pressure or traction and then press "Enter". Multiple surfaces can be selected by holding down the key. The dialog 208


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Appendix C – Linear Loads and Constraints shown in Figure C.9 will appear when applying hydrostatic pressures to solid element surfaces in a linear static stress analysis.

Figure C.9: Surface Hydrostatic Pressure Object Dialog for Solid Elements Parameters section: Y Reference: Enter the Y-coordinate of the top of the surface of the fluid that is creating the hydrostatic pressure. The distance from this point to the face of the element will be multiplied by the value in the "Fluid Density" field to calculate the pressure at that face. Figure C.10 shows how the hydrostatic pressure is applied to the model. Fluid Density: Enter the weight density of the fluid that is creating the hydrostatic pressure. This value will be multiplied by the distance from the top of the fluid to calculate the pressure for that face.

Figure C.10: Hydrostatic Pressure of Brick Elements


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Appendix C – Linear Loads and Constraints NOTE: When applying hydrostatic pressures to plate elements in a linear static stress analysis or to any applicable element type in a nonlinear stress analysis (including solid elements) a different dialog box from that shown in the preceding Figure C.9 will be obtained. For linear plates and for nonlinear stress analyses, the model is not limited to an orientation with +Y up for hydrostatic loads, as it is for linear bricks and tetrahedra. The alternate dialog box includes additional input fields for specifying a point on the surface of the fluid (rather than just a Y value). It also contains fields for specifying the surface normal direction of the fluid. This is specifically the direction of increasing depth and increasing load, which corresponds to the direction of gravity. Surface Variable Pressure Surface variable pressure can be applied to any surface on a brick, tetrahedral or plate part. To add a surface variable load, first select the "Selection" tab and then click on "Surfaces" button in the "Select" panel. Also select "Point" in the "Shape" panel and then select the "Setup" tab. Select the options button in the "Loads" panel and then click on the "Variable Pressure" button. Click on the surface to which you want to apply a pressure or traction and then press "Enter". Multiple surfaces can be selected by holding down the key. The dialog shown in Figure C.11 will appear.

Figure C.11: Surface Variable Pressure Dialog For the first variable load applied to a model, The "Active Function" drop-down box will display "New function…". You must use this field to specify a name for the function. If you already have variable loads on the model, you will be able to select a previously defined function name in this drop-down box. If you change the parameters of the function, the changes will be applied to every variable load in the model that uses that function. If you do not wish to alter a previously defined function, specify a new active function name. 210


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Select the coordinate system that the variable load will follow in the "Coordinate System" drop-down box. All local coordinate systems defined in the FEA Editor environment will be listed in addition to the global coordinate system. For example, If you want a surface variable load to start at zero at an edge of a surface, you should create a coordinate system that has the origin at one of the nodes along that edge. Select that coordinate system in this drop-down box. The coordinate systems can be rectangular, cylindrical or spherical. If the direction of the variable load will always be normal to the surface, select the "Normal to Surface" radio button in the "Load Orientation" section. If the variable load will be applied in a constant direction, select the "Traction" radio button in the "Load Orientation" section and define the direction as a vector in the "X", "Y" and "Z" fields. Define the function in the "Expression" field. The magnitude will be input as a pressure. Use the variable r for the local X coordinate, s for the local Y coordinate and t for the local Z coordinate, where the meaning of the local X,Y and Z coordinate depends on the coordinate system. You can use basic operators such as +,-,*,/, () and ^. Pressing the "Available Primitives >>" button will allow you to access several common functions. Pressing the "View" button will allow you to see a graphical view of the load along a specific direction. You can select the radio button for the direction along which you want to see the magnitude of the variable load since the load can be dependent on the other directions. You will then have to define the other two coordinates. For example, if you have a load that increases linearly in the X direction you will want to select the "X" radio button. This will generate a straight line at a constant slope. Since the load does not vary in the Y or Z directions, it does not matter what values are entered for these coordinates. If you were to select the "Y" or "Z" radio buttons, you will view a horizontal line. The value of the horizontal line will vary with the value in the "X" field. You can view the graph at multiple X coordinates by changing the coordinate and pressing the "Recalculate" button. Specify the load case in which you want the variable load to be placed in the "Load Case / Load Curve" field. If you are going to perform a transient stress (direct integration) analysis, this field will determine the load curve that this force will follow throughout the analysis. Since the variable load will be converted into nodal forces, the load in the Results environment may not appear to follow the function exactly. If the mesh is not evenly spaced, numerous forces of low magnitude may be applied in an area with a fine mesh and fewer forces of higher magnitudes may be applied in an area with a coarse mesh. Also, nodes that are not shared by multiple elements will have a force with a lower magnitude than the others. This is because the node gets a force applied from each element that it is shared by. Surface Prescribed Displacement A surface prescribed displacement can be applied to any surface on a model. To add a surface prescribed displacement, first select the "Selection" tab and then click on "Surfaces" button in the "Select" panel. Also select "Point" in the "Shape" panel and then select the "Setup" tab. Click on the "Prescribed Displacement" button in the "Constraints" panel. Click on the surface to which you want to apply a surface displacement boundary and then press "Enter". Multiple surfaces can be selected by holding down the key. A prescribed displacement will be applied to every node on the selected surface. If any of the lines meeting at a certain node are in the selected surfaces, a displacement boundary element will be applied to that node. Refer to the section about nodal displacement boundary elements for the definitions of the commands on this dialog.


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Appendix C – Linear Loads and Constraints Surface Temperature A surface temperature can be applied to any surface on a model. To add a surface temperature, first select the "Selection" tab and then click on "Surfaces" button in the "Select" panel. Also select "Point" in the "Shape" panel. Then Select the "Setup" tab. Click on the "Temperature" button in the "Loads" panel. Click on the surface to which you want to apply a temperature and then press "Enter". Multiple surfaces can be selected by holding down the key. A temperature will be applied to every node on the selected surface. If any of the lines meeting at a certain node are in the selected surfaces, a temperature will be applied to that node. Refer to the section about nodal temperatures for the definitions of the commands on this dialog. Surface Voltage A surface voltage can be applied to any surface on a model. To add a surface voltage, first select the "Selection" tab and then click on "Surfaces" button in the "Select" panel. Also select "Point" in the "Shape" panel and then select the "Setup" tab. Select the options button in the "Loads" panel and then click on the "Voltage" button. Click on the surface to which you want to apply a voltage then press "Enter". Multiple surfaces can be selected by holding down the key. A voltage will be applied to every node on the selected surface. If any of the lines meeting at a certain node are in the selected surfaces, a voltage will be applied to that node. Refer to the section about nodal voltage for the definitions of the commands on this dialog.

Element Loading Gravity /Acceleration An acceleration load is defined by clicking on the "Gravity" button within the "Loads" panel. A value can then be specified within the "Gravity/Acceleration" tab of the "Analysis Parameters" dialog. Alternatively the "Analysis Parameters" dialog can be accessed by clicking the "Parameters" button in the "Model" Setup panel in the "Setup" tab.. The "Gravity/Acceleration" tab is shown in Figure C.12. In addition to these parameters, a value must be applied in the "Accel/Gravity" column of the "Load Case Multipliers" table in the "Multipliers" tab of the "Analysis Parameters" dialog.

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Figure C.12: Gravity/Acceleration Tab of the Analysis Parameters Dialog Acceleration/Gravity Load section: Set for standard gravity: Pressing this button will enter the standard acceleration of gravity value for Earth in the "Acceleration due to body force" field. Acceleration due to body force: Enter the magnitude of the acceleration in this field. This will be applied to every part in the assembly. You must enter a value in the "Mass Density" field in the "Element Material Specification" dialog for each part in order for the acceleration to take effect. This dialog can be accessed by right-clicking on the "Material" heading for the each part in the tree view and selecting the "Modify Material…" command. This will access the "Element Material Selection" dialog. You can select any material and press the "Edit Properties" button to access the "Element Material Specification" dialog for that material. X multiplier: The value in this field will be multiplied by the value in the "Acceleration due to body force" field. The resulting acceleration will be applied to the assembly in the X direction. Y multiplier: The value in this field will be multiplied by the value in the "Acceleration due to body force" field. The resulting acceleration will be applied to the assembly in the Y direction. Z multiplier: The value in this field will be multiplied by the value in the "Acceleration due to body force" field. The resulting acceleration will be applied to the assembly in the Z direction.


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Appendix C – Linear Loads and Constraints Centrifugal The "Multipliers" tab of the Analysis Parameters dialog for linear static stress analyses includes multiplier columns labeled "Rotation" and "Angular Accel." Centrifugal forces acting on elements, due to their mass being rotated around a user-defined axis, are enabled by entering a non-zero value in one or both of these columns. The speed of rotation, angular acceleration rate and axis of rotation are defined within the "Centrifugal" tab of the "Analysis Parameters" screen The geometry is not actually rotated by the solver and the model should be properly constrained against rigid body motion in all three global directions, as for all linear static analyses (i.e., the model must be statically stable). The force is calculated and applied to each individual element based on its mass density and volume, as if it were actually rotating at the specified speed and/or acceleration rate. The axis of rotation must be parallel to one of the global axes. The user chooses the axis orientation and specifies the X, Y and Z coordinates of a single point through which the rotational axis passes. Since this is a global load, all parts of the model will be subjected to it. However, if there are non-rotating parts in the assembly, enter a material mass density of zero for these parts and the centrifugal load will have no effect on them. Please be aware that a rotation multiplier of "2" results in four times the centrifugal force. This is because the rotational speed is multiplied by the factor and the centrifugal force is a function of the angular speed squared (F = m*ω2/R). The "Centrifugal" tab of the "Analysis Parameters" screen is shown in Figure C.13.

Figure C.13: Centrifugal Tab of the Analysis Parameters Dialog

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Constraints General Constraint General constraints can be applied to any node, edge or surface on the models. General constraints on edges can only be applied to models that originated from CAD solid models. To add a general constraint, first select the "Setup" tab and then click on the "General Constraint" button in the "Constraints" panel. Then click on the vertex, edge or surface to which you want to apply the boundary condition. This selection will be initially predefined in the "Selection" tab. A dialog similar to the dialog shown in Figure C.14 will appear if 1 node was selected before accessing this command.

Figure C.14: General Constraints Dialog Constrained DOFs section: This section contains a checkbox for each DOF. By activating any of the checkboxes, no translation (T) or no rotation (R) will be allowed in that direction at that node. In order for the boundary condition to take effect, the element type to which the boundary condition is applied must have that DOF available. Predefined section: Fixed: When this button is pressed, every checkbox in the "Constrained DOFs" section will be activated. No translation or rotation will be permitted at these nodes. Free: When this button is pressed, every checkbox in the "Constrained DOFs" section will be deactivated. No constraints will be applied to these nodes. Pinned: When this button is pressed, the "Tx", "Ty" and "Tz" checkboxes in the "Constrained DOFs" section will be activated. These nodes will not be able to translate but will be able to rotate in any direction. No Rotation: When this button is pressed, the "Rx", "Ry" and "Rz" checkboxes in the "Constrained DOFs" section will be activated. These nodes will not be able to rotate but will be able to translate in any direction.


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Appendix C – Linear Loads and Constraints X Symmetry: When this button is pressed, the "Tx", "Ry" and "Rz" checkboxes in the "Constrained DOFs" section will be activated. This should be applied to a model that is being constructed using symmetry where the plane of symmetry is the YZ plane. For symmetry to exist in a model, both the geometry and the loading must be symmetric. Y Symmetry: When this button is pressed, the "Ty", "Rx" and "Rz" checkboxes in the "Constrained DOFs" section will be activated. This should be applied to a model that is being constructed using symmetry where the plane of symmetry is the XZ plane. For symmetry to exist in a model, both the geometry and the loading must be symmetric. Z Symmetry: When this button is pressed, the "Tz", "Rx" and "Ry" checkboxes in the "Constrained DOFs" section will be activated. This should be applied to a model that is being constructed using symmetry where the plane of symmetry is the XY plane. For symmetry to exist in a model, both the geometry and the loading must be symmetric. X Antisymmetric: When this button is pressed, the "Ty", "Tz" and "Rx" checkboxes in the "Constrained DOFs" section will be activated. This should be applied to a model that is being constructed using antisymmetry where the plane of antisymmetry is the YZ plane. For antisymmetry to exist in a model, the geometry must be symmetric and the loading must by antisymmetric. Y Antisymmetric: When this button is pressed, the "Tx", "Tz" and "Ry" checkboxes in the "Constrained DOFs" section will be activated. This should be applied to a model that is being constructed using antisymmetry where the plane of antisymmetry is the XZ plane. For antisymmetry to exist in a model, the geometry must be symmetric and the loading must by antisymmetric. Z Antisymmetric: When this button is pressed, the "Tx", "Ty" and "Rz" checkboxes in the "Constrained DOFs" section will be activated. This should be applied to a model that is being constructed using antisymmetry where the plane of antisymmetry is the XY plane. For antisymmetry to exist in a model, the geometry must be symmetric and the loading must by antisymmetric. Description: This field allows you to apply a name for this set of boundary conditions. This description will be used to name each boundary condition in the tree view. 3D Spring Support 3D spring support can be applied to any node, edge or surface on the model. A 3D spring support will apply a translational or rotational stiffness along one or more of the global X, Y or Z directions. To add a 3D spring support, first select the "Setup" tab and then click on the "3D Spring Support" button in the "Constraints" panel. Then click on the vertex, edge or surface to which you want to apply the boundary condition. This selection will be initially predefined in the "Selection" tab. A dialog similar to the dialog shown in Figure C.15 will appear if 1 node was selected before accessing this command.

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Figure C.15: 3D Spring Support Dialog Fixed section: By activating one or more of the checkboxes in this section, you can specify along which global directions the rigid boundary elements will be applied. During the analysis process, an individual element will be generated for each direction. The rigid boundary elements will constrain translation and rotation in both directions along the selected axes. Type section: Select the radio button for the type of movement that will be constrained by these rigid boundary elements in this section. Stiffness: During the analysis, an element will be generated between the selected node and a new node located an arbitrary distance from the selected node in the specified direction. This element will be a line connecting the two nodes. The translation or rotation constraint will be applied to the new node. The value in this field will control how much of the translation or rotation affects the selected node. A large stiffness (~1e8) will cause less movement of the selected node. This is useful for modeling springs or other supports in a model. Description: This field allows you to apply a name for this set of rigid boundary elements. 1D Spring Support 1D Spring support can be applied to any node, edge or surface on the model. A 1D spring support will apply a translational or rotational stiffness along any user-defined direction. Elastic boundary elements are often used to simulate springs. To add an elastic boundary element, first select the "Setup" tab and then click on the "1D Spring Support" button in the "Constraints" panel. Then click on the vertex, edge or surface to which you want to apply the boundary condition. This selection will be initially predefined in the "Selection" tab. A dialog similar to the dialog shown in Figure C.16 will appear if 1 node was selected before accessing this command.


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Figure C.16: 1D Spring Support Dialog Type section: Select the radio button for the type of movement that will be constrained by the elastic boundary elements in this section. Stiffness: During the analysis, an element will be generated between the selected node and a new node located an arbitrary distance from the selected node in the specified direction. This element will be a line connecting the two nodes. The translation or rotation constraint will be applied to the new node. The value in this field will control how much of the translation or rotation affects the selected node. A large stiffness (~1e8) will cause less movement of the selected node. This is useful for modeling springs or other supports in a model. Description: This field allows you to apply a name for the set of elastic boundary elements. Pin Constraint Pin constraint can be applied to only a surface on the model. Pin constraint will allow too restrict the motion in the radial, tangential and axial directions about the coordinate system defined by the circular surface selected. Pin constraints are often used to simulate pin connection. To add a pin constraint, first select the "Setup" tab and then click on the "Pin Constraint" button in the "Constraints" panel. Then click on the surface to which you want to apply the pin constraint. This selection will be initially predefined in the "Selection" tab. A dialog similar to the dialog shown in Figure C.17 will appear if 1 node was selected before accessing this command.

Figure C.17: Pin Constraint Dialog

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Appendix D – Material Model Options


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Appendix D – Material Model Options Autodesk® Simulation provides twenty-three different material models to choose from. The type of material model will depend on the element type and the analysis type to be performed. For example, when working with a type of steel, choose "Standard" since steel is an isotropic material. The table below lists material model, the analysis type that can be performed, and also a short description of the material model.

Material Model

Structural

Standard Isotropic – Elastic/Plastic, Thermal, Electrical Properties

Truss Beam 2-D Membrane Plate Brick Tetrahedral

Orthotropic Elastic/Plastic, Thermal, Electrical Properties Standard Temperature Dependent – Elastic/Plastic Properties Orthotropic Temperature Dependent – Elastic/Plastic, Thermal Properties Piezoelectric – Voltage induced stresses General Piezoelectric – Voltage induced stresses Anisotropic Stress versus Strain – Stress versus strain curve data Bulk Modulus versus Strain – Bulk modulus of elasticity versus strain data – for rock structures Mooney-Rivilin – For rubber like materials

Brick Plate Composites

MES/Nonlinear Structural Truss Beam 2-D Plate/Shell Membrane Brick Tetrahedral Kinematic Pipe 2-D Brick Tetrahedral Composite/Shell

Fluid Flow

Thermal

Electrostatics

None

2-D Bricks Tetrahedral Rod Plate

2-D Bricks Tetrahedral

None

2-D Bricks Tetrahedral Plate


None

Rod Plate



None

2-D Brick Tetrahedral

2-D Membrane

Brick Tetrahedral

None

2-D Bricks Tetrahedral Plate

Brick Tetrahedral

Brick Tetrahedral

None

None

None

Brick Tetrahedral

Brick Tetrahedral

None

None

None

Brick Tetrahedral

None

None

None

None

None

Truss

None

None

None

None

Brick Tetrahedral

None

None

None

None


None

None

None


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Material Model

Structural

Ogden – For higher order rubber like materials

None

Drucker-Prager – For soil like materials

None

Variable Tangent – For rock like materials

None

Viscoelastic – Creep

None

Viscoplastic – Creep

None

Fluid – Fluid flow material properties Hydrodynamic – Fluid properties for stress calculations Hyperfoam – For hyperelastic, compressible materials Blatz-Ko – For hyperelastic, compressible materials Arruda-Boyce – For hyperelastic, compressible materials Gasket – for modeling seals between parts

222

None

None

None

None

None None

MES/Nonlinear Structural 2-D Brick Tetrahedral 2-D Brick Tetrahedral

Fluid Flow

Thermal

Electrostatics

None

None

None

None

None

None

2-D

None

None

None

None

None

None

None

None

None

2-D Brick

None

None

None

None

None

None

None

None

None

None

None

None

None

None

None

None

None

2-D Brick Shell Tetrahedral 2-D Brick Tetrahedral None 2-D Brick Tetrahedral 2-D Brick Tetrahedral 2-D Brick Tetrahedral 2-D Brick Tetrahedral 2-D Gasket 3-D Gasket

Concrete

None

Brick

None

None

None

Duncan-Chang – For soil

None


None

None

None


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Autodesk® Simulation Mechanical 2012 Part 1 – Solutions Manual

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Autodesk® Simulation Mechanical 2012 – Part 1 – Solutions Manual

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SOLUTIONS MANUAL TABLE OF CONTENTS Foreword ......................................................1 Exercise A.......................................................................................................................... 3 Exercise B.......................................................................................................................... 9 Exercise C........................................................................................................................ 19 Exercise D........................................................................................................................ 25 Exercise E ........................................................................................................................ 33 Exercise F ........................................................................................................................ 41 Exercise G ....................................................................................................................... 47 Exercise H........................................................................................................................ 53 Exercise I ......................................................................................................................... 59


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Foreword Starting Autodesk® Simulation The software may be started by: •

Accessing the Windows "Start" menu and selecting the "All Programs" pull-out menu, followed by selecting the "Autodesk" group and the "Autodesk Algor Simulation" folder within it. Select the "Autodesk Simulation… 2012" command.

•

In addition, the program may be started by choosing the "Start Simulation" command within supported CAD solid modeling applications. This method starts the program and transfers-in the CAD solid model in one operation.

Defaults Each exercise is written using the default program settings, as if the software has been opened for the first time after installation. In this way, a user can work through the exercises in any order. If a user will be working through several exercises during one session, some settings from one exercise may be retained, creating incorrect or invalid steps in the following exercise. To minimize this possibility, exit the program at the end of each exercise and reopen it to begin a new exercise. It is possible for an experienced user to work through several exercises without this precaution, but extra care should be taken to review that input is correct and appropriate. It is important that the user access view commands exactly as described, except as otherwise indicated (that is, from the Orientation pull-down menu in the Navigation panel of the View tab of the ribbon). These commands ensure a constant and repeatable view orientation that is not ensured when using the View Cube. Specifically, while the displayed plane will be correct, the rotational position may not be as expected when using the View Cube. Several program settings are global. That is, once set, they will influence the program behavior for every model until the settings are changed again. In particular, the solution steps in this manual may be invalidated if a deviation is made from any of the settings listed below. These are the program settings upon which the solution procedures are based: •

"Application Menu: Options " … "Analysis" … "Automate Analysis" – Activated "Ask to show mesh results after CAD meshing" – Deactivated "Default Modeling Units…" = English (in) "CAD Import: Global CAD Import Options…" … "Knit surfaces on import:" = No Automatically generate contact pairs:" = No "Graphics: Navigation Tools: View Cube" … "Fit-to-View on view change" – Activated "Mouse Options: Mouse settings templates" = Autodesk Simulation


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Forward "Views Options: Views settings templates" = Autodesk Simulation

Archives A Solutions CD is affixed to the inside back cover of this manual. The Solutions CD contains the input files and result archives for all of the exercises in the Solutions Manual. There are clearly identified subfolders containing the appropriate files for each exercise. Within a classroom setting, this solutions archive will typically be extracted to a shared network location or will be pre-installed onto each student's workstation. If being provided via a shared drive on the network, the input files and results archives must be copied to the local computer before being opened. Do not try to open any models directly from the CD. This will fail because files cannot be written to the read-only disk.

Opening Archives 1. Copy the set of folders and files to your local computer from the class directory or from the Solutions CD. 2. Start Autodesk Simulation and select the "Open" icon at the left side of the dialog. 3. Select the "Autodesk Simulation Archive (*.ach)" option in the Autodesk Simulation Files section of the "Files of type:" drop-down box. 4. Double-click to open the desired folder, highlight the desired file, and press the "Open" button. 5. In the "Browse for Folder" screen, select a folder on the hard drive for the location of the restored model files. 6. Press the "OK" button. The model will be restored to the selected folder and automatically opened in the FEA Editor environment. For exercises based on CAD solid models, the input files will be universal format CAD solid model files, rather than Autodesk® Simulation® archives.

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Exercise A Frame – Full to Quarter-Symmetry Model Comparison Brick Elements Concepts that will be illustrated: • • • •

Merging two CAD solid models into a single FEA model Applying pressure loads Applying symmetry constraints Comparing full model results to symmetry model results

Objective:

Mesh and analyze the frame shown below. Analyze the whole model and a quartersymmetry version of the model, side-by-side, and verify that the results are the same.

Geometry:

Start with the file Exercise A (Full).step and then merge in the second file Exercise A (Quarter).step. Both files are in the "Exercise A\Input Files" folder of the class directory or in the copy of the solutions folders on your computer. By merging the two together, they can be solved simultaneously and compared more easily.

Mesh:

For a precise comparison, use a relatively small, absolute mesh size of 0.15 inch.

Constraints:

Fully fix the holes at the top of each part (half-holes in the case of the symmetry version). Apply proper symmetry boundary conditions for the quarter-symmetry model.


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3

Exercise A Loads:

Apply a 10,000 psi pressure normal to one surface of each part, as indicated in the preceding diagram.

Element:

Brick

Material:

Steel (ASTM-A36)

Results:

Assembly Description

Maximum von Mises Stress (psi) *

Maximum Displacement Magnitude (in)

Full Model

30,765

0.00759

Quarter-Symmetry Model

30,743

0.00759

* – Note that the stress variation between the two parts is less than onetenth of 1%. This small variation can easily be explained by the differences in the surface and/or interior meshes of the two solids.

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Exercise A

Solution Opening the Model Start Autodesk® Simulation, if it is not already running. Also, before starting this exercise, copy the Exercise A (Full).step and Exercise A (Quarter).step files from the "Exercise A\Input Files" folder in the class directory – if they are not already on your computer. We will first open the complete model and will then merge in the quarter-symmetry model. "Getting Started: Launch: Open" "STEP (*.stp, *.ste, *.step)" "Exercise A (full).step" "Open" "Use STEP file units" "OK" Mouse "Linear: Static Stress with Linear Material Models"

Click on the "Open" button in the Launch panel. Alternatively you select “Open” from the quick access toolbar or Application Menu. Select the "STEP (*.stp, *.ste, *.step)" option in the CAD Files section of the "Files of type:" drop-down box. Navigate to the location of the "Exercise A (Full).step" file on your computer and highlight it. Press the "Open" button. Choose the option to "Use STEP file units" if it is not already selected and click the "OK" button. The original STEP file length unit is inches. If the desired analysis type is not already set, press the menu button to the right of the analysis type field. Select the "Linear" pull-out menu, and choose the "Static Stress with Linear Material Models" option. Press the "OK" button.

"OK" "Application Menu: Merge" "STEP files (*.stp, *.ste, *.step)" "Exercise A (Quarter).step" "Open"

Click on the "Application Menu" and select the "Merge" command. Select the " STEP files (*.stp, *.ste, *.step)" option as this is the file type to be merged. Select the file Exercise A (Quarter).step in "Exercise A\Input Files" directory. Press the "Open" button

Since the model's units system has already been set, you won't be prompted regarding the units to use when importing the second STEP file. The parts will be initially displayed using an isometric view by default.

Meshing the Model "Mesh: Mesh: 3D Mesh Settings"


"Options"

Press the "Options" button.


Press the down-arrow to access the pull-down menu in the "Type" field under the "Mesh Size" heading and select the "Absolute mesh size" option.


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Exercise A 0.15

Type "0.15" in the "Size" field.

"OK"

Press the "OK" button to exit the Options dialog.

"Mesh model"

Press the "Mesh model" button.

Adding Loads and Constraints "Selection: Select: Surfaces"

Select the "Selection" tab. Make sure the "Surfaces" button is selected in the "Select" panel.

"Add: Surface Pressure/Tractions…"

Click on one of the two surfaces where the pressure load is to be applied. Holding down the key, click on the remaining load application surface. Select the "Setup" tab. Click on the "Pressure" button in the "Loads" panel.

10000


"OK"


Mouse Mouse


Select the "View" tab. Click on the options arrow to the bottom of "Orientation" button in the "Navigate" panel. Select "Top View" from the pull-out menu. Note you can also use the view cube. Select the "Selection" tab. Click on the "Rectangle" button in the "Shape" panel. Draw a box enclosing all four holes in the full part, being careful not to enclose any other surfaces. Only the surfaces of the holes should be fully enclosed within the selection rectangle. Holding down the key, draw a second box enclosing the two half-holes in the quarter-symmetry part, again being careful not to enclose any other surfaces. Select the "Setup" tab. Click on the "General Constraint" button in the "Constraints" panel.

"Fixed"


"OK"



"Selection: Shape: Rectangle"

Mouse

Mouse

In order to properly model symmetry, we must constrain the out-of-plane translation and the two in plane rotations, assuming the element type has rotational DOFs. In this case we are using brick elements, which have only translational DOFs. There are two symmetry planes—one parallel to the XZ plane (requiring Ty constraint) and the other lying on the YZ plane (requiring Tx constraint). We define the symmetry direction as being normal to the mirror plane. The individual DOFs can be set manually using the DOF checkboxes or set automatically by choosing the appropriate symmetry button within the boundary conditions dialog. The automatically assigned rotational constraints have no effect on brick models and will be ignored. Mouse "Setup: Constraints: General Constraint"

6

Draw a box enclosing only the bottom edge of the quartersymmetry part, as currently displayed. Click on the "General Constraint" button in the "Constraints" panel.


4/27/2011

Exercise A "Y Symmetry"


"OK"



Draw a box enclosing only the right edge of the quartersymmetry part, as currently displayed. Click on the "General Constraint" button in the "Constraints" panel.

"X Symmetry"


"OK"



Select the "View" tab. Click on the options arrow to the bottom of "Orientation" button in the "Navigate" panel. Select "Isometric View" from the pull-out menu. Note you can also use the view cube to get the desired view

Mouse

Defining the Material Data Mouse

Click on the "Material" heading for Part 1 in the tree view.

Mouse


Mouse


"Edit Material…"


"Steel (ASTM-A36)"


"OK"


Running the Analysis "Analysis: Analysis: Check Model" "Tools: Environments: FEA Editor"

Select the "Analysis" tab. Click on the "Check Model" button in the "Analysis" panel. Select the "Tools" tab. Click on the "FEA Editor" button in the "Environments" panel.


Select the "Analysis" tab, if not already selected. Click on the "Run Simulation" button in the "Analysis" panel.

Viewing the Results The von Mises stress results will be displayed by default. We will compare the maximum stress magnitude and location for the two parts. Mouse "Results Contours: Displacement: Displaced Options"

Select the "Results Options" tab. Click on the "Loads and Constraints" button in the "View" panel. Select the "Results Contours" tab. Select the options button to the right of Show Displaced and click on the "Displaced Option" button in the "Displacement" panel..


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7

Exercise A

Mouse Mouse Mouse

Move the slider in the "Scale Factor" section to control the scale factor of the displaced model. Do the displacements look correct? Press the cross button in the upper right corner of the "Displaced Model Options" dialog. Select the "Results Inquire" tab. Click on the "Maximum" button in the "Probes" panel.

Notice that the maximum stress occurs at the fillet adjacent to the load application surface on the quartersymmetry part. Compare the stress to the value shown in the table at the end of the exercise description. In order to confirm that the results for the full model are essentially the same, we will hide the quarter-model. The legend box values should not change significantly. The legend box displays the maximum and minimum values in the current display. Mouse


"Visibility"

Select the "Visibility" command to hide Part 2

Since the legend box did not change significantly, we know that the range of values is nearly identical in the two models. Notice the new location of the maximum stress. Once again, it occurs at the fillet adjacent to the load application surface. Compare the stress to the value shown in the table at the end of the exercise description. They should be in close agreement. Alternately, the probe tool could also have been used to compare stresses at various nodes. The slight difference in the maximum stress value is caused by the difference in the meshes. Now we will compare the displacement results. "Results Contours: Displacement: Displacemnt"

Select the "Results Contours" tab. Click on the "Displacement" button in the "Displacement" panel. Note maximum value on Part 1

Mouse


"Visibilty"

Select the "Visibilty" command to show part 2.

A completed archive of the combined full and quarter models, with results, "Exercise A (Complete).ach" is available in the "Exercise A\Results Archives" folder in the class directory or on the Solutions CD.

8


4/27/2011

Exercise B Yoke – Evaluation of Results and Generation of a Report Brick Elements Concepts that will be illustrated: • • • •

Applying a surface variable load Creating a local coordinate system Reviewing reaction forces Creating a path plot

Objective:

Knowing what we have learned in the last two chapters, we will refine our analysis of the yoke that was performed in Chapter 1. Review the reaction forces. Generate a report that includes an image of the von Mises stress contour, an animation of the deflections, and a path plot of the stresses along one of the straight edges at the top of the slot.

Geometry:

Use the file Exercise B.step in the "Exercise B\Input File" folder of the class directory or in the copy of the solutions folders on your computer. Use the default mesh settings.

Loading:

Use a surface variable load to apply the 800 lbf to the left half of the hole. The load should have a magnitude of 0 at the ends of the diameter and should have a parabolic profile.

Constraints:

Only constrain the radial and axial translation at the small hole. The tangential direction is free.

Element:

Brick

Materials:

Steel (ASTM-A36)

Questions:

Are the specified constraints adequate for a statically stable model? If not, what can be done to achieve this? How do these results compare to the results of the Chapter 1 example? If the loads are developed by pins or shafts passing through the holes, which result is more realistic? Do the support reactions sum to 800 lbf?


4/27/2011

9

Exercise B

Equation of Parabolic Load: -400y2 + 400 Results:

10



2,048

0.00044


4/27/2011

Exercise B

Solution Opening the Model Start Autodesk® Simulation, if it is not already running. Also, before starting this exercise, copy the Exercise B.step file from the "Exercise B\Input File" folder in the class directory – if they are not already on your computer. "Getting Started: Launch: Open" "STEP (*.stp, *.ste, *.step)" "Exercise B.step" "Open" "Use STEP file units" "OK" Mouse "Linear: Static Stress with Linear Material Models"

Click on the "Open" button in the Launch panel. Alternatively you select “Open” from the quick access toolbar or Application Menu. Select the "STEP (*.stp, *.ste, *.step)" option in the CAD Files section of the "Files of type:" drop-down box. Navigate to the location of the "Exercise B.step" file on your computer and highlight it. Press the "Open" button. Choose the option to "Use STEP file units" if it is not already selected and click the "OK" button. The original STEP file length unit is inches. If the desired analysis type is not already set, press the menu button to the right of the analysis type field. Select the "Linear" pull-out menu, and choose the "Static Stress with Linear Material Models" option. Press the "OK" button.

"OK"



"Mesh model"


Adding Loads and Constraints







"View: Navigate: Orbit"

Select the "View" tab and then click on the "Orbit" button within the "Navigate" panel. Alternatively you can access the Orbit tool from the "Navigate bar".


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11

Exercise B Mouse

Rotate the model so that the surfaces where the constraint will be applied are visible.

Press to exit rotate mode.

"Setup: Constraints: Pin Constraint

Select the "Setup" tab. Click on the "Pin Constraint" button in the "Constraints" panel.

Mouse

Click on one of the surfaces to which the load will be applied.

Mouse

Holding down the key, click on the other surface to which the load will be applied. Press "Enter"abolic

Mouse

Select "Fix Radial" and "Fix Axial" constraints. Press OK

"View: Navigate: Orbit" Mouse

Select the "View" tab and then click on the "Orbit" button within the "Navigate" panel. Alternatively you can access the Orbit tool from the "Navigate bar". Rotate the model so that the surfaces where the load will be applied are visible.

Press to exit rotate mode.

Mouse

Click on one of the surfaces to which the load will be applied.

"Setup: Loads: Variable Pressure"

Holding down the key, click on the other surface to which the load will be applied. Select the "Setup" tab. Click on the "Loads" panel option and then select " Variable Pressure " button

"Normal to Surface"

Select the "Normal to Surface" radio button

-400*s^2+400

Type "-400*s^2+400" in the "Expression ("Use 'r', 's', and 't' as variables)" field.

Parabolic Load

Type "Parabolic Load" in the "Active function" field.

"View"

Press the "View" button.

"Y"

Select the "Y" radio button. A graph of the parabolic profile will appear.

"Close"


"OK"


Mouse

Question: Are the specified constraints adequate for a statically stable model? If not, what can be done to achieve this? Answer: No, the specified constraints are not adequate. Since only the radial and axial translations are constrained, the yoke will be able to rotate freely about the center of the small hole. There are various methods that can be used to stabilize the model. For example, elastic boundary elements with low stiffness values can be applied to resist the translation. However it is important to run the model several times with different stiffness values. A weak stiffness will allow the model to move more than it should and a strong stiffness will prevent it from moving the distance it should. In this case, there is a better option. Since we expect the displacement results to be symmetric, we know that there should be no displacement in the Y direction along the centerline of the model, where Y=0. Therefore we can constrain the Y translation of a node or edge along the centerline of the model.

"View: Navigate: Top View" "Selection: Select: Edges"

12

Select the "View" tab. Click on the options button to the bottom of "Orientation" button in the "Navigate" panel. Select "Top View" from the pull-out menu. Select the "Selection" tab. Also make sure the "Edges" button is selected in the "Select" panel.


4/27/2011

Exercise B


Also make sure the "Rectangle" button is selected in the "Shape" panel Draw a rectangle enclosing the left end of the model. Make sure the outer edge is only selected @ 9 o’clock position. Select the "Setup" tab. Click on the "General Constraint" button in the "Constraints" panel.

Mouse

Activate the "Ty" checkbox.

"OK"



Access the VIEW pull-down menu and select the "Orientation" pull-out menu. Select the "Isometric View" command.

"Selection: Shape: Edges" Mouse

Defining the Material Data Mouse

Right-click on the "Material" heading for Part 1 in the tree view.

"Edit Material…"

Select the "Edit Material…" command in the menu.

"Steel (ASTM A36)"


"OK"



Select the "Analysis" tab. Click on the "Check Model" button in the "Analysis" panel. Select the "Tools" tab. Click on the "FEA Editor" button in the "Environments" panel.


Select the "Analysis" tab, if not already selected. Click on the "Run Simulation" button in the "Analysis" panel.


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13

Exercise B

Viewing the Results Initially, the von Mises stress results will be shown by default. Compare the maximum stress to the value shown in the results table in the exercise description. We will now verify that the total X-reaction force is 800 lbf.

Mouse

"View: Navigate: Top View" "Results Contours: Displacement: Show Displaced" "Results Contours: Other Results: Reaction Force: X" "Selection: Shape: Circle" "Selection: Select: Nodes"

Mouse "Results Inquire: Inquire: Current Results" "Sum"

Notice the force distribution at the inside of the large hole. Select the "Results Options" tab. Click on the "Load and Constraint" button in the "View" panel with the "Results Options" tab to hide the load and constraint symbols. Select the "View" tab. Click on the options button to the bottom of "Orientation" button in the "Navigate" panel. Select "Top View" from the pull-out menu. Select the "Results Contours" tab. Select the "Show Displaced" button in the "Displacement" panel. This will not show the model in displaced mode now. Select the options button below "Reactions" button in the "Other Results" panel. Then select Reaction Force and then X value. Select the "Selection" tab. Also make sure the "Circle" button is selected in the "Shape" panel. Select the "Setup" tab. Also make sure the "Nodes" button is selected in the "Select" panel. Draw a circle enclosing the nodes of the small hole. Only the constrained nodes will have a residual force value, so you needn't be concerned about selecting nodes around the entire inside diameter surface. Select the "Results Inquire" tab. Select the "Current Results” button in the "Inquire" panel. Select the "Sum" option in the "Summary:" drop-down box. The result is approximately -793 lbf. This is within 1% of the 800 lbf that was expected. A finer mesh would reduce the error.

Mouse

Close the dialogue box

Press to clear the selected nodes.

Saving an Image "Results Contours: Stress: von Mises" Mouse "View Cube" "Results Contours: Displacement: Displaced Options"

14

Select the "Results Contours" tab. Click on the "von Mises" button in the "Stress" panel. Select "Home" on the View Cube to get the default isometric view Select the options button below Show Displaced and click on the "Displaced Option" button in the "Displacement" panel.


4/27/2011

Exercise B Mouse

Activate the "Show Displaced Model" checkbox.

10

Type "10" in the "Scale Factor" field and press the key.

"Transparent"

Select the "Transparent" radio button.

Mouse

Close the dialogue box

Captures: Save Image"

Click on the "Save Image" button in the "Captures" panel.

Press to save the entire display area to a file.

Mouse von Mises Stress "Save"

Select "Portable network graphics file (*.png)" from the "Save as type:" pull-down list, if it is not already selected. Rather than using the default file name, type "von Mises Stress" into the "File name:" field. Press the "Save" button.

Creating an Animation For the animation, we will switch the current results from von Mises stress to Displacement Magnitude. "Results Contours: Displacement: Displacement" "Results Contours: Displacement: Displaced Options" Mouse "Captures: Start Animation" "Captures: Stop Animation" "Captures: Animate: Save as AVI" Displacement Animation

Click on the "Displacement" button in the "Displacement" panel. Select the options button below Show Displaced and click on the "Displaced Option" button in the "Displacement" panel. Activate the "Do Not Show" checkbox. Close the dialogue box Click on the "Start Animation" button in the "Captures" panel. Click on the "Stop Animation" button in the "Captures" panel. Select the options to the right of the "Animate" button and click on the "Save as AVI " button. Rather than using the default file name, type "Displacement Animation" into the "File name:" field.

"Save"

Press the "Save" button.

"No"

Press the "No" button when asked if you want to view the animation now.

Creating a Path Plot "Results Contours: Stress: von Mises" "View: Appearance: Shaded with Mesh" "View: Navigate: Top View"

Click on the "von Mises" button in the "Stress" panel. Select the "View" tab. Click on the options button to the bottom of "Visual Style" button in the "Appearance" panel. Select "Shaded with Mesh" from the pull-out menu. Select the "View" tab. Click on the options button to the bottom of "Orientation" button in the "Navigate" panel. Select "Top View" from the pull-out menu.


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15

Exercise B "Results Contours: Displacement: Show Displaced" <•

Mouse

Select the "Results Contours" tab. Click on the "Show Displaced" button in the "Displacement" panel. This will now show the model without deformation Holding the key, press the cursor down key, <㺓‬睴捩⹥ † This will rotate the model 30 degrees about the X-axis with the top of the model moving towards you. Select "Zoom Window" option from the "Navigate Bar" to define a zoom area enclosing the straight edge along the top of the yoke's slot. Press the key to exit the zoom area mode.

We will use the polyline method to select the nodes for our path plot. An irregular selection area is defined by drawing a series of polylines forming a closed-loop border around the desired entities. "Selection: Shape: Polyline"

Mouse

Select the "Selection" tab. Click on the "Polyline" button in the "Shape" panel. Click the mouse several times to define a selection area that tightly encloses the sixteen nodes along the top edge of the slot (see image below). Press the key to complete the last segment and close the polyline loop. Verify that all of the desired nodes, and no others, are selected.

Polyline Selection Area: Click at 1, 2, 3, 4, and 5. Then, press . "Results Inquire: Graphs: Create Path Plot" Mouse

Select the "Results Inquire" tab. Click on the "Create Path Plot" button in the "Graphs" panel. Right-click on the list of nodes in the Path Plot Definition dialog.

"Sort by X Coordinate"

Choose the "Sort by X Coordinate" command.

"Create"

Press the "Create" button to create the Path

The resulting plot will show the stress along the subject edge against the distance along the edge moving from the large end of the yoke towards the small end (+X direction). The stresses should trend upward as you move along the edge in this direction. Now, let's export a PNG image of the graph.

16

Captures: Save Image"

Click on the "Save Image" button in the "Captures" panel.

"PNG"

Activate the "PNG" radio button.

"File"

Activate the "File" radio button.

"Browse"

Press the "Browse" button.

von Mises Path Plot

Navigate to the folder where you wish to place the image and type "von Mises Path Plot" into the "File name:" field.


4/27/2011

Exercise B "Save"

Press the "Save" button.

1024 768 100

Enter "1024" into the "Width:" field, press , and enter "768", press , and enter "100" to define a 1024 x 768 pixel image at 100 dpi resolution.

"Export"

Press the "Export" button.

Mouse

Close graph plot window

Generating a Report "Tools: Environments: Report"

Select the "Tools" tab. Click on the "Report" button in the "Environment" panel.

"Report: Setup: Configure"

Click on the "Configure" button in the "Setup" panel.

NOTE: When selecting portions of the report to modify, click on the item name and not on the checkbox. Clicking on the checkbox will toggle the inclusion state of the item (i.e. whether it is to be included or excluded from the HTML report). Mouse Mouse: Exercise B Mouse: Analysis of Yoke under 800 lbf Loading

Select the "Project Name" heading. Click and drag the mouse to select the text "Design Analysis" and type "Exercise B" to replace it. Click and drag the mouse to select the text "Project Name Here" and replace this text by typing "Analysis of Yoke under 800 lbf Loading".

Mouse

Select the "Title and Author" heading.

Your Name

Type your name into the "Author" field.

Your Department

Type your department name into the "Department" field.

Mouse Mouse Mouse "Tree: Add Image File(s)..." Mouse "von Mises Stress.png" "von Mises Path Plot.png" "Open" "von Mises Stress" Deformation exaggerated by 10% for visibility.

Deselect the "Executive Summary" item by clicking on the associated checkbox. This item will be excluded from the report. Click on the checkbox next to the "Results Presentations" heading to deselect it. Click on the checkbox next to the "Processor Log Files" heading to deselect it. Access the TREE pull-down menu and select the "Add Image File(s)..." command. This will allow you to include user-specified images within the report. Select "Portable network graphics file (*.png)" from the "Save as type:" pull-down list, if it is not already selected. Browse to and select both of the previously created image files, "von Mises Stress.png" and "von Mises Path Plot.png". Press the "Open" button. Two new headings will appear in the report tree view. The headings will match the respective filenames that had been selected. Click on the "von Mises Stress" heading to select it. Do not click on the checkbox or this item will be deactivated. Type "Deformation exaggerated by 10% for visibility." in the "Caption" field.


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17

Exercise B "von Mises Path Plot"

Click on the "von Mises Path Plot" heading to select it.

Stresses along edge of slot moving in the +X direction.

Type "Stresses along edge of slot moving in the +X direction." in the "Caption" field. Access the TREE pull-down menu and select the "Add AVI File(s)..." command. This will allow you to include a user-specified animation file within the report. Browse to and select the previously created AVI file, "Displacement Animation.avi". Press the "Open" button. A "Displacement Animation" heading will appear in the report tree and it will be selected. Type " Deformation exaggerated by 10% for visibility." in the "Caption" field. Press the "Generate Report" button. The completed report will appear. You can scroll down and review the full report, verifying the presence of the stress plot and displacement animation, which will be looping continuously.

"Tree: Add AVI File(s)..." "Displacement Animation.avi" "Open" Deformation exaggerated by 10% for visibility "Generate Report"

A completed archive with results is located in the "Exercise B\Results Archive" folder in the class directory or in the copy of the solutions folders on your computer.

18


4/27/2011

Exercise C Midplane Meshing and Plate Element Orientation Plate Elements Concepts that will be illustrated: • • • •

Creating a midplane mesh Modeling with plate elements Properly defining plate element orientations Applying pressures to plate elements

Objective:

Generate a plate model of the duct and nozzle assembly shown below, apply an internal pressure throughout the assembly, and analyze it.

Geometry:

Use the file Exercise C.step from the "Exercise C\Input File" directory in the class directory or in the copy of the solutions folders on your computer. Perform a midplane mesh using an absolute mesh size of 0.2 inch for all parts. Use the automatically calculated midplane mesh thickness for all parts.


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19

Exercise C Loading:

20 psi internal pressure throughout assembly

Constraints:

Fully constrained at inlet and outlet edges (as shown on diagram)

Element:

Plate

Material:

Stainless Steel (AISI 302) Cold-rolled



~37,198

0.0178

* * * Hints:

20

• • •

The coordinate origin is in the exact center of the square header The centerline of the rectangular inlet is at Z = 6.75" The centerlines of the round outlets are at Y = +/- 4.5" and Z • -5"


4/27/2011

Exercise C

Solution Opening the Model Start Autodesk® Simulation, if it is not already running. Also, before starting this exercise, copy the Exercise C.step file from the "Exercise C\Input File" folder in the class directory – if they are not already on your computer. "Getting Started: Launch: Open" "STEP (*.stp, *.ste, *.step)" "Exercise C.step" "Open" "Use STEP file units" "OK" Mouse "Linear: Static Stress with Linear Material Models"

Click on the "Open" button in the Launch panel. Alternatively you select “Open” from the quick access toolbar or Application Menu. Select the "STEP (*.stp, *.ste, *.step)" option in the CAD Files section of the "Files of type:" drop-down box. Navigate to the location of the "Exercise C.step" file on your computer and highlight it. Press the "Open" button. Choose the option to "Use STEP file units" if it is not already selected and click the "OK" button. The original STEP file length unit is inches. If the desired analysis type is not already set, press the menu button to the right of the analysis type field. Select the "Linear" pull-out menu, and choose the "Static Stress with Linear Material Models" option. Press the "OK" button.

"OK"



"Midplane"

Select the "Midplane" radio button in the "Mesh type" section of the "Model Mesh Settings" dialog.

"Options"




0.2


"OK"


"Mesh model"


Mouse

Click and drag using the middle mouse button to rotate the model around for inspection of the mesh. This mesh appears to be acceptable.


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21

Exercise C

Adding Loads and Constraints "Selection: Shape: Point"




Mouse

Click on one of the four edges at the rectangular inlet.


Holding the key, select the remaining three inlet edges and the four, half-circle outlet edges. Select the "Setup" tab. Click on the "General Constraint" button in the "Constraints" panel.

"Fixed"


"OK"



Select the "Selection" tab. Click on the "Surfaces" button in the "Select" panel.

Mouse

A "Setup: Loads: Pressure"

While holding , press the "A" key. This will select all surfaces of the model. Select the "Setup" tab. Click on the "Pressure" button in the "Loads" panel.

20

In the "Magnitude" field, type in "20".

"OK"


Defining the Element and Material Data Based on the hints given at the end of the exercise description and a quick investigation of the surface number assignments, it can be seen that the default element normal point (0, 0, 0) will work for all surfaces of Part 1 except for surfaces 15 and 29. The table below summarizes the element normal point settings required for proper load orientation. Item Description

Coordinates of Normal Point

Orientation Method

Part 1, Surfaces 1 – 34 and 36

(0, 0, 0)

Surface-based

Part 1, Surfaces 35 and 37

(0, 0, 6.75)

Surface-based

Part 2

(0, 4.5, -5)

Part-based

Part 3

(0, -4.5, -5)

Part-based

We will now enter the necessary plate element data and material properties. Mouse Mouse "Surface-based" 6.75

22

Double-click on the "Element Definition" heading under Part 1 in the tree view. Access the pull-down menu to the right of the "Properties" input field and select "Surface-based." Type "6.75" in the "Normal Point (Z)" column for Surface 35 and 37 (two places total).


4/27/2011

Exercise C Press the "OK" button.

"OK" Mouse 4.5 -5

Double-click on the "Element Definition" heading under Part 2 in the tree view. Type "4.5" in the "Normal Point (Y)" cell, press , and type "-5" in the "Normal Point (Z)" cell. Press the "OK" button.

"OK" Mouse -4.5 -5

Double-click on the "Element Definition" heading under Part 3 in the tree view. Type "-4.5" in the "Normal Point (Y)" cell, press , and type "-5" in the "Normal Point (Z)" cell.

"OK"


Mouse

Click on the "Material" heading under Part 1 in the tree view.

Mouse

Holding the key, also select the "Material" headings under Part 2 and Part 3.

Mouse


"Edit Material…"


"Stainless Steel (AISI 302) Cold-rolled"

Expand the Steel folder and then expand the "Stainless" folder. Select "Stainless Steel (AISI 302) Cold-rolled" within the Autodesk Simulation Material Library.

"OK"


Running the Analysis "Analysis: Analysis: Check Model"

Select the "Analysis" tab. Click on the "Check Model" button in the "Analysis" panel.

To make it easier to see if the load directions are correct, we will make the vector orientations consistent. "Results Options: View: Loads and Constraints" "Tools: Application Options"

Select the "Results Options" tab. Click on the "Loads and Constraints" button in the "View" panel. If not already selected Select the "Tools" tab. Click on "Application Options" button in the Options panel.

Mouse

Select the "Results" tab within the Options dialog.

"Global FEA Objects Preferences…"

Press the "Global FEA Objects Preferences…" button.

"All arrows point at point of attachment" "OK" "OK"

Under the "Arrow Pointing" heading, activate the "All arrows point at point of attachment" option for the "Current" model (left radio button). Press the "OK" button to close the Global FEA Objects Preferences dialog. Press the "OK" button to exit the Options dialog.

Careful examination will reveal that the lines protruding through the exterior of the assembly are the tail ends of the pressure vectors, due to their length. The arrow heads should all be pointing against the inside surfaces’, indicating that the element normal point is correctly defined for all plate elements.


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23

Exercise C "Tools: Environments: FEA Editor"

Once you are finished inspecting the model. Cick on the "FEA Editor" button in the "Environments" panel.



Viewing the Results Note the maximum von Mises stress and compare it to the value shown in the results table at the end of the exercise description. Show the mesh lines so that the deformed shape of the assembly will be more clearly visible. "Results Options: View: Loads and Constraints" "View: Appearance: Visual Style" "Results Contours: Displacement: Displacement"

Select the "Results Options" tab. Click on the "Loads and Constraints" button in the "View" panel. This will remove Load and Constraint symbols Select the "View" tab. Select the options below "Visual Style" button in the "Appearance" panel. Select the "Shaded with Mesh" option. Select the "Results Contours" tab. Click on the "Displacement" button in the "Displacement" panel.

A completed archive with results is located in the "Exercise C\Results Archive" folder in the class directory or in the copy of the solutions folders on your computer.

24


4/27/2011

Exercise D Yoke and Clevis Assembly Brick Elements Concepts that will be illustrated: • • •

Using refinement points Adding a joint to a model Using the Bolt Wizard to create a bolted connection

Objective:

If you review the results of the yoke analysis performed in Chapter 1, you will notice that the stress results are not perfectly symmetrical, as would be expected. Perform the analysis again using the refinement options. Also, add a pin joint to the large hole and specify a bolted connection at the small hole. Apply the load to the center of the joint.

Geometry:

Use the file Exercise D.step in the "Exercise D\Input File" folder of the class directory or in the copy of the solutions folders on your computer.

Meshing:

After meshing initially using a mesh size setting of 85 percent, apply refinement points using the "Refinement Points: Automatic" command. Adjust the slider towards the right until approximately 45 refinement points are created. Then, regenerate the surface mesh. Create the pin joint and the bolt after the refined mesh has been finalized. Regenerate the mesh one more time after specifying the bolt so that the head and nut will be properly connected to the sides of the clevis.

Loading:

800 lbf total (400 lbf per node) in the –X direction at the center of the pin joint in the large hole


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25

Exercise D Constraints:

Fully constrain the four edges of the clevis base. This will simulate the behavior of a full perimeter weld. Do not fix the entire base surface. Constrain Ty at the center of the large hole's joint. This will prevent rotation of the yoke about the center of the small hole and ensure symmetrical behavior of the top and bottom halves of the yoke.

Element:

Brick (Yoke), Beam (Bolt), and Truss (Joint, 0.1 in2 cross-sectional area)

Material:

Steel (ASTM-A36) – Yoke and Clevis Steel (AISI 4130) – Joint and Bolt

Bolt Specifications: Bolt Diameter = 0.75" Head and Nut Diameter = 1.125" Number of Spokes = 12 Specify a "Tight Fit" for all bolt hole surfaces Axial Force (Preload) = 500 lbf Results:

26

Description



Yoke (Part 1)

~1,595

0.00059

Clevis (Part 2)

~2,306

0.000150


4/27/2011

Exercise D

Solution Opening the Model Start Autodesk® Simulation, if it is not already running. Also, before starting this exercise, copy the Exercise D.step file from the "Exercise D\Input File" folder in the class directory – if they are not already on your computer. "Getting Started: Launch: Open" "STEP (*.stp, *.ste, *.step)" "Exercise D.step" "Open" "Use STEP file units" "OK" Mouse "Linear: Static Stress with Linear Material Models"

Click on the "Open" button in the Launch panel. Alternatively you select “Open” from the quick access toolbar or Application Menu. Select the "STEP (*.stp, *.ste, *.step)" option in the CAD Files section of the "Files of type:" drop-down box. Navigate to the location of the "Exercise D.step" file on your computer and highlight it. Press the "Open" button. Choose the option to "Use STEP file units" if it is not already selected and click the "OK" button. The original STEP file length unit is inches. If the desired analysis type is not already set, press the menu button to the right of the analysis type field. Select the "Linear" pull-out menu, and choose the "Static Stress with Linear Material Models" option. Press the "OK" button.

"OK"

Meshing the Model We will mesh the model at the 85% of the default mesh size. Then we will generate automatic refinement points. "Mesh: Mesh: 3D Mesh Settings"


"Mesh: Refinement Points: Automatic"

Move the slider towards the right to change the mesh size to "85%." Press the "Mesh model" button in the "Model Mesh Settings" dialog. Click on the "Automatic" button in the "Refinement Points" panel.

Mouse

Move the slider to two tick marks away from the right end.

"Generate"

Press the "Generate" button. The dialog should indicate the generation of approximately 45 refinement points.

"Close"


"Mesh: Mesh: Generate 3D Mesh"

Select the "Generate 3D Mesh" button in the Mesh panel.

Mouse "Mesh model"


4/27/2011

27

Exercise D

Creating the Bolt and Joint "View: Navigate: Bottom View"

Select the "View" tab. Click on the options button to the bottom of "Orientation" button in the "Navigate" panel. Select "Bottom View" from the pull-out menu.





"Mesh: CAD Additions: Bolt"

Select the "Mesh" tab. Click on the "Bolt" button in the "CAD Additions" panel.

Mouse

Click on the side surface of the clevis that is facing you.

"Add" "View: Navigate: Reverse View" Mouse "Add" "Selection: Shape: Circle" Mouse

"Add"

Press the "Add" button within the "Bolt head" section of the "Generate Bolted Connection" dialog. Select the "View" tab. Click on the options button to the bottom of "Orientation" button in the "Navigate" panel. Select "Reverse View" from the pull-out menu. Click on the side surface of the clevis that is now facing you. Press the "Add" button within the "Nut" section of the "Generate Bolted Connection" dialog. Select the "Selection" tab. Click on the "Circle" button in the "Shape" panel. Click near the center of the small hole and drag the mouse to create a selection circle enclosing the I.D. surfaces of the hole. There are a total of six half-cylinder surfaces. Press the "Add" button within the "Interior hole surface(s) for one hole" section of the "Generate Bolted Connection" dialog.

Mouse

Activate the "Tight Fit" checkboxes for all six surfaces.

0.75

Enter "0.75" into the "Bolt diameter" field.

1.125

Enter "1.125" into the "Head diameter" field.

1.125

Enter "1.125" into the "Nut diameter" field.

500

Enter "500" into the "Magnitude" field to the right of the "Axial Force" radio button.

"OK"

Press the "OK" button to create the bolt.

Notice the construction vertices that have been placed at the ends of the spokes representing the bolt head and nut. We must now regenerate the mesh so that nodes will be created on the surface mesh of the clevis to connect to these spokes. The purpose of the construction vertices is to force the creation of a node wherever one of them lies on the surface of a CAD solid. "Mesh: Mesh: Generate 3D Mesh"

28

Select the "Generate 3D Mesh" button in the "Mesh" panel.


4/27/2011

Exercise D Now we will add the joint to the large hole.

Mouse "Mesh: Create Joint…" "OK"

Click near the center of the large hole and drag the mouse to create a selection circle enclosing the I.D. surfaces of the hole. There two half-cylinder surfaces. Click on the "Joint" button in the "CAD Additions" panel. Press the "OK" button to create a joint with the default settings.

Defining Element and Material Data Mouse


Mouse


Mouse


"Edit Material…"


"Steel (ASTM-A36)"

Expand the Steel folder and then expand the ASTM folder. Select "Steel (ASTM-A36)" within the Autodesk Simulation Material Library. Press the "OK" button.

"OK" Mouse "Steel (AISI 4130)"

Double-click the "Material" heading for Part 3 in the tree view. Expand the Steel folder and then expand the AISI folder. Select "Steel (AISI 4130)" within the Autodesk Simulation Material Library.

"OK"


Mouse

Double-click the "Element Definition" heading for Part 4 in the tree view.

0.1

Type "0.1" in the "Cross-sectional area" field.

"OK"


Mouse "Steel (AISI 4130)"

Double-click the "Material" heading for Part 4 in the tree view. Expand the Steel folder and then expand the AISI folder. Select "Steel (AISI 4130)" within the Autodesk Simulation Material Library. Press the "OK" button.

"OK"

Adding Loads and Constraints "Selection: Shape: Rectangle"

Select the "Selection" tab. Click on the "Rectangle" button in the "Shape" panel.



Mouse

Draw a box enclosing the top edge of the clevis, as currently displayed.


4/27/2011

29

Exercise D "Setup: Constraints: General Constraint" "Fixed"

Select the "Setup" tab. Click on the "General Constraint" button in the "Constraints" panel. Press the "Fixed" button. The title bar of the dialog should indicate that four edges are selected.

"OK"


"Selection: Select: Vertices"

Select the "Selection" tab. Click on the "Vertices" button in the "Select" panel.

Mouse

Draw a box enclosing the center of the joint in the large hole.


Select the "Setup" tab. Click on the "General Constraint" button in the "Constraints" panel. Activate the "Ty" checkbox under the "Constrained DOFs" heading.

"Ty" "OK"



With the joint's center nodes still selected. Click on the "Force" button in the "Loads" panel

-400

Type "-400" in the "Magnitude" field.

"X"

Select the "X" radio button.

"OK"


Analysis "Analysis: Analysis: Check Model" "Tools: Environments: FEA Editor"

Select the "Analysis" tab. Click on the "Check Model" button in the "Analysis" panel. Select the "Tools" tab. Press the "FEA Editor" button in the "Environments" panel.



Viewing the Results "View: Orientation: Isometric View"


Mouse

Select the Part 3 heading in the tree view.

Mouse "Visibility" Mouse

30

Holding the key, also select the Part 4 heading in the tree view. Right click mouse and select the "Visibility" command to hide the bolt and joint. Select the "Results Inquire" tab. Click on the "Maximum" button in the "Probes" panel.


4/27/2011

Exercise D Notice that the maximum von Mises stress occurs in the clevis (Part 2). Compare the value to the one shown in the results table at the end of the exercise description. Mouse


"Visibility"

Right click and select the "Visibility" command to hide the bolt and joint.

Now compare the maximum von Mises stress for the yoke to the value shown in the results table at the end of the exercise description. We will now compare the displacement results. "Results Contours: Displacement: Displacement"

Select the "Results Contours" tab. Click on the "Displacement" button in the "Displacement" panel.

Compare the yoke's maximum displacement to the value shown in the results table at the end of the exercise description. Mouse


"Visibility"

Right click and select the "Visibility" command to show the clevis.

Mouse


"Visibility"

Right click and select the "Visibility" command to hide the clevis.

Finally, compare the maximum displacement of the clevis to the value shown in the results table at the end of the exercise description.

A completed archive with results is located in the "Exercise D\Results Archive" folder in the class directory or in the copy of the solutions folders on your computer.


4/27/2011

31

Exercise D

32


4/27/2011

Exercise E Yoke Assembly with Contact Brick Elements Concepts that will be illustrated: •

Applying surface contact between parts in an assembly.

Objective:

Analyze the yoke model again, but include the pins in the CAD solid model. The loads and constraints will be applied to the pins and contact will be defined between the pins and the yoke.

Geometry:

Use the file Exercise E.step in the "Exercise E\Input File" folder of the class directory or in the copy of the solutions folders on your computer. Mesh the model at 90% of the default mesh size.

Loading:

Apply a total of 800 lbf in traction to the end faces of the pin in the large hole.

Constraints:

Fully constrain the end faces of the pin in the small hole. Constrain the Z translation of the shaft in the large hole.

Element:

Brick

Material:

Steel (ASTM-A36) for all parts

Questions:

Are the specified constraints adequate to ensure a statically stable model and to prevent unwanted motion of the parts? If not, add the necessary constraints. As always, constrain the model in a way that will provide the necessary stability but will not impede the expected natural deformation of the parts. How do the results compare to the previous results? How do the runtimes compare?


4/27/2011

33

Exercise E Results: Part Description


Yoke (Part 1)

3,429

Small Pin (Part 2)

3,591

Large Pin (Part 3)

425


Full Assembly

34


0.00047

4/27/2011

Exercise E

Solution Opening the Model Start Autodesk® Simulation, if it is not already running. Also, before starting this exercise, copy the Exercise E.step file from the "Exercise E\Input File" folder in the class directory – if they are not already on your computer. "Getting Started: Launch: Open" "STEP (*.stp, *.ste, *.step)" "Exercise E.step" "Open" "Use STEP file units" "OK" Mouse "Linear: Static Stress with Linear Material Models"

Click on the "Open" button in the Launch panel. Alternatively you select “Open” from the quick access toolbar or Application Menu. Select the "STEP (*.stp, *.ste, *.step)" option in the CAD Files section of the "Files of type:" drop-down box. Navigate to the location of the "Exercise E.step" file on your computer and highlight it. Press the "Open" button. Choose the option to "Use STEP file units" if it is not already selected and click the "OK" button. The original STEP file length unit is inches. If the desired analysis type is not already set, press the menu button to the right of the analysis type field. Select the "Linear" pull-out menu, and choose the "Static Stress with Linear Material Models" option. Press the "OK" button.

"OK"

Meshing the Model Since all places where one part intersects another are to be defined as surface contact, we could simply make the default contact type = "Surface Contact." However, this will lump all contact results under a single heading in the Results environment. The total contact force is automatically calculated and presented as one of the analysis results. In order to differentiate between the total contact force at the small pin and at the large pin, we will make each interface a separate contact pair definition. This will produce two contact pair headings within the Results environment. Mouse


Mouse


Mouse


"Contact: Surface Contact"

Select the "Contact" pull-out menu and select the "Surface Contact" command.

Mouse


Mouse


Mouse



4/27/2011

35

Exercise E "Contact: Surface Contact"

Select the "Contact" pull-out menu and select the "Surface Contact" command.

"Mesh: Mesh: 3D Mesh Settings"


Mouse "Mesh model"

Move the slider to 90% of the default mesh size in the "Model Mesh Settings" dialog. Press the "Mesh model" button in the "Model Mesh Settings" dialog.








Mouse

Click on the surface at the end of the large pin.

"View: Navigate: Reverse View" Mouse "Setup: Loads: Force"

Select the "View" tab. Click on the options button to the bottom of "Orientation" button in the "Navigate" panel. Select "Reverse View" from the pull-out menu. Holding down the key, click on the surface at this end of the large pin. Select the "Setup" tab. Click on the "Force" button in the "Loads" panel.

-400


"X"

Select the "X" radio button.

"OK"


Mouse

Click on the surface at the end of the small pin.

"View: Navigate: Reverse View"

Select the "View" tab. Select "Reverse View" .

"Setup: Constraints: General Constraint”

Holding down the key, click on the surface at this end of the small pin. Select the "Setup" tab. Click on the "General Constraint" button in the "Constraints" panel.

"Fixed"


"OK"


Mouse

We must prevent Z-translation of the yoke and the large pin. Since these parts are symmetrical and we expect the yoke to deform symmetrically, the best place to constrain Z-translation is at the center plane of each part (i.e. the plane of symmetry). There would be no normal translation of nodes lying on the plane of Z-symmetry. Therefore, we can prevent Z-translation without inhibiting the natural deformation of the part or exaggerating its stiffness. For your convenience, the inside surfaces around the yoke slot and the cylindrical surface of the large pin have been split in half to provide edges in the middle of the parts.

36


4/27/2011

Exercise E

"View: Appearance: Mesh"

Mouse

"View: Navigate: Front View" "Selection: Shape: Rectangle" "Selection: Select: Edges"

Mouse


Select the "View" tab. Click on the options button to the bottom of "Visual Style" button in the "Appearance" panel. Select "Mesh" from the pull-out menu. Click on the "Load and Constraint" button in the "View" panel with the "Results Options" tab to hide the load and constraint symbols. Click on the options button to the bottom of "Orientation" button in the "Navigate" panel. Select "Front View" from the pull-out menu. Select the "Selection" tab. Make sure the "Rectangle" button is selected in the "Shape" panel. Also make sure the "Edges" button is selected in the "Select" panel. Click and drag the mouse to draw a selection rectangle enclosing the middle edges of the yoke slot and large pin in one operation. Keep the rectangle narrow so as not to accidentally select any edges on the face of the yoke. Select the "Setup" tab. Click on the "General Constraint" button in the "Constraints" panel. Note that the title bar of the boundary condition dialog should indicate (10 edges)

Mouse

Activate the "Tz" checkbox.

"OK"



Click on the options button to the bottom of "Orientation" button in the "Navigate" panel. Select "Top View" from the pull-out menu.

We must prevent rotation of the large pin and rotation of the yoke about the centerline of the small pin. This must be done using translational constraints, since brick elements have no rotational degrees of freedom and applying rotational constraints would have no effect. Another method would be to attach a set of beam elements and apply the rotational constraint to the beams. That is not necessary in this case. The cylindrical surfaces of the large pin and associated hole are split at the three o'clock and nine o'clock locations. If Y-translation constraints are applied to these edges (Y being the tangential direction), the undesired rotations will be prevented but the natural stretching of the yoke and bending of the pin will not be impeded. In this case, we are taking advantage of the fact that the top and bottom halves of the yoke assembly are symmetrical and there will theoretically be no nodal translations normal to the plane of Y-symmetry.

Mouse

Click and drag the mouse to draw a selection rectangle enclosing the nine o'clock and three o'clock edges of the large pin and hole in one operation.

Mouse



Click on the "General Constraint" button in the "Constraints" panel. Note that the title bar of the boundary condition dialog should indicate (12 edges)

Mouse

Activate the "Ty" checkbox.

"OK"

Click the "OK" button.

"View: Appearance: Shaded with Mesh"

Select the "View" tab. Click on the options button to the bottom of "Visual Style" button in the "Appearance" panel. Select "Shaded with Mesh" from the pull-out menu.


4/27/2011

37

Exercise E "View: Orientation: Isometric View"


Defining the Material Data Mouse Mouse Mouse

Click on the "Material" heading for Part 1 in the tree view. Holding down the key, click on the "Material" heading for Part 2 in the tree view. Holding down the key, click on the "Material" heading for Part 3 in the tree view.

Mouse


"Edit Material…"


"Steel (ASTM-A36)"


"OK"


Running the Analysis "Analysis: Analysis: Run Simulation"


Viewing the Results Rotate and zoom in or out as desired to inspect the von Mises stress distribution. The maximum stress is in the small pin. We will now selectively hide and show the parts to determine the maximum stress in the others. As we do, compare your results to those listed in the table at the end of the exercise description.

“Visibility”

“Visibility”

Right-click on the Part 2 heading in the tree view and select the “Visibility” command. The maximum stress result will change based on the remaining visible pars. The yoke stress is much higher than the large pin stress. Right-click on the Part 1 heading in the tree view and choose the “Visibility” command. Now, the legend shows the stress range in the large pin only.

Now, we will look at the displacement magnitude for the assembly and compare your results to the value shown in the table at the end of the exercise description.

38

Mouse


Mouse

Holding the key, also select the Part 2 heading in the tree view.


4/27/2011

Exercise E “Visibility” "Results Contours: Displacement: Displacement"

Right-click on one of the selected headings and choose the “Visibility” command. Select the "Results Contours" tab. Click on the "Displacement" button in the "Displacement" panel.

Finally, we will also check the total contact forces between the yoke and the two pins. Mouse "Contact Force…"


"OK" Mouse "Contact Force…" "OK"

Right-click on the heading for the contact pair between the large pin and the yoke in the tree view. Select the "Contact Force…" command. The total contact force is approximately -1,330 lbf. Right-click on the heading for the contact pair between the small pin and the yoke in the tree view. Select the "Contact Force…" command. The total contact force is approximately -1,179lbf. Press the "OK" button.

A completed archive with results is located in the "Exercise E\Results Archive" folder in the class directory or in the copy of the solutions folders on your computer.


4/27/2011

39

Exercise E

40


4/27/2011

Exercise F Concrete Platform Brick Elements Concepts that will be illustrated: • •

Setting up, running, and reviewing a modal analysis Setting up, running, and reviewing a critical buckling analysis

Objective:

Determine the first six (6) natural frequencies and their mode shapes for the concrete platform. Then, in a second design scenario, perform a critical buckling analysis. Solve for the first five (5) critical buckling modes (default setting).

Geometry:

Use the file Exercise F.SAT in the "Exercise F\Input File" folder of the class directory or in the copy of the solutions folders on your computer. Specify an absolute mesh size of 3 inches.

Constraints:

Fully fixed the bottom surface at each of the four legs.

Loading (for Critical Buckling Analysis): Standard gravity (-Z direction) 100,000 lbf normal force acting on top surface Element:

Brick

Material:

Concrete (High Strength)


4/27/2011

41

Exercise F Modal Results: Mode Number

Frequency (Hz)

1

10.8

2

12.0

3

17.6

4

20.8

5

36.7

6

42.8

Mode Number

Buckling Load Multiplier

1

170

2

200

3

229

4

236

5

293

Buckling Results:

Note:

42

The buckling safety factor is very high, indicating that this structure is clearly not susceptible to buckling due to geometric instability. Nonetheless, a linear static stress analysis would show that the applied load already produces tensile stresses exceeding the strength of non-reinforced concrete, which is typically less than 500 psi. So the structure would collapse due to material failure. This is stated to emphasize the importance of checking a design with regard to both static stress and buckling criteria.


4/27/2011

Exercise F

Solution Opening the Model Start Autodesk® Simulation, if it is not already running. Also, before starting this exercise, copy the Exercise F.step file from the "Exercise F\Input File" folder in the class directory – if they are not already on your computer. "Getting Started: Launch: Open" "STEP (*.sat)" "Exercise F.sat"

Click on the "Open" button in the Launch panel. Alternatively you select “Open” from the quick access toolbar or Application Menu. Select the "STEP STEP (*.sat)" option in the CAD Files section of the "Files of type:" drop-down box. Navigate to the location of the "Exercise F.sat" file on your computer and highlight it.

"Open"

Press the "Open" button.

Mouse "Linear: Natural Frequency (Modal)"

If the desired analysis type is not already set, press the menu button to the right of the analysis type field. Select the "Linear" pull-out menu, and choose the “Natural Frequency (Modal)" option.

"OK"




"Options"




3

Type "3" in the "Size" field.

"OK"


"Mesh model"


Adding Constraints "View: Navigate: Bottom View"

Select the "View" tab. Click on the options button to the bottom of "Orientation" button in the "Navigate" panel. Select "Bottom View" from the pull-out menu.




4/27/2011

43

Exercise F




Click on one of the small square surfaces at the four corners of the model. Holding down the key, select the remaining three small square surfaces. Select the "Setup" tab. Click on the "General Constraint" button in the "Constraints" panel.

"Fixed"


"OK"




Mouse Mouse

Defining the Material Data and Analysis Parameters Mouse "Concrete (High Strength)"

Double-click on the "Material" heading for Part 1 in the tree view. Expand the Concrete folder and then select "Concrete (High Strength)" within the Autodesk Simulation Material Library.

"OK"



Select the "Setup" tab. Click on the "Parameters" button in the "Model Setup" panel. Type "6" into the "Number of frequencies/modes to calculate" input field.

6


"OK"

Running the Modal Analysis

44

"Analysis: Analysis: Check Model" "Tools: Environments: FEA Editor"





4/27/2011

Exercise F

Viewing the Modal Results Note the frequency of the first vibration mode and compare it to the value in the modal results table near the end of the exercise description. We will advance through the remaining modes and compare each of these values to the table as well. "Captures: Start Animation" "Captures: Stop Animation" "Results Contours: Load Case Options: Next"

Click on the "Start Animation" button in the "Captures" panel. Click on the "Stop Animation" button in the "Captures" panel. Click on the "Next" button in the "Load Case Options" panel.

Repeat the preceding three steps until you've reviewed all six mode shapes and natural frequencies.

Creating a New Design Scenario for the Buckling Analysis "Tools: Environments: FEA Editor"

Select the "Tools" tab. Press the "FEA Editor" button in the "Environments" panel.

Mouse

Right-click on the "Analysis Type" heading in the tree view.

"Set Current Analysis Type: Linear: Critical Buckling Load" "Yes"

Select the "Set Current Analysis Type" pull-out menu and then the "Linear" pull-out menu. Choose the "Critical Buckling Load" option. Press the "Yes" button to create a new design scenario for this analysis.

Defining the Loads The loads for the buckling analysis include a surface force, which will be applied directly to the model's top surface, and a gravitational load, which will be defined within the analysis parameters screen. The selection mode should remain as point-selection of surfaces, as it was for the prior design scenario. "View: Orientation: Isometric View"


Mouse

Click on the large rectangular surface at the top of the platform.


Select the "Setup" tab. Click on the "Force" button in the "Loads" panel.

100000


"OK"



Click on the "Parameters" button in the "Model Setup" panel.

1

Type "1" into the "Acceleration multiplier" input field.

Mouse

Click on the "Gravity/Acceleration" tab.


4/27/2011

45

Exercise F

"Acceleration/Gravity Load"

Press the "Acceleration/Gravity Load" button to set the acceleration magnitude to equal standard gravity (386.4 in/sec2). Notice that the default direction (-Z) is correct for this model.

"OK"


Running the Critical Buckling Analysis Since the buckling model was copied from the completed modal analysis model, it is already solid meshed and has already been checked previously. The only reason to check the model again would be to verify the direction of the load on the top surface. For this phase of the exercise, we will skip checking the model. "Analysis: Analysis: Run Simulation"


Viewing the Buckling Results Note the load multiplier for the first buckling mode and compare it to the value in the buckling results table at the end of the exercise description. We will advance through the remaining modes and compare each of these values to the table as well. " Results Contours: Captures: Start Animation" "Captures: Stop Animation" "Results Contours: Load Case Options: Next"

Select the "Results Contours " tab. Click on the "Start Animation" button in the "Captures" panel. Click on the "Stop Animation" button in the "Captures" panel. Click on the "Next" button in the "Load Case Options" panel.

Repeat the preceding three steps until you've reviewed all five buckling multipliers and shapes.

A completed archive with results is located in the "Exercise F\Results Archive" folder in the class directory or in the copy of the solutions folders on your computer. The results archive includes a third design scenario (static stress analysis) showing tensile stresses in excess of the strength of non-reinforced concrete.

46


4/27/2011

Exercise G Infrared Detector Model Brick Elements Concepts that will be Illustrated: • • •

Defining internal heat generation Specifying a surface radiation load Running a steady-state heat transfer analysis

Objective:

Determine the temperature of an infrared detector that is submerged in liquid nitrogen and has a specified amount of heat generated by an electrical heater.

Geometry:

Use the file Exercise G.ach in the "Exercise G\Input File" folder copied to your computer from the class directory or Solutions CD. Mesh the model using an absolute mesh size of 0.5 mm.

The cold finger has been built as two parts. One part represents the portion that is submerged in the liquid nitrogen. Loading:

The bottom 25 mm of the finger has surface applied temperatures of -196°C. The top surface of the detector radiates to an ambient temperature of 27°C with a radiation function of 0.9. The heat generated by the electrical heater is 0.025 J/(mm3*s).

Element:

Brick Autodesk® Simulation Mechanical 2012 – Part 1 – Solutions Manual

4/27/2011

47

Exercise G

Materials:

Electrical heater and detector: Thermal conductivity = 1.00 J/(s*mm*°C) Cold finger: Thermal conductivity = 0.01 J/(s*mm*°C)

Results: Maximum Temperature 55.9 °C

48


4/27/2011

Exercise G

Solution Opening the Model Start Autodesk® Simulation, if it is not already running. Use the file, Exercise G.ach, in the "Exercise G\Input File" folder copied to your computer from the class directory or Solutions CD. "Getting Started: Launch: Open" "Autodesk Simulation Archive (*.ach)" "Exercise G.ach"

Click on the "Open" button in the Launch panel. Alternatively you select “Open” from the quick access toolbar or Application Menu. Select the "Autodesk Simulation Archive (*.ach)" option in the Autodesk Simulation Files section of the "Files of type:" drop-down box. Select the file "Exercise G.ach" in the "Exercise G\Input File" directory.

"Open"


"OK"

Select the location where you want the model to be extracted and press the "OK" button.



"Options…"


"Absolute mesh size"

Select the "Absolute mesh size" option in the "Type" drop-down box.

0.5


"OK"


"Mesh model"


Defining the Element and Material Data Mouse


Mouse


Mouse


"Edit Material…"


"Edit Properties"


1.00

Type "1.00" in the "Thermal conductivity" field.

"OK"

Press the "OK" button. Autodesk® Simulation Mechanical 2012 – Part 1 – Solutions Manual

4/27/2011

49

Exercise G "OK"


Mouse


Mouse


Mouse


"Edit Material…"


"Edit Properties"


0.01


"OK"


"OK"


Adding Loads and Constraints "Selection: Shape: Point"




Mouse Mouse Mouse

50

Click on one of the lower, half-cylindrical surfaces of the cold finger (-Y end). Holding down the key, click on the other lower, half-cylindrical surface of the cold finger. Holding down the key, click on the bottom surface of the cold finger.


Select the "Setup" tab. Click on the "Controlled Temperature” button in the "Thermal Loads" panel.

-196


"OK"


Mouse

Click and drag using the middle mouse button to rotate the view so that the top surface of the model can be seen (+Y end).

Mouse

Click on the surface at the top of the detector.

"Setup: Thermal Loads: Radiation"

Click on the "Radiation” button in the "Thermal Loads" panel.

0.9

Type "0.9" in the "Function" field.

27


"OK"


"Selection: Select: Parts"

Select the "Selection" tab. Click on the "Parts" button in the "Select" panel.

Mouse

Select Part 4 in the display area

"Setup: Thermal Loads: Internal Heat Generation"

Select the "Setup" tab. Click on the "Internal Heat Generation” button in the "Thermal Loads" panel.

0.025

Type "0.025" in the "Internal Heat Generation" field. Autodesk® Simulation Mechanical 2012 – Part 1 – Solutions Manual

4/27/2011

Exercise G "OK"


"Setup: Model Setup: Parameter"

Click on the "Parameters" button in the "Model Setup" panel.

Mouse

Click on the "Advanced" tab.

Mouse

Activate the "Perform" checkbox. Nonlinear iterations are required because radiation is a nonlinear function.

"OK"






Mouse

Click on the "Load and Constraint" button in the "View" panel with the "Results Options" tab to hide the load and constraint symbols.

Viewing the Results By default, the temperature profile will be displayed in the Results environment. It can be seen that the temperature at the top of the electric heater and throughout the detector is approximately 55.9°C and that this is the hottest part of the model.

A completed archive, with results, is located in the "Exercise G\Results Archive" folder copied to your computer from the class directory or Solutions CD.


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Exercise G

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Exercise H Transistor Case Model Brick Elements Concepts that will be Illustrated: • • •

Defining internal heat generation Specifying surface convection load Setting up and running a transient heat transfer analysis

Objective:

Perform a transient heat transfer analysis to determine the cooling effect of air blown over a transistor case.

Geometry:

Use the file, Exercise H.ach, in the "Exercise H\Input File" folder copied to your computer from the class directory or Solutions CD. Use the default mesh size.

Loading:

The free ends of the wires are 150°C. Apply convection to these surfaces at an ambient temperature of 150°C with a convection coefficient of 100 J/(s*°C*mm2). 25°C air is blown across the top surface of the case. At the beginning of the analysis, the convection coefficient is 2.5E-7 J/(s*°C*mm2). After 10 minutes, the convection coefficient is 2.5E-3 J/(s*°C*mm2).

Element:

Brick

Material:

Wires: Mass density = 8.933E-9 N*s2/mm/mm3 Thermal conductivity = 0.005 J/(s*mm*°C) Specific heat = 385,000 J/(N*s2/mm*°C) Case:

Mass density = 2.65E-10 N*s2/mm/mm3 Thermal conductivity = 0.0104 J/(s*mm*°C) Specific heat = 745,000 J/(N*s2/mm*°C)


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Exercise H Analysis Parameters:

Number of time steps = 20 Duration = 600 s

Load Curve: Time (s)

Factor

0

1

600

10000

Results:

Minimum Temperature at 10 Minutes 27.5 °C

54


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Exercise H

Solution Opening the Model Start Autodesk® Simulation, if it is not already running. Use the file, Exercise H.ach, in the "Exercise H\Input File" folder copied to your computer from the class directory or Solutions CD. "Getting Started: Launch: Open" "Autodesk Simulation Archive (*.ach)" "Exercise H.ach"

Click on the "Open" button in the Launch panel. Alternatively you select “Open” from the quick access toolbar or Application Menu. Select the "Autodesk Simulation Archive (*.ach)" option in the Autodesk Simulation Files section of the "Files of type:" drop-down box. Select the file "Exercise H.ach" in the "Exercise H\Input File" directory.

"Open"


"OK"

Select the location where you want the model to be extracted and press the "OK" button.



"Mesh model"

Press the "Mesh model" button on the "Model Mesh Settings" dialog to generate a mesh using the default settings.

Defining the Element and Material Data Mouse


Mouse "Edit Material…"

Holding down the key, click on the "Material" heading for Part 3 in the tree view. Holding down the key, click on the "Material" heading for Part 4 in the tree view. Right-click on one of the selected headings and choose the "Edit Material…" command.

"Edit Properties"


8.933e-9

Type "8.933e-9" in the "Mass density" field.

0.005


385000

Type "385000" in the "Specific heat" field.

"OK"

Press the "OK" button to close the "Element Material Specification" dialog.

Mouse Mouse


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Exercise H "OK" Mouse

Press the "OK" button to close the "Element Material Selection" dialog. Right-click on the "Material" heading for Part 2 in the tree view.

"Edit Material…"


"Edit Properties"


2.65e-10

Type "2.65e-10" in the "Mass Density" field.

0.0104

Type "0.0104" in the "Thermal Conductivity" field.

745000

Type "745000" in the "Specific heat" field. Press the "OK" button to close the "Element Material Specification" dialog. Press the "OK" button to close the "Element Material Selection" dialog.

"OK" "OK"


"View: Navigate: Top View" "Selection: Shape: Rectangle"

56

Select the "View" tab. Click on the options button to the bottom of "Orientation" button in the "Navigate" panel. Select "Top View" from the pull-out menu. Select the "Selection" tab. Make sure the "Rectangle" button is selected in the "Shape" panel.



Mouse

Draw a box enclosing the bottoms of all wires.



100

Type "100" in the "Temperature Independent Convection Coefficient" field.

150


"OK"


Mouse

Rotate the model slightly so that you can see the top surface of the transistor case.



Mouse

Click on the top surface of the transistor case.



2.5e-7

Type "2.5e-7" in the "Temperature Independent Convection Coefficient" field.

"1"

Select the "1" option in the "Load Curve" field.

"View / Edit Load Curve…"

Press the "View / Edit Load Curve…" button in the "Convection Coefficient" section.

1

Type "1" in the first row of the "Multiplier" column.


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Exercise H "Add Row"

Press the "Add Row" button.

600

Type "600" in the second row of the "Time" column.

10000

Type "10000" in the second row of the "Multiplier" column.

"OK"

Press the "OK" button to close the "Multiplier Table Editor."

25


"OK"


Mouse


"Edit Analysis Parameters…"

Select the "Edit Analysis Parameters…" command.

600

Type "600" in the first row of the "Time" column.

20

Type "20" in the first row of the "Steps" column.

"OK"



Select the "Analysis" tab. Click on the "Check Model" button in the "Analysis" panel. Once you are finished inspecting the model select the "Tools" tab. Press the "FEA Editor" button in the "Environments" panel.



Mouse

Click the "Toggle Load and Constraint Display" button to hide the load and constraint symbols if they are visible.

Viewing the Results "Results Contours: Load Case Options: Previous" or " Results Contours: Load Case Options: Next"

Click on the "Previous" and "Next" buttons in the "Load Case Options" panel to toggle through the load cases to find where the maximum temperature occurs.

A completed archive with results is located in the "Exercise H\Results Archive" folder in the class directory or in the copy of the solutions folders on your computer.


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Exercise H

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Exercise I Disk Brake Rotor Heat-up and Stress Brick Elements Concepts that will be illustrated: •

Applying a surface heat flux load

•

Using the temperature results from a transient heat transfer analysis as a thermal load in a linear static stress analysis

Objective:

Perform a transient heat transfer analysis to determine the temperature profile of the rotor during braking. Choose the time step with the maximum temperature differential and use these temperatures to determine the thermal stress via a second design scenario. Use mirror planes to observe a full-model representation.

Geometry:

Use the one-eight symmetry model file, Exercise I.step, in the "Exercise I\ Input File" folder copied to your computer from the class directory or Solutions CD. Use 50% of the default mesh size.

Thermal Loading:

Define a constant applied temperature of 100° F at the hub bore surface. Specify a heat flux of 4000 in.lbf/(s*in2). The heat flux will decrease linearly from the full magnitude to zero during the duration of the simulation event.

Constraints (Stress Analysis):

Apply the appropriate symmetry boundary conditions to each of the model's three planes of symmetry. Autodesk® Simulation Mechanical 2012 – Part 1 – Solutions Manual

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59

Exercise I

Element:

Brick

Material:

Thermal Analysis:

Mass density = 6.9e-4 lbf*s2/in/in3 Thermal conductivity = 6 in*lbf/(s*in*°F) Specific heat = 500,000 in*lbf/(lbf*s2/in*°F)

Stress Analysis:

Mass density = 6.9e-4 lbf*s2/in/in3 Modulus of Elasticity = 18e6 psi Poisson's Ratio 0.265 Thermal Coef. of Expansion = 7.2e-6 /° F

Thermal Analysis Parameters:

Duration = 20 s Number of Steps = 10 Default Nodal Temperature = 100° F

Thermal Load Curve:

Element Data (Stress Analysis):

Time (s)

Factor

0

1

20

0

Stress Free Reference Temperature = 80° F

Results:

60

Maximum Temperature at 12 Seconds

Maximum von Mises Stress

~321 °F

~23,316 psi


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Exercise I

Solution Starting the Model Start Autodesk® Simulation, if it is not already running. Use the file, Exercise I.step, in the "Exercise I\Input File" folder copied to your computer from the class directory or Solutions CD. "Getting Started: Launch: Open" "STEP (*.stp, *.ste, *.step)" "Exercise I.step" "Open"

Click on the "Open" button in the Launch panel. Alternatively you select “Open” from the quick access toolbar or Application Menu. Select the " STEP (*.stp, *.ste, *.step)" option in the CAD Files section of the "Files of type:" drop-down box. Navigate to the location of the "Exercise I.step" file on your computer and highlight it. Press the "Open" button.

Mouse "Thermal: Transient Heat Transfer"

Choose the option to "Use STEP file units" if it is not already selected and click the "OK" button. The original STEP file length unit is inches. Press the menu button to the right of the analysis type field. Select the "Thermal" pull-out menu, and choose the "Transient Heat Transfer" option.

"OK"


"Use STEP file units" "OK"

Meshing the Model "Mesh: Mesh: 3D Mesh Settings" Mouse "Mesh model"

Select the "Mesh" tab. Click on the "3D Mesh Settings" button in the "Mesh" panel. Move the slider towards the right to change the mesh size to "50%." Press the "Mesh model" button in the "Model Mesh Settings" dialog.

Applying the Thermal Loads Mouse

Click on the hub bore surface.


Select the "Setup" tab. Click on the "Controlled Temperature" button in the "Thermal Loads" panel.

100

Type "100" into the "Magnitude" field.

"OK"


Mouse "Setup: Thermal Loads: Heat Source"

Click on the annular surface of the rotor where the disk brake pad would be in contact. Select the "Setup" tab. Click on the ": Heat Source" button in the "Thermal Loads" panel.


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Exercise I 4000

Type "4000" into the "Magnitude" field.

1

Specify "1" in the "Load Curve" field.

"OK"


Defining the Thermal Material Data and Analysis Parameters Mouse

Double-click the "Material" heading under Part 1 in the tree view.

"Edit Properties"


6.9e-4 6 500000

Type "6.9e-4" into the "Mass density" field, press , enter "6" into the "Thermal conductivity" field, press , and enter "500000" into the "Specific heat" field. Press the "OK" button to dismiss the "Element Material Specification" dialog. Press the "OK" button to exit the "Element Material Selection" dialog. Click on the "Parameters" button in the "Model Setup" panel. Type "20" into the first row of the "Time" column in the Event table.

"OK" "OK" "Setup: Model Setup: Parameter" 20 10

Type "10" into the first row of the "Steps" column.

"Load Curves…"

Press the "Load Curves…" button.

"Insert Row"

Press the "Insert Row" button.

0 1 20 0

"OK" Mouse

Type "0" in the first row of the "Time" column, press , type "1" in the first row of the "Factor" column, press , type "20" in the second row of the "Time" column, press , and type "0" in the second row of the "Factor" column. Press the "OK" button to close the "Load Curve Input" dialog. Click on the "Options" tab of the "Analysis Parameters" dialog.

100

Type "100" into the "Default nodal temperature" field.

"OK"


Running the Thermal Analysis "Analysis: Analysis: Run Simulation"


"View: Appearance: Loads and Constraints "

Select the "View" tab. Click on the "Loads and Constraints" button in the "Appearance" panel.

The display will continue to be updated during the analysis as each time step computation is completed. Observe how the temperatures rise at first and then begin to decrease later in the braking cycle. Initially, 62


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Exercise I temperature results will be shown by default. We will identify the time step in which the maximum temperature is reached. Then, we will use mirror planes to visualize a full-model representation of the disk brake rotor.

Viewing the Results "Results Contours: Load Case Options: Previous" or " Results Contours: Load Case Options: Next" Mouse Mouse Mouse

Select the "Results Contours" tab. Click on the "Previous" and "Next" buttons in the "Load Case Options" panel to toggle through the load cases to find where the maximum temperature occurs. Select the "Plane 1 < XY >" heading under "Mirror Planes" in the tree view Holding the key, also select the "Plane 2 < YZ >" and "Plane 3 < XZ >" headings under "Mirror Planes." Right-click on one of the selected headings and choose the "Activate" command.

"View: Navigate: Enclose"

Select the "View" tab. Click on the "Enclose (Fit All)" button in the "Navigate" panel.

Mouse

Click and drag using the middle mouse button to dynamically rotate the model in the display window. Inspect the temperature profile as desired.

Creating a New Design Scenario for the Stress Analysis "Tools: Environments: FEA Editor"

Select the "Tools" tab. Press the "FEA Editor" button in the "Environments" panel.

Mouse


"Set Current Analysis Type: Linear: Static Stress with Linear Material Models "

Select the "Set Current Analysis Type" pull-out menu and then the "Linear" pull-out menu. Choose the "Static Stress with Linear Material Models" option. Press the "Yes" button to create a new design scenario for this analysis.

"Yes"

Compare the maximum temperature magnitude and the time of its occurrence to the values shown in the results table at the end of the exercise description. Note the time step number. It should be half of the time, in seconds, when the maximum temperature occurred because we were calculating one time step for each 2-second interval.

Defining the Constraints and Load The constraints consist of symmetry boundary conditions at the three planes of symmetry, which are consistent with the global Cartesian coordinate system planes. The only load for the stress analysis will be the temperatures from Design Scenario 1, which will be specified within the analysis parameters dialog.

"View: Navigate: Top View" "Selection: Shape: Rectangle"

Select the "View" tab. Click on the options button to the bottom of "Orientation" button in the "Navigate" panel. Select "Top View" from the pull-out menu. Select the "Selection" tab. Click on the "Rectangle" button in the "Shape" panel.


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Exercise I


Click and drag the mouse to draw a rectangle enclosing only the left edge of the model as currently displayed (-X end). Do not enclose any of the small slot surfaces. Select the "Setup" tab. Click on the "General Constraint" button in the "Constraints" panel.

"X Symmetry"


"OK"


Mouse


Click and drag the mouse to draw a rectangle enclosing only the bottom edge of the model as currently displayed (-Y end). Do not enclose any of the small slot surfaces. Select the "Setup" tab. Click on the "General Constraint" button in the "Constraints" panel.

"Y Symmetry"


"OK"


Mouse

"View: Navigate: Front View" Mouse Mouse


"Add: Surface Boundary Conditions…"

Select the "Add" pull-out menu and select the "Surface Boundary Conditions…" command.

"Z Symmetry"

Press the "Z Symmetry" button.

"OK"


"View: Orientation: Isometric View" "Setup: Model Setup: Parameter" 1

64

Select the "View" tab. Click on the options button to the bottom of "Orientation" button in the "Navigate" panel. Select "Front View" from the pull-out menu. Click and drag the mouse to draw a rectangle enclosing only the top edge of the model as currently displayed (-Z end).

Select the "View" tab. Click on the options button to the bottom of "Orientation" button in the "Navigate" panel. Select "Isometric View" from the pull-out menu. Click on the "Parameters" button in the "Model Setup" panel. Enter a value of "1" into the "Thermal" column for Index 1of the "Load Case Multipliers" table.

Mouse

Select the "Thermal/Electrical" tab.

"Transient analysis"

Using the provided pull-down menu, select the "Transient analysis" option in the "Source of nodal Temperatures" field.

"Browse…"

Press the "Browse…" button.

Mouse

Navigate to and select the file "ds.tto" located in the "Exercise I.ds_data\1" folder. This is the transient temperature output file from design scenario 1.

"Open"


"Specified"

Using the provided pull-down menu, select the "Specified" option in the "Time step from heat transfer analysis" field.

6

Type "6" into the "Time step" input field.

"OK"



4/27/2011

Exercise I

Defining the Material Properties The mass density will already be defined, since this was specified as part of the material's thermal properties. We must now add the elastic properties needed for stress analysis. Mouse

Double-click the "Material" heading under Part 1 in the tree view.

"Edit Properties"


18e6 0.265 7.2e-6

"OK" "OK"

Type "18e6" into the "Modulus of Elasticity" field, press , enter "0.265" into the "Poisson's Ratio" field, press , and enter "7.2e-6" into the "Thermal Coefficient of Expansion" field. We do not need to specify the shear modulus. This will be calculated automatically for isotropic materials. Press the "OK" button to dismiss the "Element Material Specification" dialog. Press the "OK" button to exit the "Element Material Selection" dialog.

Running the Static Stress Analysis "Analysis: Analysis: Run Simulation"


"View: Appearance: Loads and Constraints "

Select the "View" tab. Click on the "Loads and Constraints" button in the "Appearance" panel.

Once the model appears in the Results environment, compare the maximum von Mises stress to the value shown in the results table at the end of the exercise description. If desired, once again activate the mirror planes to visualize a full-model representation of the rotor and/or rotate the model to inspect the overall stress pattern. A completed archive is located in the "Exercise I\Results Archive" folder in the class directory or in the copy of the solutions folders on your computer.


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Exercise I

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Autodesk Simulation 2012 Part-1

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