Abaqus Analysis Intro-book

www.3ds.com | © Dassault Systèmes

Introduction to Abaqus/Standard and Abaqus/Explicit

R 6.12

About this Course Course objectives


Upon completion of this course you will be able to: Complete finite element models using Abaqus keywords. Submit and monitor analysis jobs. View and evaluate simulation results. Solve structural analysis problems using Abaqus/Standard and Abaqus/Explicit, including the effects of material nonlinearity, large deformation and contact.

Targeted audience Simulation Analysts

Prerequisites None

3 days

1

Day 1 Lesson 1

Workshop 1


Lesson 2

Workshop 2

Lesson 3

Workshop 3

Defining an Abaqus Model

Basic Input and Output

Linear Static Analysis

Linear Static Analysis of a Cantilever Beam: Multiple Load Cases

Nonlinear Analysis in Abaqus/Standard

Nonlinear Statics

Day 2 Lesson 4

Workshop 4


Lesson 5

Workshop 5

Lesson 6

Workshop 6

2

Multistep Analysis in Abaqus

Unloading Analysis

Constraints and Contact

Seal Contact

Introduction to Dynamics

Dynamics

Day 3 Lesson 7

Workshop 7


Lesson 8

Workshop 8

Lesson 9

Workshop 9

Using Abaqus/Explicit

Contact with Abaqus/Explicit

Quasi-Static Analysis in Abaqus/Explicit

Quasi-Static Analysis (Optional)

Combining Abaqus/Standard and Abaqus/Explicit

Import Analysis (Optional)

Additional Material Element Selection Criteria

Appendix 2

Contact Issues Specific to Abaqus/Standard

Appendix 3

Contact Issues Specific to Abaqus/Explicit


Appendix 1

3


Legal Notices The Abaqus Software described in this documentation is available only under license from Dassault Systèmes and its subsidiary and may be used or reproduced only in accordance with the terms of such license. This documentation and the software described in this documentation are subject to change without prior notice. Dassault Systèmes and its subsidiaries shall not be responsible for the consequences of any errors or omissions that may appear in this documentation. No part of this documentation may be reproduced or distributed in any form without prior written permission of Dassault Systèmes or its subsidiary. © Dassault Systèmes, 2012. Printed in the United States of America Abaqus, the 3DS logo, SIMULIA and CATIA are trademarks or registered trademarks of Dassault Systèmes or its subsidiaries in the US and/or other countries. Other company, product, and service names may be trademarks or service marks of their respective owners. For additional information concerning trademarks, copyrights, and licenses, see the Legal Notices in the Abaqus 6.12 Release Notes and the notices at: http://www.3ds.com/products/simulia/portfolio/product-os-commercial-programs.


Revision Status

4

Lecture 1

5/12

Updated for 6.12

Workshop 1

5/12

Updated for 6.12

Lecture 2

5/12

Updated for 6.12

Workshop 2

5/12

Updated for 6.12

Lecture 3

5/12

Updated for 6.12

Workshop 3

5/12

Updated for 6.12

Lecture 4

5/12

Updated for 6.12

Workshop 4

5/12

Updated for 6.12

Lecture 5

5/12

Updated for 6.12

Workshop 5

5/12

Updated for 6.12

Lecture 6

5/12

Updated for 6.12

Workshop 6

5/12

Updated for 6.12

Lecture 7

5/12

Updated for 6.12

Workshop 7

5/12

Updated for 6.12

Lecture 8

6/12

Minor edits

Workshop 8

5/12

Updated for 6.12

Lecture 9

5/12

Updated for 6.12

Workshop 9

5/12

Updated for 6.12

Appendix 1

5/12

Updated for 6.12

Appendix 2

5/12

Updated for 6.12

Appendix 3

5/12

Updated for 6.12

Notes

5

Notes

6

Lesson 1: Defining an Abaqus Model

L1.1


Lesson content:

Introduction Documentation Components of an Abaqus Model Details of an Abaqus Input File Abaqus Input Conventions Abaqus Output Example: Cantilever Beam Model Parts and Assemblies (optional) Workshop Preliminaries Workshop 1: Basic Input and Output (IA) Workshop 1: Basic Input and Output (KW)

Both interactive (IA) and keywords (KW) versions of the workshop are provided. Complete only one.

2 hours

L1.2

Introduction (1/14) SIMULIA is the Dassault Systèmes brand that delivers a scalable portfolio of Realistic Simulation solutions including The Abaqus product suite for Unified FEA


Multiphysics solutions for insight into challenging engineering problems Lifecycle management solutions for managing simulation data, processes, and intellectual property Headquartered in Providence, RI, USA R&D centers in Providence and in Velizy, France

7

L1.3

Introduction (2/14) Course preliminaries

This course introduces Abaqus/Standard and Abaqus/Explicit; basic knowledge of finite element analysis is assumed.


This course introduces concepts in a manner that gives users a working knowledge of Abaqus as quickly as possible—the lecture notes do not attempt to cover all the details of Abaqus completely.

There are several sources for additional information on the topics presented in this course: SIMULIA Home Page (available via the Internet at http://www.3ds.com/products/simulia/overview). Abaqus documentation—all usage details are covered in the user’s manuals. Extensive library of courses developed by SIMULIA on particular topics (course descriptions available at http://www.3ds.com/products/simulia/overview).

L1.4

Introduction (3/14)


Abaqus FEA is a suite of finite element analysis modules

8

L1.5

Introduction (4/14) Abaqus/CAE


Complete Abaqus Environment for modeling, managing, and monitoring Abaqus analyses, as well as visualizing results. Intuitive and consistent user interface throughout the system. Based on the concepts of parts and assemblies of part instances, which are common to many CAD systems. Parts can be created within Abaqus/CAE or imported from other systems as geometry (to be meshed in Abaqus/CAE) or as meshes. Built-in feature-based parametric modeling system for creating parts.

Abaqus/CAE main user interface

L1.6


Introduction (5/14) Analysis modules Abaqus/Standard and Abaqus/Explicit provide the user with two complementary analysis tools.* Abaqus/Standard’s capabilities: General analyses Static stress/displacement analysis: I. Rate-independent response II. Rate-dependent (viscoelastic/creep/viscoplastic) response Transient dynamic stress/displacement analysis Transient or steady-state heat transfer analysis Transient or steady-state mass diffusion analysis Steady-state transport analysis

Articulation of an automotive boot seal

Abaqus/CFD is a computational fluid dynamics analysis product; it is not discussed in this course.

9

L1.7

Introduction (6/14) Multiphysics: Thermal-mechanical analysis Structural-acoustic analysis


Linear piezoelectric analysis Thermal-electrical (Joule heating) analysis Thermal-electrical-structural analysis

Thermal stresses in an exhaust manifold

Fully or partially saturated pore fluid flow-deformation Fluid-structure interaction

L1.8

Introduction (7/14) Linear perturbation analyses

Harmonic excitation of a tire

Static stress/displacement analysis:


I. Linear static stress/displacement analysis II. Eigenvalue buckling load prediction Dynamic stress/displacement analysis: I. Determination of natural modes and frequencies II. Transient response via modal superposition III. Steady-state response resulting from harmonic loading » Includes alternative ―subspace projection‖ method for efficient analysis of large models with frequency-dependent properties (like damping) IV. Response spectrum analysis V. Dynamic response resulting from random loading

10

L1.9

Introduction (8/14) Abaqus/Explicit’s capabilities:

High-speed dynamics Quasi-static analysis


Coupled Eulerian-Lagrangian (CEL) Adaptive meshing using ALE Multiphysics Thermal-mechanical analysis I. Fully coupled: Explicit algorithms for both the mechanical and thermal responses II. Can include adiabatic heating effects Structural-acoustic analysis

Drop test of a cell phone

Fluid-structure interaction

L1.10

Introduction (9/14) Comparing Abaqus/Standard and Abaqus/Explicit


Abaqus/Standard

Abaqus/Explicit

A general-purpose finite element program. I. Nonlinear problems require iterations.

A general-purpose finite element program for explicit dynamics. I. Solution procedure does not require iteration.

Can solve for true static equilibrium in structural simulations.

Solves highly discontinuous high-speed dynamic problems efficiently.

Provides a large number of capabilities for analyzing many different types of problems. I. Nonstructural applications. II. Coupled or uncoupled response.

Coupled-field analyses include: I. Thermal-mechanical II. Structural-acoustic III. FSI

11

L1.11

Introduction (10/14) Interactive postprocessing

Abaqus/Viewer is the postprocessing module of Abaqus/CAE.


Available with Abaqus/CAE or as a stand-alone product

Can be used to visualize Abaqus results whether or not the model was created in Abaqus/CAE Provides efficient visualization of large models

Contour plot of an aluminum wheel hitting a curb in Abaqus/Viewer

L1.12


Introduction (11/14)

12

What is covered in this course Introduction to the analysis modules and interactive postprocessing Details of using Abaqus to solve a variety of structural analysis problems: Linear Static Analysis Workshop 1: Basic Input and Output— analysis of forces on a connecting lug Workshop 2: Linear Static Analysis of a Cantilever Beam—multiple load cases

L1.13

Introduction (12/14) Nonlinear Finite Element Analysis Workshop 3: Nonlinear Statics—large deformation analysis of a skew plate Simulations with Several Analysis Steps Workshop 4:Unloading analysis—unloading of a skew plate


Contact among Multiple Bodies Workshop 5: Seal Contact—compression analysis of a rubber seal.

L1.14

Introduction (13/14) Linear and Nonlinear Dynamic Analysis Workshop 6: Dynamics—frequency analysis and implicit and explicit free vibration analysis of a cantilever beam High-Speed Dynamics in Abaqus/Explicit


Workshop 7: Contact with Abaqus/Explicit— pipe whip problem

13

L1.15


Introduction (14/14) Quasi-Static Combined Analysis in Abaqus/Standard and Abaqus/Explicit Workshop 8 (Optional): Quasi-Static Analysis—deep drawing of a can bottom Workshop 9 (Optional): Import Analysis— springback analysis of formed can bottom Nonstructural applications—such as heat transfer, soils consolidation, and acoustics— are not discussed. All Abaqus analysis techniques use the same framework. The knowledge gained in this course will help in learning to use Abaqus for other applications.

L1.16


Documentation (1/7)

14

Primary reference materials Abaqus Analysis User’s Manual Abaqus/CAE User’s Manual Abaqus Example Problems Manual Abaqus Benchmarks Manual Abaqus Verification Manual Abaqus Keywords Reference Manual Abaqus User Subroutines Reference Manual Abaqus Theory Manual All documentation is available in HTML and PDF format The documentation is available through the Help menu on the main menu bar of Abaqus/CAE.

L1.17


Documentation (2/7) Additional reference materials Abaqus Installation and Licensing Guide (print version available) Installation instructions Abaqus Release Notes Explains changes since previous release Advanced lecture notes on various topics (print only) Tutorials Getting Started with Abaqus: Interactive Edition Getting Started with Abaqus: Keywords Edition Programming Scripting and GUI Toolkit manuals SIMULIA home page http://www.3ds.com/products/simulia/overview/

L1.18

Documentation (3/7)


HTML documentation The documentation for Abaqus is organized into a collection, with manuals grouped by function. Viewed through a web browser. Can search entire collection or individual manuals

15

L1.19

Documentation (4/7)


Searching the documentation Enter one or more search terms in the search field

Terms in the search field: Appear in any order May or may not be adjacent Appear within the proximity criterion (default is a single section)

The table of contents entry is highlighted The text frame displays the corresponding section

L1.20

Documentation (5/7)


Searching the documentation (cont’d) Use quotes to search for exact strings

16

L1.21

Documentation (6/7)


Advanced search Advanced search allows you to control the proximity criterion

L1.22

Documentation (7/7)


Advanced search (cont’d)

17

L1.23

Components of an Abaqus Model (1/6) The Abaqus analysis modules run as batch programs.

The primary input to the analysis modules is an input file, which contains options from element, material, procedure, and loading libraries.


These options can be combined in any reasonable way, allowing a tremendous variety of problems to be modeled.

The input file is divided into two parts: model data and history data. Model data

Geometric options—nodes, elements Material options Other model options

History data

Procedure options Loading options Output options

L1.24

Components of an Abaqus Model (2/6)


Model data—define the physical model

Discretized model geometry— nodes,elements

Material properties

18

L1.25

Components of an Abaqus Model (3/6) Model data ENCASTRE

pin

dof 2 fixed


Fixed constraints

v0

Initial conditions

L1.26

Components of an Abaqus Model (4/6)


History data—specify what happens to the model Types of analysis procedures—static, dynamic, soil, heat transfer, etc. Loadings Prescribed constraints Output requests— stresses, strains, reaction forces, contact pressure, etc.

ENCASTRE

X-symmetry Y-symmetry

19

L1.27

Components of an Abaqus Model (5/6) History subdivided into analysis steps

Steps are convenient subdivisions in an analysis history. Different steps can contain different analysis procedures—for example, static followed by dynamic.


Distinction between general and linear perturbation steps: General steps define a sequence of events that follow one another. I. The state of the model at the end of the previous general step provides the initial conditions for the start of the next general step. II. This is needed for any history-dependent analysis. Linear perturbation steps provide the linear response about the base state, which is the state at the end of the most recent general step.

L1.28

Components of an Abaqus Model (6/6) Example: Bow and arrow simulation


Step 3 = natural frequency extraction

Step 1 = pretension

Step 2 = pull back

Step 4 = dynamic release

Step 1: String the bow Step 2: Pull back on the bow string Step 3: Linear perturbation step to extract the natural frequencies of the system— has no effect on subsequent steps Step 4: Release the arrow

20

L1.29

Details of an Abaqus Input File (1/9) Option blocks


All data are defined in ―option blocks‖ that describe specific aspects of the problem definition, such as an element definition, etc. Together the option blocks build the model.

Property reference option block

Node option block

Model data

Material option block

Element option block

Contact option block History data

Analysis procedure option block

Boundary conditions option block

Initial conditions option block

Loading option block

Output request option block

L1.30

Details of an Abaqus Input File (2/9) Each option block begins with a keyword line (first character is *).

Data lines, if needed, follow the keyword line. Comment lines, starting with **, can be included anywhere.


All input lines have a limit of 256 characters (including blanks). Names can be up to 80 characters long and must begin with a letter. For example, the following would be a permissible name: nodes_at_the_top_of_the_block_next_to_the_gasket Note: Regardless of whether you specify only a file name, a relative path name, or a full path name, the complete name including the path can have a maximum of 80 characters .

21

L1.31

Details of an Abaqus Input File (3/9) Keyword lines

Begin with a single * followed directly by the name of the option. May include a combination of required and optional parameters, along with their values, separated by commas. www.3ds.com | © Dassault Systèmes

Example: A material option block defines a set of material properties. *MATERIAL, NAME=material name

keyword parameter parameter value

The first line in a material option block

L1.32

Details of an Abaqus Input File (4/9) Data lines

Define the bulk data for a given option; for example, element definitions.


A keyword line may have many data lines associated with it. Example: An element option block defines elements by specifying the element type, the element numbers, and the nodal connectivity. *ELEMENT, 560, 101, 564, 102, 572, 103, : :

TYPE=B21 102 103 104

keyword line data lines

node numbers (as required for beam B21 elements) element numbers

22

L1.33

Details of an Abaqus Input File (5/9) Example: The elastic material option block defines the type of elasticity model as well as the elastic material properties.


*ELASTIC, TYPE=ISOTROPIC 200.0E4, 0.30, 20.0 150.0E3, 0.35, 400.0 · ·

keyword line data lines temperature Poisson’s ratio modulus of elasticity

L1.34

Details of an Abaqus Input File (6/9) Ordering of option blocks

Each option block belongs in either the model data or the history data—one or the other—as specified in the user’s manual.


The ordering within the model data or history data is arbitrary, except for a few cases. Examples: *HEADING must be the first option in the input file. *ELASTIC, *DENSITY, and *PLASTIC are suboptions of *MATERIAL. As such, they must follow *MATERIAL directly. Suboptions have no name references of their own. Procedure options (*STATIC, *DYNAMIC, and *FREQUENCY, etc.) must follow *STEP to specify the analysis procedure for the step.

23

L1.35

Details of an Abaqus Input File (7/9) Node sets and element sets

Used for efficient cross-referencing.


Allow you to refer to a set all at once instead of each node or element individually.

Example: Node sets *NODE, NSET=TOPNODES 101, 0.345, 0.679, 0.223 102, 0.331, 0.699, 0.234 . . *BOUNDARY, TYPE=DISPLACEMENT TOPNODES, YSYMM

Node set TOPNODES contains nodes 101,102, ...

Boundary condition applied to all nodes in node set TOPNODES

L1.36

Details of an Abaqus Input File (8/9)


Example: Element sets

24

*ELEMENT, TYPE=B21, ELSET=SEATPOST 560, 101, 102, Element set SEATPOST 564, 102, 103 contains elements 560, . 564, ... . *BEAM SECTION, SECTION=PIPE, MATERIAL=STEEL, ELSET=SEATPOST These beam cross-section 0.12, 0.004 properties apply to all elements in element set wall thickness SEATPOST pipe radius

L1.37

Details of an Abaqus Input File (9/9) Including data from other files

Abaqus reads data from an include file as if the data were directly in the Abaqus input file. An include file can include any portion of an input file and can contain references to other include files. www.3ds.com | © Dassault Systèmes

Data must be in the same format as required for input file data—all rules that apply to input file syntax apply to data from included files. Example: Input file referencing an include file *HEADING *INCLUDE, INPUT=node_and_element_numbers.txt . . Contents of include file node_and_element_numbers.txt: *NODE, NSET=TOPNODES 101, 0.345, 0.679, 0.223 102, 0.331, 0.699, 0.234 *ELEMENT, TYPE=B21, ELSET=SEATPOST 560, 101, 102, 564, 102, 103

L1.38

Abaqus Input Conventions (1/8)


Units Abaqus uses no inherent set of units. It is the user’s responsibility to use consistent units. Example: I. N, kg, m, s or II. N, 103 kg, mm, s etc.

Common systems of consistent units

25

L1.39

Abaqus Input Conventions (2/8)


Example: Properties of mild steel at room temperature

Quantity

U.S. units

SI units

Conductivity

28.9 Btu/ft hr ºF

50 W/m ºC

2.4 Btu/in hr ºF Density

15.13 slug/ft3 (lbf s2/ft4)

7800 kg/m3

0.730 × 10−3 lbf s2/in4

0.282 lbm/in3 Elastic modulus

30 × 106 psi

207 × 109 Pa

Specific heat

0.11 Btu/lbm ºF

460 J/kg ºC

Yield stress

30 ×

207 × 106 Pa

103

psi

L1.40

Abaqus Input Conventions (3/8) Time measures

Abaqus keeps track of both total time in an analysis and step time for each analysis step.


Time is physically meaningful for some analysis procedures, such as transient dynamics.

26

Time is not physically meaningful for some procedures. In rate-independent, static procedures ―time‖ is just a convenient, monotonically increasing measure for incrementing loads.

L1.41

Abaqus Input Conventions (4/8) Coordinate systems

For input of initial nodal coordinates:


The default is a rectangular Cartesian system. Specify an alternative system using *SYSTEM or *NODE, SYSTEM=[RECTANGULAR | CYLINDRICAL | SPHERICAL]. Do not affect loading or output because automatically converted internally to the global rectangular Cartesian system.

L1.42

Abaqus Input Conventions (5/8) For nodal loads, boundary conditions, initial conditions:

The default is a rectangular Cartesian system. Specify an alternative system using the *TRANSFORM option.


These directions do not rotate with the material in large-displacement analyses. Example: Boundary conditions on a skew edge.

Use *TRANSFORM on these nodes with YSYMM boundary conditions

27

L1.43

Abaqus Input Conventions (6/8) For material point directions (directions associated with each element’s material or integration points): Affect input: Anisotropic material directions.


Default material directions for solid elements

Affect output: Stress/strain output directions. The default depends on the element type. I. Solid elements use a global rectangular Cartesian system. II. Shell and membrane elements use a projection of the global Cartesian system onto the surface.

Default material directions for shell and membrane elements

L1.44

Abaqus Input Conventions (7/8) Alternative local material coordinate systems can be specified using the *ORIENTATION option.

These directions rotate with the material in large-displacement analyses. 1


2

28

L1.45

Abaqus Input Conventions (8/8) Degrees of freedom

Primary solution variables at the nodes.


Available nodal degrees of freedom depend on the element type. Each degree of freedom is labeled with a number: 1=x-displacement, 2=y-displacement, 11=temperature, etc.

L1.46

Abaqus Output (1/8) Output

Four types of output are available:


Neutral binary output can be written to the output database (.odb) file using the *OUTPUT option and related suboptions. Printed output can be written to the data (.dat) file.

I. This is available only for Abaqus/Standard. Restart output can be written to the restart (.res) file using the *RESTART option for the purpose of conducting restart analyses (discussed in Lecture 4). Results (.fil) file output can be written for use with third-party postprocessors.

29

L1.47

Abaqus Output (2/8) Output to the output database file


The output database file is used by Abaqus/Viewer. An interface (API) is available in Python and C++ to use for external postprocessing (e.g., to add data to display in Abaqus/Viewer). Two types of output data: field and history data. Field data is used for model (deformed, contour, etc.) and X–Y plots: *OUTPUT, FIELD History data is used for X–Y plots: *OUTPUT, HISTORY

L1.48

Abaqus Output (3/8) Frequency of output for either type can be controlled


Field output can be requested according to

30

Number of increments (Abaqus/Standard only) *OUTPUT, FIELD, FREQUENCY=n

Every n increments

Number of intervals *OUTPUT, FIELD, NUMBER INTERVAL=n

At n evenly spaced time intervals

Time intervals *OUTPUT, FIELD, TIME INTERVAL=x

Every x units of time

Time points *OUTPUT, FIELD, TIME POINTS=t_out *TIME POINTS, name = t_out

At user-specified time points

L1.49

Abaqus Output (4/8) History output can be requested according to:

Number of increments *OUTPUT, HISTORY, FREQUENCY=n


Number of intervals (Abaqus/Standard only) *OUTPUT, HISTORY, NUMBER INTERVAL=n Time intervals *OUTPUT, HISTORY, TIME INTERVAL=x Time points (Abaqus/Standard only) *OUTPUT, HISTORY, TIME POINTS=t_out *TIME POINTS, name=t_out

L1.50

Abaqus Output (5/8) Requesting output to the output database file

If you have no output requests in your model, behavior depends on environment file (abaqus_v6.env) settings:


odb_output_by_default=ON: pre-selected output is written to the ODB I. This is the default setting; output depends on the procedure type odb_output_by_default=OFF: no ODB will be generated for your analysis Default output can be overridden using any of the following suboptions of *OUTPUT : *NODE OUTPUT *ELEMENT OUTPUT *ENERGY OUTPUT *CONTACT OUTPUT *INCREMENTATION OUTPUT (Abaqus/Explicit only)

31

L1.51

Abaqus Output (6/8) Pre-selected ODB output

Pre-selected output depends on the procedure type. For example, for a general static procedure:


The default field output requests are for: Stresses – S Total Strains – E (or logarithmic strain LE if NLGEOM is active) Plastic Strains – PE, PEEQ, and PEMAG Displacements and Rotations – U Reaction Forces and Moments– RF Concentrated (applied) Forces and Moments – CF Contact Stresses – CSTRESS Contact Displacements – CDISP The default history output request includes all model energies For other procedures, see the Abaqus Analysis User’s Manual

L1.52

Abaqus Output (7/8) Output to the printed output file

These options allow tabular data to be written to an ASCII file that can be read with a text editor. These options are available only for Abaqus/Standard.


Syntax:

32

*NODE PRINT *EL PRINT *ENERGY PRINT

L1.53

Abaqus Output (8/8) Output to the restart file

If a simulation stops prematurely, the restart data can be used to start the simulation from some intermediate point without repeating any calculations.


*RESTART, WRITE This option is discussed further in Lecture 4. Output to the results file The results file can be used by third-party postprocessors. *FILE OUTPUT *NODE FILE *EL FILE *ENERGY FILE

(This option required for Abaqus/Explicit only)

Select specific output variables

L1.54


Example: Cantilever Beam Model (1/11)

Finite element model using beam elements

boundary conditions

node number

element number

point load

33

L1.55


Example: Cantilever Beam Model (2/11) Abaqus input file with some annotations This line will appear on each page of output. Model data *HEADING CANTILEVER BEAM EXAMPLE UNITS IN MM, N, MPa *NODE 1, 0.0, 0.0 : 11, 200.0, 0.0 *NSET, NSET=END 11, *ELEMENT, TYPE=B21, ELSET=BEAMS 1, 1, 3 : 5, 9, 11 *BEAM SECTION, SECTION=RECT, ELSET=BEAMS, MATERIAL=MAT1 50.0, 5.0 ** Material from XXX testing lab *MATERIAL, NAME=MAT1 *ELASTIC elastic option block 2.0E5, 0.3 *BOUNDARY 1, ENCASTRE

heading option block

node option block

node set definition

element option block property reference option block comment line material option block fixed boundary condition option block

L1.56

Example: Cantilever Beam Model (3/11)


History data

34

*STEP APPLY POINT LOAD *STATIC *CLOAD 11, 2, -1200.0 *OUTPUT, FIELD, VARIABLE=PRESELECT, FREQUENCY=10 *OUTPUT, HISTORY, FREQUENCY=1 *NODE OUTPUT, NSET=END U, *EL PRINT, FREQUENCY=10 S, E *NODE FILE, FREQUENCY=5 U, *END STEP

The history data begin with the first *STEP option.

The history data end with the last *END STEP option.

L1.57

Example: Cantilever Beam Model (4/11) Property references using set names


*ELEMENT, TYPE=B21, ELSET=BEAMS 1, 1, 3 *BEAM SECTION, SECTION=RECT, ELSET=BEAMS, MATERIAL=MAT1 50.0, 5.0 *MATERIAL, NAME=MAT1 *ELASTIC 2.0E5, 0.3 The property reference *BEAM SECTION associates the element set BEAMS with the material definition MAT1. The option can also provide geometric information. In this case the cross-section type is rectangular (RECT); the width is 50.0, and the height is 5.0. All elements in a model must have an appropriate property reference. Solid elements reference *SOLID SECTION, shell elements reference *SHELL SECTION, etc.

L1.58

Example: Cantilever Beam Model (5/11) Material data *MATERIAL, NAME=MAT1 *ELASTIC 2.0E5, 0.3

material name Poisson’s ratio


elastic modulus

Definition for an isotropic linear elastic material Abaqus interprets the options following a *MATERIAL option as part of the same material option block until the next *MATERIAL option or the next nonmaterial property option, such as the *NODE option, is encountered. Options such as *ELASTIC are called suboptions and must be used in conjunction with the *MATERIAL option.

35

L1.59

Example: Cantilever Beam Model (6/11) Fixed boundary conditions *BOUNDARY 1, 1, 6 range of degrees of freedom or type of BC (pinned, encastre, symmetry, antisymmetry) node or node set


Fixed boundary condition constraints are applied to active DOFs. Prescribed nonzero boundary conditions can be included only in the history data. Abaqus activates only the necessary degrees of freedom at a node. Thus, for this two-dimensional example with only degrees of freedom 1, 2, and 6 active, the following are equivalent input data: 1, 1, or 1, or 1,

1, 2 6, 6 1, 6

The input file processor will issue a warning about inactive degrees of freedom.

ENCASTRE

L1.60

Example: Cantilever Beam Model (7/11) History definition *STEP APPLY POINT LOAD *STATIC

Begins the history data This line appears on every page of results Specifies a static analysis procedure


The *STEP option block can include a title of any length.

36

The procedure definition must be the first option after *STEP.

L1.61

Example: Cantilever Beam Model (8/11) Loading Definition of a concentrated load in the global negative 2-direction:

*CLOAD 11, 2, -1200.0


magnitude degree of freedom node or node set

Many distributed loadings are also available, including surface pressure, body forces, centrifugal and Coriolis loads, etc.

L1.62

Example: Cantilever Beam Model (9/11) Output requests


*OUTPUT, FIELD, VARIABLE=PRESELECT, FREQUENCY=10 *OUTPUT, HISTORY, FREQUENCY=1 *NODE OUTPUT, NSET=END U,

output to the output database file

In this case we have requested field output of a preselected set of the most commonly used output variables. We have also requested history output of displacements for the previously defined node set END. Since history output is usually requested at relatively high frequencies, the sets should be as small as possible. Each output request includes a FREQUENCY parameter. If the analysis requires many increments, the FREQUENCY parameter specifies how often results will be written.

37

L1.63

Example: Cantilever Beam Model (10/11) *EL PRINT, FREQUENCY=10 S, E *NODE FILE, FREQUENCY=5 U,

Printed output to the data file Output to the results file


Tabular output is printed to the data (.dat) file for visual inspection using the *EL PRINT option. In this case we have requested output of the stress (S) and strain (E) components. Binary output is written to the legacy Abaqus results (.fil) file using the *NODE FILE option; output is used for postprocessing in other postprocessors. In this case we have requested output of the displacement (U) components.

L1.64

Example: Cantilever Beam Model (11/11) End of step *END STEP

ends the analysis step

Each analysis step ends with the *END STEP option.


The final option in the input file is the *END STEP option for the final analysis step.

38

L1.65

Parts and Assemblies (1/4) The input file can be defined in terms of parts, part instances, and an assembly.

The same concept is employed when building a model in Abaqus/CAE.


Provides an inherent means of referring to distinct regions of the model. The user need not define separate sets for this purpose. Allows reuse of part definitions, which is valuable for creating large, complex models. Labels—node and element numbers, set names—need be unique only within the level in which they are defined.

L1.66

Parts and Assemblies (2/4) Defining parts

A part is defined by using the *PART and *END PART options, which must appear outside of the assembly definition. Each part must have a unique name.


Defining part instances A part instance is defined by using the *INSTANCE and *END INSTANCE options within the assembly definition. Each part instance must have a unique name. Defining an assembly The assembly is defined by using the *ASSEMBLY and *END ASSEMBLY options. Only one assembly can be defined in a model. Additional sets and surfaces, as well as constraints and rigid body definitions, must appear in the assembly definition.

39

L1.67

Parts and Assemblies (3/4) Example assembly input file *HEADING ... *PART, NAME=Tire

Node, element, section, set, and surface definitions


*END PART *PART, NAME=Rim

Node, element, section, set, and surface definitions *END PART ... *ASSEMBLY, NAME=Tire_and_rim *INSTANCE, NAME=I_Tire, PART=Tire

set and surface definitions (optional) *END INSTANCE *INSTANCE, NAME=I_Rim, PART=Rim

set and surface definitions (optional)

... *MATERIAL, NAME=Rubber *AMPLITUDE *INITIAL CONDITIONS *PHYSICAL CONSTANTS ... *STEP *STATIC *BOUNDARY I_Rim.101, 1, 3, 0.0 *CLOAD I_Tire.514, 2, 1000.0 *OUTPUT, HISTORY, FREQUENCY=10 *NODE OUTPUT, NSET=Output RF, CF *END STEP

*END INSTANCE

Additional set and surface definitions *NSET, NSET=Output I_Tire.514, I_Tire.520 I_Rim.101, I_Rim.102 *END ASSEMBLY

L1.68

Parts and Assemblies (4/4) Node labels for parts and the assembly

node label: I_Rim.101


node label: 101

Part: Rim

node label: 514

node label: I_Tire.514 Part: Tire

40

Assembly: Tire_and_rim

Workshop Preliminaries (1/2)

L1.69


1. Objectives a. When you complete this exercise you will be able to extract all the files necessary to complete the demonstrations and workshops associated with this course 2. Workshop file setup (option 1: installation via plug-in) a. From the main menu bar, select Plug-ins→Tools →Install Courses. b. In the Install Courses dialog box: i. Specify the directory to which the files will be written. ii. Chooses the course(s) for which the files will be extracted. iii. Click OK.

5 minutes

Workshop Preliminaries (2/2)

L1.70

3. Workshop file setup (option 2: manual installation) a. Find out where the Abaqus release is installed by typing abqxxx whereami where abqxxx is the name of the Abaqus execution procedure on your system. It can be defined to have a different name. For example, the command for the 6.12–1 release might be aliased to abq6121.


This command will give the full path to the directory where Abaqus is installed, referred to here as abaqus_dir. b. Extract all the workshop files from the course tar file by typing UNIX: Windows NT:

abqxxx perl abaqus_dir/samples/course_setup.pl abqxxx perl abaqus_dir\samples\course_setup.pl

c. The script will install the files into the current working directory. You will be asked to verify this and to choose which files you wish to install. Choose y for the appropriate lecture series when prompted. Once you have selected the lecture series, type q to skip the remaining lectures and to proceed with the installation of the chosen workshops.

5 minutes

41

Workshop 1: Basic Input and Output (IA)


1.

L1.71

Interactive version. Choose either the interactive Workshop tasks or keywords version of this workshop. 1. Use some of the Abaqus utility programs. 2. Open the online documentation, and search for useful information. 3. Use the online documentation to determine the syntax for various options. 4. Complete the model of a connecting lug. 5. Submit analyses a few different ways (datacheck only, complete analysis, interactive, and batch submission). 6. View the results using Abaqus/Viewer. 7. Become familiar with the contents of the printed output files. 8. Modify the model, and understand the changes to the results.

1 hour

Workshop 1: Basic Input and Output (KW)


1.

Keywords version. Choose either the interactive Workshop tasks or keywords version of this workshop. 1. Use some of the Abaqus utility programs. 2. Open the online documentation, and search for useful information. 3. Use the online documentation to determine the syntax for various options. 4. Add some details to an existing input file to complete the model of a connecting lug. 5. Submit analyses a few different ways (datacheck only, complete analysis, interactive, and batch submission). 6. View the results using Abaqus/Viewer. 7. Become familiar with the contents of the printed output files. 8. Modify the model, and understand the changes to the results.

1 hour

42

L1.72

Notes

43

Notes

44

Lesson 2: Linear Static Analysis

L2.1


Lesson content:

Linear and Nonlinear Procedures Linear Static Analysis and Multiple Load Cases Multiple Load Case Usage Examples Workshop 2: Linear Static Analysis of a Cantilever Beam (IA) Workshop 2: Linear Static Analysis of a Cantilever Beam (KW)


2 hours

L2.2

Linear and Nonlinear Procedures (1/6) A fundamental concept in Abaqus is the division of the problem history into steps.

A step is any convenient phase of the history—a thermal transient, a creep hold, a dynamic transient, etc.


In its simplest form a step can be just a static analysis of a load change from one magnitude to another.

For each step the user chooses an analysis procedure. This choice defines the type of analysis to be performed during the step: static stress analysis, dynamic stress analysis, eigenvalue buckling, transient heat transfer analysis, etc. The rest of the step definition consists of load, boundary, and output request specifications.

45

L2.3

Linear and Nonlinear Procedures (2/6) For example, consider the bow and arrow in the figure. The analysis consists of four steps:


Step 1: Pretension the bowstring (static response).

Step 3 = Natural frequency extraction

Step 2: Pull back the string (static response). Step 3: Investigate the natural frequencies of the loaded system. Step 4: Release the bowstring (dynamic response).

L2.4

Linear and Nonlinear Procedures (3/6) Abaqus distinguishes between two kinds of analysis procedures:

General analysis procedures* Response can be linear or nonlinear.


Steps that use general procedures are known as general steps. The starting point for each general step is the state of the model at the end of the last general step. Linear perturbation procedures Response can only be linear. The linear perturbation is about a base state, which can be either the initial or the current configuration of the model. I. Response prior to reaching the base state can be nonlinear. Steps that use linear procedures are known as perturbation steps.

* Abaqus/Explicit offers only general analysis steps.

46

L2.5

Linear and Nonlinear Procedures (4/6)


General procedures

Linear procedures

Static

Static

Direct cyclic

Eigenvalue buckling

Dynamic (transient)

Linear dynamics

Implicit

Natural frequency extraction

Explicit

Transient modal dynamics

Heat transfer

Steady-state dynamics

Mass diffusion

Response spectrum analysis

Coupled-field analysis

Random response analysis

Thermal-mechanical Thermal-electrical Thermal-electrical-structural Pore fluid diffusion/stress

L2.6

Linear and Nonlinear Procedures (5/6)


Default amplitude references Different defaults for different analysis procedures AMPLITUDE=RAMP for procedures without natural time scales: *STATIC *HEAT TRANSFER, STEADY STATE *COUPLED TEMPERATURE-DISPLACEMENT, STEADY STATE *SOILS, STEADY STATE *COUPLED THERMAL-ELECTRICAL, STEADY STATE *STEADY STATE TRANSPORT

47

L2.7


Linear and Nonlinear Procedures (6/6) AMPLITUDE=STEP for procedures with natural time scales: *DYNAMIC *VISCO *HEAT TRANSFER (transient) *COUPLED TEMPERATURE-DISPLACEMENT (transient) *DYNAMIC TEMPERATURE-DISPLACEMENT, EXPLICIT *COUPLED THERMAL-ELECTRICAL (transient) *SOILS, CONSOLIDATION *STEADY STATE DYNAMICS Note: Frequency domain proceduresamplitude *RANDOM RESPONSE references define load versus frequency. *MODAL DYNAMIC A nonzero displacement boundary condition prescribed in an explicit dynamic procedure (*DYNAMIC, EXPLICIT) must refer to an amplitude option.

L2.8


Linear Static Analysis and Multiple Load Cases (1/5)

48

Static analysis is the only procedure that can be performed as either a general or perturbation step: General step: response can be linear or nonlinear *STEP *STATIC Perturbation step: linear response *STEP, PERTURBATION *STATIC One advantage of static linear perturbation steps is that they can consider multiple load cases. A load case defines a set of loads and boundary conditions and may contain the following: Concentrated and distributed loads Boundary conditions (may change from load case to load case) Inertia relief In addition to the static linear perturbation procedure, multiple load cases can also be used for steadystate dynamic (SSD) analysis (either direct or SIM-based modal analysis). For SIM-based SSD analysis, base motion may also be defined as part of a load case.

L2.9


Linear Static Analysis and Multiple Load Cases (2/5) Multiple load cases are advantageous when analyzing components that are subjected to many different types of loads. Common in many industries. For example, an aircraft experiences different loads during take-off, climb, cruise, descent, landing, and taxiing. Each load case is applied independently. If the stiffness of the structure is assumed constant over all phases of the loading history (linear assumption), a multiple load case analysis is an attractive option to determine the loading envelope. When investigating the linear static response of a structure subjected to distinct sets of loads and boundary conditions, it is convenient (and generally more efficient) to use multiple load cases in a single linear perturbation step rather than using multiple general or linear perturbation steps.

L2.10



Multiple *LOAD CASE

Multiple *STEP, PERTURBATION

Element loop (stiffness/ multiple RHS)

Element loop (stiffness/ single RHS)

Primary factorization (w/ possibly multiple small factorizations)

Factorization (or read factorized matrix from .fct file)

Simultaneous backsubstitution

Backsubstitution

Element loop (simultaneous recovery)

Element loop (recovery)

Next *STEP

49

L2.11



Example: An agricultural implement This is an agricultural implement attached to and towed behind a tractor through a 3-point hitch. The purpose of the hitch is to transfer towing loads to the implement, but otherwise to allow the implement to float and move more or less independently of the tractor.

L2.12



Three load cases The connection is very flexible and the loads on the implement are not well defined, but are a combination of many different types of loads.

Forward Loads

Lateral Loads

Vertical Loads

50

L2.13

Multiple Load Case Usage (1/7)


Example: Bending of a plate

*Step, perturbation *Static *Load Case, name="Bending A" *Boundary right, 1, 6 *Cload left, 3, 1. *End Load Case *Load Case, name="Bending B" *Boundary left, 1, 6 *Cload right, 3, 1. *End Load Case *End Step

Node set right

Bending A Node set left

Bending B

L2.14

Multiple Load Case Usage (2/7) Basic rules • Load case names (Load Case, name=...) must be unique.

• • •

Load options specified outside of load cases apply to all load cases. Base state boundary conditions propagate to all load cases. Rules for using OP=NEW:


•

•

If used anywhere in a load case step, must be used everywhere in that step. • If used on any BOUNDARY in a load case step, propagated boundary conditions will be removed in all load cases. LOAD CASE options do not propagate.

51

L2.15


Multiple Load Case Usage (3/7) Changing boundary conditions from load case to load case No performance penalty when boundary conditions change only in magnitude. Limit number of boundary conditions that change location from load case to load case. Depending on number and distribution of boundary conditions that change location, multiple load case analysis may be significantly slower than equivalent multiple step analysis (very problem dependent). If in doubt, run datacheck analyses (multiple step versus multiple load case) and compare solver information in data (.dat) file (e.g., memory requirements, number of floating point operations, etc.).

L2.16



52

Problem size Combination of number of degrees of freedom and number of load cases determines “problem size.” Multiple load case analyses may require more: Memory than equivalent multiple step analyses (e.g., all right-hand sides must be kept in core during backsubstitution). Disk space (element and nodal databases). If necessary, “spread” load cases over several steps to reduce memory/disk usage per step. Worst case: Resort to multiple perturbation steps (again, compare solver information in data (.dat) file).

L2.17



Output Output requested per step (not per load case) Available for the output database (.odb) and data (.dat) files For the output database file: All output variables for a load case are mapped to a frame. I. Similar to the way increments are mapped to frames. Frame contains load case name. Field output only (no history output).

L2.18



Postprocessing with Abaqus/Viewer Operations on entire frames supported For selected frames, can create: Linear combinations (e.g., linear combination of load cases) Min/Max envelope (e.g., find max stresses over all load cases)

53

L2.19


Mises stress: Bending B


Mises stress: Bending A

Max value of Mises stress over both frames

L2.20

Examples (1/5) Square plate benchmark


Model

54

# nodes/edge

# variables (# dof)

1

101

61206

2

201

242406

3

501

1506006

4

751

3384006 Changing BCs

Number of load cases: 8 and 16 *Static, perturbation Changing boundary condition locations at corners Default output

L2.21

Examples (2/5) Performance results: Total CPU time

4.E+04

CPU time (sec)


8 Steps 8 Load Cases

3.E+04

16 Steps 16 Load Cases

2.E+04

1.E+04

0.E+00 0.E+00

1.E+06

2.E+06

3.E+06

4.E+06

Number of variables

L2.22

Examples (3/5) Performance: Details for 751  751 model


Relative CPU time—3.4 M variable case 8 steps/8 load Cases

16 steps/16 load cases

Solver

7.52

14.3

Total

5.04

7.48

55

L2.23

Examples (4/5) Modify 501  501 model 8 load cases Boundary conditions on opposite edges changing per load case


Relative total CPU time: ~0.153 (multiple load case ~6.6 slower!) Watch number and location of changing boundary conditions!

Changing BCs

L2.24

Examples (5/5)


A steady-state dynamics example : Chassis-bracket mobility analysis Number of variables: 534,000 Number of equations: 483,000 Number of load cases: 60 *Steady-state dynamics, direct (10 frequency points) Output: U (output database)

CPU time (sec)

56

60 steps (projected based on 1 step)

60 load cases

Solver

1290  60 = 77,400

1990 (39 faster)

Total

1965  60 = 117,600

11,600 (10 faster)

Workshop 2: Linear Static Analysis of a Cantilever Beam (IA) 1.

L2.25

Interactive version. Choose either the interactive or keywords version of this workshop.

Objectives


a. When you complete this workshop you will be able to i. Run a linear static analysis using a perturbation procedure with linear load cases ii. Combine load case results and create envelope plots

Force-X

Force-Y

Force-Z

Moment-X

Moment-Y

Moment-Z

1 hour

Workshop 2: Linear Static Analysis of a Cantilever Beam (KW) 1.

L2.26

Keywords version. Choose either the interactive or keywords version of this workshop.

Objectives


a. When you complete this workshop you will be able to i. Run a linear static analysis using a perturbation procedure with linear load cases ii. Combine load case results and create envelope plots

Force-X

Force-Y

Force-Z

Moment-X

Moment-Y

Moment-Z

1 hour

57

58

Notes

59

Notes

60

Lesson 3: Nonlinear Analysis in Abaqus

L3.1


Lesson content:

Nonlinearity in Structural Mechanics Equations of Motion Nonlinear Analysis Using Implicit Methods Nonlinear Analysis Using Explicit Methods Input File for Nonlinear Analysis Status File Message File Output from Nonlinear Cantilever Beam Analysis Workshop 3: Nonlinear Statics (IA) Workshop 3: Nonlinear Statics (KW)


2 hours

L3.2

Nonlinearity in Structural Mechanics (1/4)


Sources of nonlinearity Material nonlinearities: Nonlinear elasticity Plasticity Material damage Failure mechanisms Etc.

Some examples of material nonlinearity Note: material dependencies on temperature or field variables do not introduce nonlinearity if the temperature or field variables are predefined.

61

L3.3



Boundary nonlinearities: Contact problems I. Boundary conditions change during the analysis. II. Extremely discontinuous form of nonlinearity.

An example of self-contact: Example Problem 1.1.17, Compression of a jounce bumper

L3.4



Geometric nonlinearities: Large deflections and deformations Large rotations Structural instabilities (buckling) Preloading effects

An example of geometric nonlinearity: elastomeric keyboard dome

62

L3.5

Nonlinearity in Structural Mechanics (4/4) Typical nonlinear problems have all three forms of nonlinearity.

Must include the nonlinear terms in the equations.


Generally, the nonlinear equations for each degree of freedom are coupled.

L3.6

Equations of Motion (1/3) Static equilibrium The basic statement of static equilibrium is that the internal forces exerted on the nodes I (resulting from the element stresses) and external forces P acting at every node must balance:

P  I  0.


Dynamic equilibrium The major difference between a static and a dynamic analysis is the inclusion of the inertial forces Mu :

P  I  Mu, where M is the mass and u is the acceleration of the structure. This equation is simply Newton’s second law of motion.

63

L3.7


Equations of Motion (2/3)

L3.8


Equations of Motion (3/3) Incremental solution schemes Nonlinear problems are generally solved in an incremental fashion. For a static problem a fraction of the total load is applied to the structure and the equilibrium solution corresponding to the current load level is obtained. I. The load level is then increased (i.e., incremented) and the process is repeated until the full load level is applied. For a dynamic problem, the equations of motion are numerically integrated in time using discrete time increments. There are two techniques available to solve the nonlinear equations: Implicit method Can solve for both static and dynamic equilibrium. Requires direct solution of a set of matrix equations to obtain the state at the end of the increment. I. Iteration required. This method is used by Abaqus/Standard and is the focus of this lecture. Explicit method Can only solve the dynamic equilibrium equations. I. Can perform quasi-static simulations, however.

The state at the end of the increment depends solely on the state at the beginning of the increment I. No iteration required. This method is used by Abaqus/Explicit and will be discussed in a later lecture.

64

L3.9


Nonlinear Analysis Using Implicit Methods (1/4) Steps, increments, and iterations Analysis steps The load history for a simulation consists of one or more steps. Increments An increment is part of a step. I. In static problems the total load applied in a step is broken into smaller increments so that the nonlinear solution path may be followed. II. In dynamic problems the total time period is broken into smaller increments to integrate the equations of motion. Iterations An iteration is an attempt at finding the equilibrium solution in an increment. Newton-Raphson method Abaqus/Standard uses an incremental-iterative solution technique based on the Newton-Raphson method. The method is unconditionally stable (any size increments can be used). Accuracy in dynamic analysis is affected by the increment size. Each increment usually requires several iterations to achieve convergence, and each step is usually made up of several increments.

L3.10


Nonlinear Analysis Using Implicit Methods (2/4)

Additional iterations not shown

Two convergence criteria: 1 Small residuals

Residual Internal force

1

2

Small corrections

2

Correction

65

L3.11



Equilibrium in a mesh: summary 1. Apply an increment of load or time. 2. Iterate until the sum of all forces acting on each node is small (statics) or is equal to the inertia force (dynamics). 3. Update the state once equilibrium has been satisfied. 4. Go back to Step 1, and apply the next increment.

L3.12



66

Automatic time incrementation Abaqus automatically adjusts the size of the increments so that nonlinear problems are solved easily and efficiently. Heuristic algorithm (based on many years of experience). In static problems it is based on number of iterations required to converge. Convergence is easily achieved: I. increase increment size Convergence difficult or divergence occurs: I. cut back increment size Otherwise: I. maintain same increment size Tip: For highly nonlinear problems, it is recommended that the initial time increment be chosen as a small fraction (e.g., 10%) of the total step time. In implicit dynamic problems, automatic time incrementation is based on the convergence behavior of the Newton iterations and the accuracy of the time integration. Details of the time increment control algorithm depend on the type of dynamic application. Discussed further later. Automatic time incrementation works very well. You should not change it without good reason.

L3.13

Nonlinear Analysis Using Explicit Methods Abaqus/Explicit solves for dynamic equilibrium using an explicit solution scheme:


u

(t )

 M 1  ( P  I )

(t ) .

Velocity and displacements at time t + Dt updated explicitly. Solution is trivial: Diagonal mass matrix. No iteration is required! Conditionally stable. The size of the time increment must be controlled. Explicit methods generally require many, many more time increments than implicit methods for the same problem. Discontinuous forms of nonlinearity (e.g., contact) are handled more easily by explicit methods. Explicit dynamics will be discussed further later.

L3.14


Input File for Nonlinear Analysis (1/4) *HEADING CANTILEVER BEAM EXAMPLE--LARGE DISPLACEMENT *NODE 1, 0., 0. 11, 200., 0. *NGEN 1, 11, 1 *ELEMENT, TYPE=B21 1, 1, 3 *ELGEN, ELSET=BEAMS 1, 5, 2, 1 *BEAM SECTION, SECTION=RECT, ELSET=BEAMS, MATERIAL=MAT1 50., 5. *MATERIAL, NAME=MAT1 *ELASTIC 2.E5, .3 *BOUNDARY 1, 1, 6 *AMPLITUDE, NAME=RAMP 0.0, 0.0, 0.5, 0.3, 1.0, 1.0 *RESTART, WRITE,FREQ=3

67

L3.15

Input File for Nonlinear Analysis (2/4)

*STEP, NLGEOM=YES, INC=25 time period of the step

APPLY POINT LOAD *STATIC


suggested initial time increment

0.1, 1.0, 0.001, 1.0

major differences from linear input minimum time increment maximum time increment

*CLOAD, AMPLITUDE=RAMP 11, 2, -1200. *END STEP

major differences from linear input

previously defined amplitude function for load application

L3.16

Input File for Nonlinear Analysis (3/4) Step and procedure input


*STEP, NLGEOM=YES, INC=25

68

NLGEOM=YES: include all nonlinear geometric effects due to: Large deflections, rotations, deformation. Preloading (initial stresses). Load stiffness. If the above effects are not significant, the predicted response of the model will be the same as with NLGEOM=NO (default), but the analysis will be more expensive. INC=25: maximum of 25 increments allowed in this example: Abaqus will stop if the maximum number of increments is reached before the total load is applied. Keeps the analysis from running too long—you can always restart. Default value is 100.

L3.17

Input File for Nonlinear Analysis (4/4)


Similar time incrementation data exist for all transient procedures, which include *STATIC *DYNAMIC *HEAT TRANSFER *VISCO *COUPLED TEMPERATURE-DISPLACEMENT *SOILS *MODAL DYNAMIC (allows only fixed time incrementation) *COUPLED THERMAL-ELECTRIC Physical or normalized time scale depending on the procedure and the presence of time-dependent or rate-dependent behavior.

L3.18

Status File Status (.sta) file


Summarizes how analysis proceeds—shows automatic time incrementation at work. You can check the status file while the job is running. One line written after each successful increment.

SUMMARY OF JOB INFORMATION: STEP INC ATT SEVERE EQUIL TOTAL DISCON ITERS ITERS ITERS 1 1 1 1 1 1

1 2 3 4 5 6

1 1 1 1 1 1

0 0 0 0 0 0

3 2 2 2 4 2

3 2 2 2 4 2

TOTAL TIME/ FREQ 0.100 0.200 0.350 0.575 0.913 1.00

STEP TIME/LPF

0.100 0.200 0.350 0.575 0.913 1.00

INC OF TIME/LPF

DOF IF MONITOR RIKS

0.1000 0.1000 0.1500 0.2250 0.3375 0.08750

THE ANALYSIS HAS COMPLETED SUCCESSFULLY

69

L3.19

Message File


Message (.msg) file includes: All convergence controls: The *CONTROLS option overrides defaults—not usually needed Details about certain model features: Nondefault model features Use of NLGEOM Frequency of restart writes All iteration details Useful troubleshooting information: Locations of highest residuals Locations of excessive deformation Locations of contact changes Solver messages Numerical singularities These indicate that so many digits are lost during linear equation solution that the results are not reliable. The most common cause is an unconstrained rigid body mode in a static stress analysis. Zero pivots These occur during linear equation solution when there is a force term but no corresponding stiffness. Common causes are unconstrained rigid body modes and overconstrained degrees of freedom. Negative eigenvalues Negative eigenvalues indicate that the stiffness matrix is not positive definite. For example, a buckling load may have been exceeded.

L3.20

Output from Nonlinear Cantilever Beam Analysis (1/17)

S T E P

1

S T A T I C

A N A L Y S I S


APPLY POINT LOAD

70

AUTOMATIC TIME CONTROL WITH A SUGGESTED INITIAL TIME INCREMENT OF AND A TOTAL TIME PERIOD OF THE MINIMUM TIME INCREMENT ALLOWED IS THE MAXIMUM TIME INCREMENT ALLOWED IS LINEAR EQUATION SOLVER TYPE

0.100 1.00 1.000E-03 1.00

DIRECT SPARSE

CONVERGENCE TOLERANCE PARAMETERS FOR FORCE CRITERION FOR RESIDUAL FORCE FOR A NONLINEAR PROBLEM CRITERION FOR DISP. CORRECTION IN A NONLINEAR PROBLEM INITIAL VALUE OF TIME AVERAGE FORCE AVERAGE FORCE IS TIME AVERAGE FORCE ALTERNATE CRIT. FOR RESIDUAL FORCE FOR A NONLINEAR PROBLEM CRITERION FOR ZERO FORCE RELATIVE TO TIME AVRG. FORCE CRITERION FOR RESIDUAL FORCE WHEN THERE IS ZERO FLUX CRITERION FOR DISP. CORRECTION WHEN THERE IS ZERO FLUX CRITERION FOR RESIDUAL FORCE FOR A LINEAR INCREMENT FIELD CONVERSION RATIO CRITERION FOR ZERO FORCE REL. TO TIME AVRG. MAX. FORCE CRITERION FOR ZERO DISP. RELATIVE TO CHARACTERISTIC LENGTH

5.000E-03 1.000E-02 1.000E-02 2.000E-02 1.000E-05 1.000E-05 1.000E-03 1.000E-08 1.00 1.000E-05 1.000E-08

L3.21



CONVERGENCE TOLERANCE PARAMETERS FOR MOMENT CRITERION FOR RESIDUAL MOMENT FOR A NONLINEAR PROBLEM CRITERION FOR ROTATION CORRECTION IN A NONLINEAR PROBLEM INITIAL VALUE OF TIME AVERAGE MOMENT AVERAGE MOMENT IS TIME AVERAGE MOMENT ALTERNATE CRIT. FOR RESIDUAL MOMENT FOR A NONLINEAR PROBLEM CRITERION FOR ZERO MOMENT RELATIVE TO TIME AVRG. MOMENT CRITERION FOR RESIDUAL MOMENT WHEN THERE IS ZERO FLUX CRITERION FOR ROTATION CORRECTION WHEN THERE IS ZERO FLUX CRITERION FOR RESIDUAL MOMENT FOR A LINEAR INCREMENT FIELD CONVERSION RATIO CRITERION FOR ZERO MOMENT REL. TO TIME AVRG. MAX. MOMENT

VOLUMETRIC STRAIN COMPATIBILITY TOLERANCE FOR HYBRID SOLIDS AXIAL STRAIN COMPATIBILITY TOLERANCE FOR HYBRID BEAMS TRANS. SHEAR STRAIN COMPATIBILITY TOLERANCE FOR HYBRID BEAMS SOFT CONTACT CONSTRAINT COMPATIBILITY TOLERANCE FOR P>P0 SOFT CONTACT CONSTRAINT COMPATIBILITY TOLERANCE FOR P=0.0 CONTACT FORCE ERROR TOLERANCE FOR CONVERT SDI=YES DISPLACEMENT COMPATIBILITY TOLERANCE FOR DCOUP ELEMENTS ROTATION COMPATIBILITY TOLERANCE FOR DCOUP ELEMENTS

5.000E-03 1.000E-02 1.000E-02 2.000E-02 1.000E-05 1.000E-05 1.000E-03 1.000E-08 1.00 1.000E-05

1.000E-05 1.000E-05 1.000E-05 5.000E-03 0.100 1.00 1.000E-05 1.000E-05

EQUILIBRIUM WILL BE CHECKED FOR SEVERE DISCONTINUITY ITERATIONS

L3.22



TIME INCREMENTATION CONTROL PARAMETERS: FIRST EQUILIBRIUM ITERATION FOR CONSECUTIVE DIVERGENCE CHECK EQUILIBRIUM ITERATION AT WHICH LOG. CONVERGENCE RATE CHECK BEGINS EQUILIBRIUM ITERATION AFTER WHICH ALTERNATE RESIDUAL IS USED MAXIMUM EQUILIBRIUM ITERATIONS ALLOWED EQUILIBRIUM ITERATION COUNT FOR CUT-BACK IN NEXT INCREMENT MAXIMUM EQUILIB. ITERS IN TWO INCREMENTS FOR TIME INCREMENT INCREASE MAXIMUM ITERATIONS FOR SEVERE DISCONTINUITIES MAXIMUM CUT-BACKS ALLOWED IN AN INCREMENT MAXIMUM DISCON. ITERS IN TWO INCREMENTS FOR TIME INCREMENT INCREASE CUT-BACK FACTOR AFTER DIVERGENCE 0.2500 CUT-BACK FACTOR FOR TOO SLOW CONVERGENCE 0.5000 CUT-BACK FACTOR AFTER TOO MANY EQUILIBRIUM ITERATIONS 0.7500 CUT-BACK FACTOR AFTER TOO MANY SEVERE DISCONTINUITY ITERATIONS 0.2500 CUT-BACK FACTOR AFTER PROBLEMS IN ELEMENT ASSEMBLY 0.2500 INCREASE FACTOR AFTER TWO INCREMENTS THAT CONVERGE QUICKLY 1.500 MAX. TIME INCREMENT INCREASE FACTOR ALLOWED 1.500 MAX. TIME INCREMENT INCREASE FACTOR ALLOWED (DYNAMICS) 1.250 MAX. TIME INCREMENT INCREASE FACTOR ALLOWED (DIFFUSION) 2.000 MINIMUM TIME INCREMENT RATIO FOR EXTRAPOLATION TO OCCUR 0.1000 MAX. RATIO OF TIME INCREMENT TO STABILITY LIMIT 1.000 FRACTION OF STABILITY LIMIT FOR NEW TIME INCREMENT 0.9500 TIME INCREMENT INCREASE FACTOR BEFORE A TIME POINT 1.000 GLOBAL STABILIZATION CONTROL IS NOT USED

4 8 9 16 10 4 50 5 50

71

L3.23


PRINT OF INCREMENT NUMBER, TIME, ETC., EVERY

RESTART FILE WILL BE WRITTEN EVERY

3

1

INCREMENTS

INCREMENTS


THE MAXIMUM NUMBER OF INCREMENTS IN THIS STEP IS

25

LARGE DISPLACEMENT THEORY WILL BE USED LINEAR EXTRAPOLATION WILL BE USED CHARACTERISTIC ELEMENT LENGTH

40.0

DETAILED OUTPUT OF DIAGNOSTICS TO DATABASE REQUESTED PRINT OF INCREMENT NUMBER, TIME, ETC., TO THE MESSAGE FILE EVERY

1

INCREMENTS

EQUATIONS ARE BEING REORDERED TO MINIMIZE WAVEFRONT COLLECTING MODEL CONSTRAINT INFORMATION FOR OVERCONSTRAINT CHECKS COLLECTING STEP CONSTRAINT INFORMATION FOR OVERCONSTRAINT CHECKS

L3.24


INCREMENT

1 STARTS. ATTEMPT NUMBER

1, TIME INCREMENT


CONVERGENCE CHECKS FOR EQUILIBRIUM ITERATION

72

0.100 1

AVERAGE LARGEST LARGEST LARGEST

FORCE 1.251E+03 TIME AVG. FORCE RESIDUAL FORCE -4.637E+03 AT NODE 11 INCREMENT OF DISP. -1.84 AT NODE 11 CORRECTION TO DISP. -1.84 AT NODE 11 FORCE EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE.

1.251E+03 DOF 1 DOF 2 × 0.005 DOF 2


MOMENT 7.200E+03 TIME AVG. MOMENT 7.200E+03 RESIDUAL MOMENT 28.8 AT NODE 9 DOF 6 INCREMENT OF ROTATION -1.382E-02 AT NODE 11 DOF 6 CORRECTION TO ROTATION -1.382E-02 AT NODE 11 DOF 6 × 0.005 ROTATION CORRECTION TOO LARGE COMPARED TO ROTATION INCREMENT . 36 CONVERGENCE CHECKS FOR EQUILIBRIUM ITERATION 2


FORCE 37.8 TIME AVG. FORCE RESIDUAL FORCE 0.215 AT NODE 11 INCREMENT OF DISP. -1.84 AT NODE 11 CORRECTION TO DISP. -1.007E-02 AT NODE 11 FORCE EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE.

37.8 DOF 1 DOF 2 DOF 1


MOMENT 7.200E+03 TIME AVG. MOMENT RESIDUAL MOMENT -0.346 AT NODE 5 INCREMENT OF ROTATION -1.382E-02 AT NODE 11 CORRECTION TO ROTATION 5.898E-07 AT NODE 11 THE MOMENT EQUILIBRIUM EQUATIONS HAVE CONVERGED

7.200E+03 × 0.005 DOF 6 DOF 6 36 DOF 6

6.25

× 0.005 0.2

L3.25




3


FORCE 37.7 TIME AVG. FORCE RESIDUAL FORCE -2.281E-06 AT NODE 11 INCREMENT OF DISP. -1.84 AT NODE 11 CORRECTION TO DISP. 3.349E-05 AT NODE 11 THE FORCE EQUILIBRIUM EQUATIONS HAVE CONVERGED



MOMENT 7.200E+03 TIME AVG. MOMENT RESIDUAL MOMENT 1.523E-05 AT NODE 7 INCREMENT OF ROTATION -1.382E-02 AT NODE 11 CORRECTION TO ROTATION 3.637E-07 AT NODE 11 THE MOMENT EQUILIBRIUM EQUATIONS HAVE CONVERGED

7.200E+03 × 0.005 DOF 6 DOF 6 36 DOF 6

× 0.005 0.2

ITERATION SUMMARY FOR THE INCREMENT: 3 TOTAL ITERATIONS, OF WHICH 0 ARE SEVERE DISCONTINUITY ITERATIONS AND 3 ARE EQUILIBRIUM ITERATIONS. TIME INCREMENT COMPLETED STEP TIME COMPLETED

0.100 0.100

, ,

FRACTION OF STEP COMPLETED TOTAL TIME COMPLETED

4 or fewer iterations (do this again and Dt can increase)

0.100 0.100

L3.26


INCREMENT


1, TIME INCREMENT



0.100

no increase

1


FORCE 75.6 TIME AVG. FORCE RESIDUAL FORCE 0.861 AT NODE 11 INCREMENT OF DISP. -1.84 AT NODE 11 CORRECTION TO DISP. -2.013E-02 AT NODE 11 FORCE EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE.




1.080E+04 DOF 6 DOF 6 DOF 6

73

L3.27





2

FORCE 144. TIME AVG. FORCE RESIDUAL FORCE -6.928E-05 AT NODE 11 INCREMENT OF DISP. -1.84 AT NODE 11 CORRECTION TO DISP. 1.701E-04 AT NODE 11 THE FORCE EQUILIBRIUM EQUATIONS HAVE CONVERGED



MOMENT 1.600E+04 TIME AVG. MOMENT 1.160E+04 RESIDUAL MOMENT 1.218E-04 AT NODE 7 DOF 6 INCREMENT OF ROTATION -1.382E-02 AT NODE 11 DOF 6 CORRECTION TO ROTATION 1.804E-06 AT NODE 11 DOF 6 THE MOMENT EQUILIBRIUM EQUATIONS HAVE CONVERGED 2 consecutive increments with TIME INCREMENT MAY NOW INCREASE TO 0.150 4 or fewer iterations: Dt = 1.5Dtold ITERATION SUMMARY FOR THE INCREMENT: 2 TOTAL ITERATIONS, OF WHICH 0 ARE SEVERE DISCONTINUITY ITERATIONS AND 2 ARE EQUILIBRIUM ITERATIONS. TIME INCREMENT COMPLETED STEP TIME COMPLETED

0.100 0.200

, ,


0.200 0.200

L3.28


INCREMENT


1, TIME INCREMENT



74

0.150

Dt = 1.5Dtold

1


FORCE 133. TIME AVG. FORCE RESIDUAL FORCE 3.02 AT NODE 11 INCREMENT OF DISP. -2.75 AT NODE 11 CORRECTION TO DISP. -3.764E-02 AT NODE 11 FORCE EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE.

105. DOF 1 DOF 2 DOF 1



1.613E+04 DOF 6 DOF 6 DOF 6

L3.29




2


FORCE 252. TIME AVG. FORCE RESIDUAL FORCE -7.965E-04 AT NODE 11 INCREMENT OF DISP. -2.75 AT NODE 11 CORRECTION TO DISP. 5.629E-04 AT NODE 11 THE FORCE EQUILIBRIUM EQUATIONS HAVE CONVERGED



MOMENT 2.798E+04 TIME AVG. MOMENT RESIDUAL MOMENT 7.461E-04 AT NODE 7 INCREMENT OF ROTATION -2.070E-02 AT NODE 11 CORRECTION TO ROTATION 5.967E-06 AT NODE 11 THE MOMENT EQUILIBRIUM EQUATIONS HAVE CONVERGED TIME INCREMENT MAY NOW INCREASE TO 0.225

1.706E+04 DOF 6 DOF 6 DOF 6

ITERATION SUMMARY FOR THE INCREMENT: 2 TOTAL ITERATIONS, OF WHICH 0 ARE SEVERE DISCONTINUITY ITERATIONS AND 2 ARE EQUILIBRIUM ITERATIONS.

TIME INCREMENT COMPLETED STEP TIME COMPLETED

0.150 0.350

, ,


RESTART INFORMATION WRITTEN IN STEP

1

AFTER INCREMENT

4 or fewer

0.350 0.350 3

L3.30


INCREMENT


1, TIME INCREMENT



0.225

Dt = 1.5Dtold

1





MOMENT 4.853E+04 TIME AVG. MOMENT RESIDUAL MOMENT -344. AT NODE 9 INCREMENT OF ROTATION -4.477E-02 AT NODE 11 CORRECTION TO ROTATION -1.371E-02 AT NODE 11 MOMENT EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE.

2.493E+04 DOF 6 DOF 6 DOF 6

75

L3.31




2


FORCE 281. TIME AVG. FORCE RESIDUAL FORCE 0.349 AT NODE 11 INCREMENT OF DISP. -5.94 AT NODE 11 CORRECTION TO DISP. -9.348E-03 AT NODE 11 THE FORCE EQUILIBRIUM EQUATIONS HAVE CONVERGED



MOMENT 4.847E+04 TIME AVG. MOMENT RESIDUAL MOMENT -2.26 AT NODE 5 INCREMENT OF ROTATION -4.471E-02 AT NODE 11 CORRECTION TO ROTATION 5.353E-05 AT NODE 11 THE MOMENT EQUILIBRIUM EQUATIONS HAVE CONVERGED TIME INCREMENT MAY NOW INCREASE TO 0.338

2.491E+04 DOF 6 DOF 6 DOF 6


0.225 0.575

, ,


0.575 0.575

L3.32


INCREMENT


1, TIME INCREMENT



76

0.338

Dt = 1.5Dtold

1



2.638E+03 DOF 1 DOF 2 DOF 2


MOMENT 1.049E+05 TIME AVG. MOMENT RESIDUAL MOMENT -4.323E+03 AT NODE 9 INCREMENT OF ROTATION -0.107 AT NODE 11 CORRECTION TO ROTATION -4.037E-02 AT NODE 11 MOMENT EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE.

4.090E+04 DOF 6 DOF 6 DOF 6


2


FORCE 556. TIME AVG. FORCE RESIDUAL FORCE 16.6 AT NODE 11 INCREMENT OF DISP. -14.2 AT NODE 11 CORRECTION TO DISP. -8.119E-02 AT NODE 11 FORCE EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE.



MOMENT 1.044E+05 TIME AVG. MOMENT RESIDUAL MOMENT -42.5 AT NODE 5 INCREMENT OF ROTATION -0.107 AT NODE 11 CORRECTION TO ROTATION 1.095E-04 AT NODE 11 THE MOMENT EQUILIBRIUM EQUATIONS HAVE CONVERGED

4.080E+04 DOF 6 DOF 6 DOF 6

L3.33





FORCE RESIDUAL FORCE INCREMENT OF DISP. CORRECTION TO DISP. FORCE EQUILIBRIUM NOT

3

559. TIME AVG. FORCE -28.9 AT NODE 11 -14.1 AT NODE 11 0.130 AT NODE 11 ACHIEVED WITHIN TOLERANCE.


AVERAGE MOMENT 1.153E+05 TIME AVG. MOMENT 4.299E+04 LARGEST RESIDUAL MOMENT 3.833E-02 AT NODE 5 DOF 6 LARGEST INCREMENT OF ROTATION -0.106 AT NODE 11 DOF 6 LARGEST CORRECTION TO ROTATION 1.112E-03 AT NODE 11 DOF 6 ESTIMATE OF ROTATION CORRECTION -1.004E-06 MOMENT EQUILIB. ACCEPTED BASED ON SMALL RESIDUAL AND ESTIMATED CORRECTION

AVERAGE LARGEST LARGEST LARGEST AVERAGE LARGEST LARGEST LARGEST

The residual is within tolerance, but the rotation CONVERGENCE CHECKS FOR EQUILIBRIUM ITERATION 4 correction is too large. The estimate of the rotation of the FORCE next iteration is acceptably small. FORCE 1.053E+03 correction TIME AVG. 354. RESIDUAL FORCE 1.092E-03 AT NODE 11 DOF 2 INCREMENT OF DISP. -14.1 AT NODE 11 DOF 2 CORRECTION TO DISP. -2.092E-04 AT NODE 11 DOF 2 THE FORCE EQUILIBRIUM EQUATIONS HAVE CONVERGED MOMENT 1.153E+05 TIME AVG. MOMENT RESIDUAL MOMENT -2.910E-02 AT NODE 7 INCREMENT OF ROTATION -0.106 AT NODE 11 CORRECTION TO ROTATION -1.875E-06 AT NODE 11 THE MOMENT EQUILIBRIUM EQUATIONS HAVE CONVERGED

4.299E+04 DOF 6 DOF 6 DOF 6


0.338 0.913

, ,


0.913 0.913

L3.34


INCREMENT


1, TIME INCREMENT




8.750E-02

1

FORCE 641. TIME AVG. FORCE RESIDUAL FORCE 74.0 AT NODE 11 INCREMENT OF DISP. -3.55 AT NODE 11 CORRECTION TO DISP. -0.180 AT NODE 11 FORCE EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE.


AVERAGE MOMENT 1.179E+05 TIME AVG. MOMENT 5.547E+04 LARGEST RESIDUAL MOMENT -99.4 AT NODE 5 DOF 6 LARGEST INCREMENT OF ROTATION -2.702E-02 AT NODE 11 DOF 6 LARGEST CORRECTION TO ROTATION 5.186E-04 AT NODE 11 DOF 6 ESTIMATE OF ROTATION CORRECTION -1.594E-05 MOMENT EQUILIB. ACCEPTED BASED ON SMALL RESIDUAL AND ESTIMATED CORRECTION CONVERGENCE CHECKS FOR EQUILIBRIUM ITERATION

2


FORCE 695. TIME AVG. FORCE RESIDUAL FORCE -0.505 AT NODE 11 INCREMENT OF DISP. -3.53 AT NODE 11 CORRECTION TO DISP. 1.386E-02 AT NODE 11 THE FORCE EQUILIBRIUM EQUATIONS HAVE CONVERGED



MOMENT 1.309E+05 TIME AVG. MOMENT RESIDUAL MOMENT 8.716E-02 AT NODE 7 INCREMENT OF ROTATION -2.687E-02 AT NODE 11 CORRECTION TO ROTATION 1.493E-04 AT NODE 11 THE MOMENT EQUILIBRIUM EQUATIONS HAVE CONVERGED

5.764E+04 DOF 6 DOF 6 DOF 6

77

L3.35



8.750E-02, 1.00 ,



RESTART INFORMATION WRITTEN IN STEP

1

AFTER INCREMENT

1.00 1.00 6

THE ANALYSIS HAS BEEN COMPLETED

ANALYSIS SUMMARY: TOTAL OF 6 0 15 15 15 Look here for warning 0 and error messages. 1 Search the message 0 file and data file to 0 determine the causes 3 of these messages. 0 0 0 0

INCREMENTS CUTBACKS IN AUTOMATIC INCREMENTATION ITERATIONS INCLUDING CONTACT ITERATIONS IF PRESENT PASSES THROUGH THE EQUATION SOLVER OF WHICH INVOLVE MATRIX DECOMPOSITION, INCLUDING DECOMPOSITION(S) OF THE MASS MATRIX REORDERING OF EQUATIONS TO MINIMIZE WAVEFRONT ADDITIONAL RESIDUAL EVALUATIONS FOR LINE SEARCHES ADDITIONAL OPERATOR EVALUATIONS FOR LINE SEARCHES WARNING MESSAGES DURING USER INPUT PROCESSING WARNING MESSAGES DURING ANALYSIS ANALYSIS WARNINGS ARE NUMERICAL PROBLEM MESSAGES ANALYSIS WARNINGS ARE NEGATIVE EIGENVALUE MESSAGES ERROR MESSAGES

L3.36



Visual diagnostics in Abaqus/Viewer

A similar display is given for rotational degrees of freedom

Toggle on to see the locations in the model where the largest residuals and displacement increments and corrections occur.

78

L3.37

Workshop 3: Nonlinear Statics (IA)



1. Workshop tasks 1. Define alternate material directions corresponding to the skew angle of the plate. 2. Analyze the deformation of the skew plate with and without considering nonlinear geometric effects. 3. Include plasticity in the material definition. 4. View the results using Abaqus/Viewer.

1 hour

Workshop 3: Nonlinear Statics (KW)



1. Workshop tasks 1. Define alternate material directions corresponding to the skew angle of the plate. 2. Analyze the deformation of the skew plate with and without considering nonlinear geometric effects. 3. Include plasticity in the material definition. 4. View the results using Abaqus/Viewer.

L3.38

1 hour

79

80

Notes

81

Notes

82

Lesson 4: Multistep Analysis in Abaqus

L4.1

Lesson content:


Multistep Analyses Restart Analysis in Abaqus Workshop 4: Unloading Analysis (IA) Workshop 4: Unloading Analysis (KW)


1 hour

L4.2

Multistep Analyses (1/9)


It is often convenient to divide an Abaqus analysis into multiple steps so that loads or boundary conditions can be applied in steps or output requests can be modified. Usually there are several general analysis steps. Response can be linear or nonlinear General steps can be punctuated by perturbation steps. Response is linear perturbation about a base state What is the ―base state?‖ The base state is the current state of the model at the end of the last general analysis step (prior to the linear perturbation step).

83

L4.3


Multistep Analyses (2/9) Possible step sequences General step followed by another general step General step continues from where previous general step ended Loads are considered total loads General step followed by perturbation step Perturbation response about preceding general step Loads are considered perturbation loads Perturbation step followed by another perturbation step These act as a series of independent steps in the analysis Some ordering rules apply (e.g., frequency extraction before modal dynamics) Perturbation step followed by a general step General step continues from end of previous general step (if any) The perturbation response is ignored in the general step that follows

L4.4



84

Some comments on following a general step with a perturbation step Perturbation step results are perturbations about the base state. If geometric nonlinearity is included in the general analysis upon which a linear perturbation study is based, stress stiffening or softening effects and load stiffness effects (from pressure and other follower forces) are included in the linear perturbation analysis. Eigenvalue buckling analyses are an exception: I. The base state in a buckling analysis always includes the effects of stresses from previous general steps even if geometric nonlinearity was not considered. The contact state of the most recent general step is enforced in the perturbation step.

L4.5



Vibrating cable simulation—Approach 1

Step

Action

Step type

1

Stretch cable

General analysis step with NLGEOM

2

Frequency extraction

Linear perturbation step performed about the ending condition of Step 1 (base state)

3

More stretching

General analysis step continuing from the ending condition of Step 1 (last nonlinear step)

4

Another frequency extraction

Linear perturbation step performed about the ending condition of Step 3 (new base state)

L4.6



Vibrating cable simulation—Approach 2 The history could be modified to be a series of separate general analysis steps to obtain the eigenfrequency of the lowest mode:

Step

Action

1

Stretch cable

2

Deflect cable in the transverse direction

3

Release the applied deflection, and watch the cable vibrate

85

L4.7



History definition: *STEP, NLGEOM STEP 1: STRETCH CABLE *STATIC *CLOAD This load remains throughout 13, 1, 500. the analysis unless it is *RESTART, WRITE explicitly modified or removed. *NODE FILE U *EL PRINT S, MISES, E *NODE PRINT U, RF, CF *END STEP ** *STEP, NLGEOM STEP 2: DEFLECT MIDPOINT *STATIC .1, 1. *BOUNDARY, OP=MOD The midpoint deflection is added to the other boundary conditions specified in the 7, 2, 2, -1. model definition. *END STEP

L4.8



86

** *STEP, NLGEOM, INC=200 STEP 3:RELEASE & SEE VIBRATE *DYNAMIC ** use fixed time incs for ** this example ** dtinit, ttot, dtmin, dtmax .0002, .04 *BOUNDARY, OP=NEW All previously specified boundary conditions are 1, 1, 2 removed, and the pin and roller conditions are 13, 2 redefined. The midpoint deflection is removed *PRINT, FREQUENCY=100 since it is not redefined. *EL PRINT, FREQUENCY=0 *NODE PRINT, FREQUENCY=0 *END STEP

L4.9



The status file (jobid.sta) summarizes the incrementation of the analysis. SUMMARY OF JOB INFORMATION: STEP INC ATT SEVERE EQUIL TOTAL TOTAL STEP INC OF DOF IF DISCON ITERS ITERS TIME/ TIME/LPF TIME/LPF MONITOR RIKS ITERS FREQ 1 1 1 0 2 2 1.00 1.00 1.000 2 1 1 0 2 2 1.10 0.100 0.1000 2 2 1 0 1 1 1.20 0.200 0.1000 2 3 1 0 1 1 1.35 0.350 0.1500 2 4 1 0 1 1 1.58 0.575 0.2250 2 5 1 0 1 1 1.91 0.913 0.3375 2 6 1 0 1 1 2.00 1.00 8.7500E-02 3 1 1 0 1 1 2.00 2.000E-04 2.0000E-04 3 2 1 0 1 1 2.00 4.000E-04 2.0000E-04 3 3 1 0 1 1 2.00 6.000E-04 2.0000E-04 --------------------------------------------------------------. . . --------------------------------------------------------------3 195 1 0 1 1 2.04 3.900E-02 2.0000E-04 3 196 1 0 1 1 2.04 3.920E-02 2.0000E-04 3 197 1 0 1 1 2.04 3.940E-02 2.0000E-04 3 198 1 0 1 1 2.04 3.960E-02 2.0000E-04 3 199 1 0 1 1 2.04 3.980E-02 2.0000E-04 3 200 1 0 1 1 2.04 4.000E-02 2.0000E-04

L4.10



The dynamic response in Step 3 can be examined as an X–Y plot in Abaqus/Viewer.

87

L4.11


Restart Analysis in Abaqus (1/7) Restart files are used to: Continue analyses that stop at intermediate points. A job may stop because: I. The maximum number of increments specified for the step was reached. II. There was not enough disk space, or the machine failed. III. The job failed to converge. You may wish to continue the job after: I. Examining results up to a particular point. II. Modifying history: procedure, loading, output, or controls. Import results between Abaqus/Standard and Abaqus/Explicit.

L4.12

Restart Analysis in Abaqus (2/7) Restart option syntax: Abaqus/Standard


*RESTART, READ, STEP= , INC= , END STEP, WRITE, FREQUENCY | NUMBER INTERVAL= , TIME MARKS=, OVERLAY

88

READ, STEP, and INC

Used to specify that restart data from a previous analysis should be read at a particular step and increment. (The default is to read from the last available restart data.)

END STEP

Used when reading restart data; described later.

WRITE, FREQUENCY, NUMBER INTERVAL,

Control when restart data are written during an analysis. Restart data and TIME MARKS are always written at the end of a step if WRITE is specified.

OVERLAY

Causes Abaqus to save only the last set of restart data. (There will be only one set of restart data per step.)

L4.13

Restart Analysis in Abaqus (3/7) Restart option syntax: Abaqus/Explicit The Abaqus/Explicit restart files allow an analysis to be completed up to a certain point (an ―interval‖ of restart output) in a particular run and restarted and continued in a subsequent run. The package, state, and initial restart files are needed to restart an Abaqus/Explicit simulation. The syntax for restarting an Abaqus/Explicit simulation is just slightly different from that used for Abaqus/Standard:


*RESTART, READ, STEP=P, INTERVAL=Q In this example the analysis is restarted just after the completion of interval Q of step P.

L4.14

Restart Analysis in Abaqus (4/7) Submission of a restart job:


abaqus job=job-name oldjob=oldjob-name name of the name of the restart file new input file created by the previous run The following model data can be changed in a restart analysis: Amplitude definitions Node sets Element sets

89

L4.15

Restart Analysis in Abaqus (5/7)


Vibrating cable simulation—Approach 3: Restart analysis Another approach to the vibrating cable simulation is to perform a restart analysis.

Analysis Job 1

Step 1

Apply tension Write restart data

Analysis Job 2

Step 2

Read restart information Deflect midpoint of cable

Step 3

Release midpoint and study vibration

L4.16



90

*HEADING READ SOLUTION AT END OF STEP 1 AND CONTINUE THE VIBRATING CABLE SIMULATION *RESTART, READ, STEP=1, INC=1 ** *STEP, NLGEOM STEP 2: DEFLECT MIDPOINT *STATIC .1, 1. *BOUNDARY, OP=MOD 7, 2, 2, -1. *END STEP ** *STEP, NLGEOM, INC=200 STEP 3: RELEASE & SEE VIBRATE *DYNAMIC .0002, .04 *BOUNDARY, OP=NEW 1, 1, 2 13, 2 *END STEP

Model definition and Step 1 data are read from the restart file that was produced by the original analysis.

L4.17



Managing complex analyses The flexible restart capabilities in Abaqus are very helpful for managing complex analyses. There are three important rules to remember: 1 It is not possible to append to a restart file. I. Abaqus always reads from an old restart file and writes to a new one. II. Analyses consisting of several restarts will also have several restart files. III. Like the restart file, the output database (.odb) file is not appended to.

2 3

» Each restart analysis has its own output database file. IV. The results (.fil) file for a restarted run contains the previous results plus the results from the current analysis (by default). All output requests and loads from the previous run remain in effect upon job restart unless explicitly modified in a new step. If Abaqus is restarting from an ―unfinished‖ run, it will first try to finish the step it was working on during the original analysis before starting any new steps. I. Abaqus will finish only the step it was working on during the original analysis. » It will not attempt any additional steps defined in the original analysis. » Those steps must be included in the restart analysis input file if they are to be performed. II. Use the END STEP parameter to terminate the step from which the restart is read before continuing with a newly defined step. III. Use the END STEP parameter to continue an analysis that stopped because the maximum number of increments was reached.

Workshop 4: Unloading Analysis (IA) Workshop tasks a. Perform a restart analysis. i. Unload the plate. b. Postprocess the results.



1.

L4.18

30 minutes

91

Workshop 4: Unloading Analysis (KW) Workshop tasks a. Perform a restart analysis. i. Unload the plate. b. Postprocess the results.


1.

30 minutes

92

L4.19


Notes

93

Notes

94

Lesson 5: Constraints and Contact

L5.1


Lesson content:

Constraints Tie Constraints Rigid Bodies Shell-to-solid Coupling Contact Defining General Contact Defining Contact Pairs Contact Pair Surfaces Local Surface Behavior Relative Sliding of Points in Contact Adjusting Initial Nodal Locations for Contact Contact Output Workshop 5: Seal Contact (IA) Workshop 5: Seal Contact (KW)

Both interactive (IA) and keywords (KW) versions of the workshop are provided. Complete only one. 2.5 hours

L5.2


Constraints (1/4) What are constraints? Constraints allow you to model kinematic relationships between points. These relationships are defined between degrees of freedom in the model. Examples: Tie constraints Rigid body constraints Shell-to-solid coupling Multi-point constraints

95

L5.3

Constraints (2/4)


Tie constraints Allow you to fuse together two regions even though the meshes created on the surfaces of the regions may be dissimilar.

Tie constraints used to join a mesh containing hexahedral and tetrahedral elements.

L5.4

Constraints (3/4)


Rigid body constraints Allow you to constrain the motion of regions of the assembly to the motion of a reference point. Used to model parts which are massive and stiff compared to other bodies in the assembly (e.g., tools in a forming analysis). Rollers are modeled as rigid Rolling of a symmetric I-section

Shell-to-solid coupling Couples the motion of a shell edge to the motion of an adjacent solid face

96

L5.5

Constraints (4/4) Multi-point constraints (MPCs) Linear or nonlinear constraints between nodes. Linear equations are a form of MPC


i th node

u1i  u1bot  0 This linear equation constraint is applied to all nodes on the right-hand edge of the model to impose generalized plane strain conditions.

Infinite plate quenching problem

bot

L5.6

Tie Constraints (1/3)


In Abaqus fully constrained contact behavior is defined using tie constraints. A tie constraint provides a simple way to bond surfaces together permanently. Easy mesh transitioning. Surface-based constraint using a master-slave formulation*. The constraint prevents slave nodes from separating or sliding relative to the master surface.

Tie constraints

*The concept of master/slave surfaces as well as the steps to define surfaces will be discussed shortly.

97

L5.7

Tie Constraints (2/3) Syntax:


*TIE, NAME=name, ADJUST=[YES | NO], [POSITION TOLERANCE | TIE NSET] SLAVE, MASTER The POSITION TOLERANCE parameter defines the distance within which nodes on the slave surface must lie from the master surface to be tied. I. Nodes on the slave surface that are farther away from the master surface than this distance will not be tied. Alternatively, the TIE NSET parameter can be used to indicate the node set that includes the nodes on the slave surface that will be tied to the master surface. I. Nodes included in the slave surface but not included in this node set will not be tied.

L5.8

Tie Constraints (3/3) The ADJUST parameter is optional. Setting it to YES moves all slave nodes (within the distance defined by the optional POSITION TOLERANCE parameter) onto the master surface in the initial configuration, without any strain. The status of a slave node (open or closed) is given in the data (.dat) file.


A warning is issued in the printed output file for slave nodes in tie constraints that are not in contact. By default, both translational and rotational degrees of freedom are constrained. Use the NO ROTATION parameter if rotation degrees of freedom should not be constrained. Do not apply boundary conditions, equations, or MPCs to the slave nodes of a tie constraint; this will cause the nodes to be overconstrained, resulting in errors in the analysis. Symptoms: I. Zero pivot warnings in the message (.msg) file in Abaqus/Standard II. Deformation wave speed errors in Abaqus/Explicit

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L5.9

Rigid Bodies (1/13) Abaqus has a general rigid body capability. A rigid body is a collection of nodes and elements whose motion is governed by the motion of a single node called a “reference node.”


Any body or part of a body can be defined as a rigid body. A rigid body can undergo arbitrarily large rigid body motions. Rigid bodies are computationally efficient. Their motion is described completely by no more than six degrees of freedom. There are no element calculations for elements making up a rigid body. Model a body as rigid if it is much stiffer than other bodies with which it will come in contact; for example, dies in a metal forming simulation.

L5.10

Rigid Bodies (2/13)


Three approaches to geometry definition for rigid bodies: Define a rigid body using a combination of element types (including rigid elements) and declaring the body to be rigid. I. Discrete geometry of general shape Define an analytical rigid surface. I. Surface geometry of limited shape Write a user subroutine (RSURFU; Abaqus/Standard only). The first two approaches are discussed in this lecture.

99

L5.11


Rigid Bodies (3/13) A rigid body definition consists of 1 reference node and at most: 1 element set (discrete rigid body) 1 tie node set 1 pin node set 1 analytical surface Each rigid body definition must be unique. Rigid body definitions cannot share nodes, elements, or reference nodes.

L5.12

Rigid Bodies (4/13)


Discrete rigid bodies Most element types can be part of a rigid body. For example, solid elements or rigid elements can be used to model the same effect as long as a *RIGID BODY option is used to assign the elements to the rigid body. Example of defining a rigid body containing solid elements:

100

*ELEMENT, TYPE=C3D8R, ELSET=SOLID1 ... *SOLID SECTION, ELSET=SOLID1, MATERIAL=STEEL *MATERIAL, NAME=STEEL *ELASTIC 200.0E9, 0.3 *DENSITY 7800.0, *RIGID BODY, REF NODE=10000, ELSET=SOLID1

L5.13

Rigid Bodies (5/13) Pin vs. Tie nodes Each rigid body slave node can be specified to be one of two types: a pin node or a tie node Even when rigid bodies contain elements, additional node sets can be included in the constraint to provide more connection points for deformable elements.


*RIGID BODY, REF NODE=10000, PIN NSET= , TIE NSET= Pin nodes have only their translational degrees of freedom associated with the rigid body. Connections from a rigid body to deformable elements through a pin node transmit only displacement and force. Tie nodes have both their translational and rotational degrees of freedom associated with the rigid body. Connections from a rigid body to deformable elements through a tie node transmit rotation and moment in addition to displacement and force.

L5.14

Rigid Bodies (6/13)


rigid

tie node

pin node

deformable

Initial configuration

Final configuration after counterclockwise rotation through 45º

101

L5.15

Rigid Bodies (7/13) The default “tie” classification takes precedence for nodes attached to more than one element type.

For example, if a node is attached to both CPE3 and B21 elements, the node will be a tie node by default.


Default node types can be overridden by including the same node in a pin or tie node set. *RIGID BODY, REF NODE=node, ELSET=element set, PIN NSET=node set, TIE NSET=node set

thickness

L5.16

Rigid Bodies (8/13) Analytical rigid surfaces


Three types of analytical surfaces are available using the *SURFACE option: Use TYPE=SEGMENTS to define a two-dimensional rigid surface. Use TYPE=CYLINDER to define a three-dimensional rigid surface that is extruded infinitely in the out-of-plane direction. Use TYPE=REVOLUTION to define a three-dimensional surface of revolution.

102

Analytical rigid surfaces are not smoothed automatically. Contact calculations are easier with smoothed surfaces, however. Use the FILLET RADIUS parameter to provide the radius used to smooth segments of the analytical rigid surface.

Use the *RIGID BODY option to assign the surface to a rigid body and assign the reference node.

L5.17

Rigid Bodies (9/13)


Example of analytical rigid surface input syntax:

TYPE=SEGMENTS

*SURFACE, TYPE=SEGMENTS, NAME=SRIGID START, 15.0, 5.0 Order of segments determines normal n by defining s. n = z × s, where z CIRCL, 10.0, 0.0, 10.0, 5.0 is a unit vector parallel to the z-axis and contact is in the direction of n. LINE, 5.0, 0.0 *RIGID BODY, ANALYTICAL SURFACE=SRIGID, REF NODE=10000

L5.18

Rigid Bodies (10/13)


Kinematics of rigid bodies The motion of a rigid body is controlled by the motion of the rigid body reference node—either by boundary conditions or by forces applied to the rigid body. The other nodes forming the rigid body are called “rigid body slave nodes.”

Nodes forming a rigid body

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L5.19



Location of the rigid body reference node You can place the rigid body reference node anywhere in a model. The location is important if the rigid body is to move freely under applied loads during the analysis; in this case the node should be placed at the center of mass of the rigid body. Abaqus can calculate the center of mass and relocate the reference node to this location automatically. Abaqus will use the mass distribution from the elements making up the rigid body to determine the center of mass.

If the reference node is relocated at the center of mass of the rigid body, the new coordinates of the reference node are also printed out at the end of the printed output file. Syntax: *RIGID BODY, REF NODE=node, ELSET=element set, POSITION=CENTER OF MASS

L5.20



Inertial properties of rigid bodies The mass and rotary inertia of a meshed rigid body can be calculated based on the contributions from its elements, or they can be assigned specifically by using MASS and ROTARYI elements defined at the slave nodes of a rigid body or the rigid body reference node. The mass, the center of mass, and the moments of inertia about the center of mass of each rigid body appear in the printed output file.

104

Using rigid bodies for model verification It may be useful to specify parts of a model as rigid for model verification purposes. For example, in complex models where all potential contact conditions cannot be anticipated, elements far away from the region of interest could be included as part of a rigid body, resulting in faster run times while developing a model. When you are satisfied with the model and contact pair definitions, rigid body definitions can be removed and an accurate deformable finite element representation can be incorporated throughout.

L5.21



Example: Tennis racket frame

Tennis racket striking a tennis ball The interactions between the ball and the strings are of primary interest. Since the frame is very stiff, it is initially modeled as a rigid body for computational efficiency. Once this analysis has been verified, the rigid body definition can be removed to consider deformation of the racket.

L5.22


Shell-to-solid Coupling (1/2) Allows for a transition from shell element modeling to solid element modeling Useful when local modeling requires 3D solid elements but other parts of the structure can be modeled as shells Couples the motion of a “line” of nodes along the edge of a shell model to the motion of a set of nodes on a solid surface Uses a set of internally defined distributing coupling constraints

105

L5.23

Shell-to-solid Coupling (2/2)


Defining shell-to-solid coupling

*SHELL TO SOLID COUPLING, CONSTRAINT NAME=C1 shell_surface, solid_surface

The shell surface must be edge based

solid_surface (face)

*SURFACE, TYPE=ELEMENT, NAME=shell_surface shell_surface_E1, E1 an edge identifier

shell_surface (edge)

L5.24

Contact (1/12) What is contact? When two solid bodies touch, force is transmitted across their common surface.


In some cases only forces normal to the contact surfaces are transmitted.

106

If friction is present, a limited amount of force tangent to the contact surfaces also can be transmitted. I. Frictional forces cause shear stresses along the contact surfaces. General objective: Determine contacting areas and stress transmitted. Contact is a severely discontinuous form of nonlinearity. Either a constraint must be applied (that the surfaces cannot interpenetrate) or the constraint is ignored.

L5.25

Contact (2/12)


Contact examples Gap contact Point contact is modeled as node-to-node contact.

This example is taken from “Detroit Edison pipe whip experiment,” Example Problem 2.1.2 in the Abaqus Example Problems Manual.

L5.26

Contact (3/12)


Hertz contact Small displacements of the contact surfaces relative to each other. Contact over a distributed surface area.

Typical Examples: bearing design, hard gaskets, and shrink fits. The example shown here comes from “Coolant manifold cover gasketed joint,” Example Problem 5.1.4 in the Abaqus Example Problems Manual.

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L5.27


Contact (4/12) Large-sliding contact between deformable bodies This is the most general category of contact. Example: threaded connector. These problems typically involve an initial interference fit (because of the tapered thread), followed by finite sliding between bodies made of similar strength materials.

Contact pressure distribution due to interference resolution This example is loosely based on “Axisymmetric analysis of a threaded connection,” Example Problem 1.1.20 in the Abaqus Example Problems Manual.

L5.28


Contact (5/12) Self-contact Self-contact is contact of a single surface with itself. It is available in twoand three-dimensional models in Abaqus. It is convenient when a surface will deform severely during the analysis and it is not possible, or it is very difficult, to determine individual contacting regions in advance. Self-contact is defined by specifying a single contact surface as a contact pair instead of two different surfaces.

SURF1 (rigid)

SURF2

Contour of minimum principal stress Example: Compression of a rubber gasket (taken from “Self-contact in rubber/foam components: rubber gasket,” Example Problem 1.1.18 in the Abaqus Example Problems Manual).

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L5.29


Contact (6/12) Deformable to rigid body contact Finite sliding between the surfaces (large displacements). Finite strain of the deforming components. Typical examples: I. Rubber seals II. Tire on road III. Pipeline on seabed IV. Forming simulations (rigid die/mold, deformable component).

Example: metal forming simulation

This example is taken from “Superplastic forming of a rectangular box,” Section 1.3.2 in the Abaqus Example Problems Manual.

L5.30


Contact (7/12) Abaqus provides two approaches for modeling surface-based contact: General contact allows you to define contact between many or all regions of a model with a single interaction. The surfaces that can interact with one another comprise the contact domain and can span many disconnected regions of a model. Contact pairs describe contact between two surfaces. Requires more careful definition of contact. I. Every possible contact pair interaction must be defined. Has many restrictions on the types of surfaces involved.

One contact domain in general contact

Multiple contact pairs required

109

L5.31


Contact (8/12) The general contact algorithm The contact domain spans multiple bodies (both rigid and deformable) Default domain is defined automatically via an all-inclusive element-based surface The method is geared toward models with multiple components and complex topology Greater ease in defining contact model

L5.32

Contact (9/12)


The contact pair algorithm Requires user-specified pairing of individual surfaces Often results in more efficient analyses since contact surfaces are limited in scope

Slave surfaces for contact pair analysis

110

L5.33


Contact (10/12) The choice between general contact and contact pairs is largely a trade-off between ease of defining contact and analysis performance Robustness and accuracy of both methods are similar In some cases, the contact pair approach is required in order to access specific features not available with general contact. These include: Analytical rigid surfaces (Abaqus/Standard) Two-dimensional models (Abaqus/Explicit) Node-based surfaces Small sliding Rough or Lagrange friction (Abaqus/Standard) See the Abaqus Analysis User’s Manual for a complete list of general contact limitations

L5.34


Contact (11/12) Some additional details Abaqus/Standard Contact pairs: "Node-to-surface" contact discretization is used by default: I. Nodes on one surface (the slave surface) contact the discretized segments on the other surface (the master surface). II. Also known as a strict master/slave formulation General contact: “Surface-to-surface" contact discretization I. Contact is enforced in an average sense. II. This form of contact discretization may also be used with contact pairs Abaqus/Explicit A balanced master/slave formulation is used in most cases. I. The contact constraints are applied twice and averaged, reversing the master and slave surfaces on the second application. II. Decreases potential contact penetrations. Shell thickness in contact By default, Abaqus considers shell thickness in contact calculations with the exception of finitesliding, node-to-surface contact in Abaqus/Standard. To ignore thickness effects, use the NO THICKNESS parameter on the *CONTACT PAIR option.

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L5.35


Contact (12/12) Contact pairs in Abaqus/Standard The default strict master/slave formulation used in Abaqus/Standard has certain implications. Slave nodes cannot penetrate master surface segments. Nodes on the master surface can penetrate slave surface segments. The contact direction is always normal to the master surface. I. The contact condition is checked along the normal to the master surface. II. Normal contact forces are transmitted along the normal direction. III. Frictional forces are transmitted tangent to the contacting surfaces.

L5.36

Defining General Contact (1/3) The simplest definition of contact quite common:

*CONTACT *CONTACT INCLUSIONS, ALL EXTERIOR “Automatic contact” for entire model


The contact definition can gradually become more detailed, as called for by the analysis

112

Global/local friction coefficients and other contact properties User control of contact thickness (especially for shells) Pair-wise specification of contact domain (instead of ALL EXTERIOR)

L5.37

Defining General Contact (2/3) Main option

*CONTACT Suboptions


Commonly used: *CONTACT INCLUSIONS *CONTACT PROPERTY ASSIGNMENT Less commonly used: *SURFACE PROPERTY ASSIGNMENT *CONTACT EXCLUSIONS

L5.38

Defining General Contact (3/3)


Can assign contact properties independently of specifying the contact domain

*CONTACT *CONTACT INCLUSIONS, ALL EXTERIOR *CONTACT PROPERTY ASSIGNMENT , , prop_1 alum_surf, steel_surf, prop_2 alum_surf, alum_surf, prop_3

(reassigns properties globally) (local modification) (local modification)

113

L5.39

Defining Contact Pairs (1/5)


Three steps for defining contact: 1

Define surfaces based on the underlying elements, analytically defined geometry, or underlying nodes.

2

Define pairs of surfaces that can interact.

3

Define surface interaction properties: friction, softened layers, etc.

L5.40



Example of the complete contact syntax in the input file:

*SURFACE, NAME=ASURF SLIDER, S1 *SURFACE, NAME=BSURF BLOCK, S3 *CONTACT PAIR, INTERACTION=FRIC1 ASURF, BSURF *SURFACE INTERACTION, NAME=FRIC1 1.0, *FRICTION 0.4,

These options are explained in detail on the following pages.

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L5.41



Defining surfaces The surfaces are defined using the *SURFACE option. The faces of each element set are specified using face label identifiers. Either element set names or element numbers can be used to specify surfaces.

*SURFACE, NAME=ASURF SLIDER, S1 *SURFACE, NAME=BSURF BLOCK, S3

Contact occurs on bottom (S1) face of element set SLIDER Contact occurs on top (S3) face of element set BLOCK

L5.42



Defining pairs of surfaces that can interact Once you have defined surfaces, you can define “contact pairs.” Each contact pair specifies two surfaces that can contact each other during the analysis. In Abaqus/Standard the first surface is the slave surface and the second surface is the master surface. In Abaqus/Explicit the order of the surfaces does not usually affect the contact calculations.

*CONTACT PAIR, INTERACTION=FRIC1 ASURF, BSURF

115

L5.43


Defining Contact Pairs (5/5) Defining surface interaction properties The *SURFACE INTERACTION option block defines the surface interaction properties. Defines surface behavior properties such as friction. Defines contact interface out-of-plane thickness for two-dimensional cases. This option is always necessary in Abaqus/Standard, even when additional properties are not specified. I. It is optional in Abaqus/Explicit. The *CONTACT PAIR option refers to a *SURFACE INTERACTION option by name.

*CONTACT PAIR, INTERACTION=FRIC1 ASURF, BSURF *SURFACE INTERACTION, NAME=FRIC1 Out-of-plane thickness 1.0, *FRICTION List surface constitutive 0.4,

properties as suboptions of *SURFACE INTERACTION

L5.44

Contact Pair Surfaces (1/8) Use the *SURFACE, TYPE=ELEMENT option to define surfaces on deformable bodies or meshed rigid bodies.

Define surfaces by specifying element face identifier labels or


Allow Abaqus to automatically determine the “free surfaces” of a body of continuum elements

116

Use the *SURFACE, TYPE=[SEGMENTS | CYLINDER | REVOLUTION] option with the *RIGID BODY option to define analytical rigid surfaces. Discussed earlier in the context of rigid bodies Use the *SURFACE, TYPE=NODE option to specify individual nodes that may experience contact.

L5.45

Contact Pair Surfaces (2/8)


Defining surfaces on solid elements Using face label identifiers Example: 4-node quad element (CPE4, CAX4, etc.) *SURFACE, NAME=EXAMPLE1 1, S4 1, S1 2, S1 2, S2 ...

L5.46



Using automatic surface definition *SURFACE, NAME=EXAMPLE2 ELSET1, No face identifier

117

L5.47


Contact Pair Surfaces (4/8) Defining surfaces on structural elements (shell, membrane, rigid, beam) Structural element normals dictate the direction of expected contact. Normals are based on element local node numbering. Positive normal direction = SPOS surface. Negative normal direction = SNEG surface.

Shells and membranes (S4R,S8R,M3D4,etc.)

2-D trusses and beams (B21,T2D2,etc.)

L5.48



118

Surface normals should be consistent within a surface definition. *ELEMENT, TYPE=B21, ELSET=BOTTOM 10, 1, 2 11, 2, 3 12, 3, 6 *ELEMENT, TYPE=B21, ELSET=TOP 20, 4, 5 21, 5, 6 *ELSET, ELSET=BEAMS BOTTOM, TOP

*SURFACE, NAME=SURF1 BEAMS, SPOS

*SURFACE, NAME=SURF1 BOTTOM, SPOS TOP, SNEG

L5.49

Contact Pair Surfaces (6/8) Node-based surfaces Alternative way to define points for contact. Instead of specifying element faces as a contact surface, a node-based surface contains only nodes. Node-based surfaces are always considered slave surfaces.


Example: tennis racket strings

Ball: elementbased surface Strings: nodebased surface

*SURFACE, TYPE=NODE, NAME=STRINGS STRINGS, *CONTACT PAIR, INTERACTION=SMOOTH STRINGS, BALL

define surface containing contact nodes

previously defined surface

L5.50


Contact Pair Surfaces (7/8) General rules All elements underlying a surface must be compatible. They must be: Of the same dimension (two- or threedimensional). I. For two-dimensional surfaces: all planar or all axisymmetric (but not both). Of the same order of interpolation (firstor second-order). All deformable or all rigid (but not both). Additional restrictions Surface normals Master surface normals must be consistent Master surface normals should point toward the slave surface. I. Otherwise convergence difficulties will occur. Rigid surfaces All surfaces defined on rigid bodies must be specified as master surfaces.

119

L5.51

Contact Pair Surfaces (8/8) Master contact pair surfaces in Abaqus/Standard (when using the default node-to-surface algorithm) and all contact pair surfaces in Abaqus/Explicit have an additional restriction: It must be possible to traverse between any two points on the surface without leaving the surface, passing through it, or passing through a single point.


Traversal cannot take place through a point. Traversal requires passing through or leaving the surface.

valid master surfaces

invalid master surfaces

L5.52

Local Surface Behavior (1/7)


Contact modeling allows for interactions in the normal and tangential contact directions. Other contact interaction properties include contact damping and geometric properties such as out-ofplane thickness.

120

L5.53

Local Surface Behavior (2/7)


Behavior in the contact normal direction Hard contact “Hard” contact is the default local behavior in all contact problems. Contact constraints enforced via a: Direct method (contact pairs only)

Pressure-clearance relationship

Lagrange Multipliers for Abaqus/Standard Precise kinematic compliance for Abaqus/Explicit Penalty method (default for general contact) *surface interaction, name=... *surface behavior, penalty

(Abaqus/Standard)

*contact pair, mechanical=penalty

(Abaqus/Explicit)

Augmented Lagrange method *surface behavior, augmented lagrange

(Abaqus/Standard only)

L5.54


Local Surface Behavior (3/7) Alternatives to hard contact The *SURFACE BEHAVIOR option is used as a suboption of the *SURFACE INTERACTION option to specify: Softened contact (exponential or tabular pressure-clearance relationship) Contact without separation Other options: Clearance-dependent viscous damping (*CONTACT DAMPING). Contact with overclosure or tensile contact forces (*CONTACT CONTROLS; Abaqus/Standard only).

121

L5.55

Local Surface Behavior (4/7) Behavior in the contact tangential direction


Frictional shear stresses, , may develop at the interface between contacting bodies. If the magnitude reaches a critical value, the bodies will slip; otherwise they will stick.

L5.56

Local Surface Behavior (5/7) Friction is a highly nonlinear effect. Solutions are more difficult to obtain. Do not use unless physically important. Friction is nonconservative.


In Abaqus/Standard friction causes the equation system to be unsymmetric. The *STEP, UNSYMM=YES option is used automatically for high  ( >0.2) .

122

Using UNSYMM=NO will give slower convergence, but the solution will be correct (if obtained). It may also use less disk space. This behavior is not an issue with Abaqus/Explicit, where there are no systems of equations to solve.

L5.57

Local Surface Behavior (6/7) Abaqus uses the Coulomb friction model by default. The critical frictional stress depends on contact pressure:

cr =  p.

Basic syntax: *FRICTION


 The friction coefficient, , can be a function of the relative slip velocity, pressure, temperature, and field variables ( eq , p,  , f i ). For computational reasons the default friction model in Abaqus/Standard uses an approximation to the ideal behavior, allowing a small amount of elastic slip before nonrecoverable slip occurs:

 p2  p1

G2 G1

 cr



L5.58

Local Surface Behavior (7/7) A combined static kinetic friction model can be defined. Exponential decay, as a function of  , of  from s (static) to k (kinetic). Other alternatives are available for frictional behavior, including user-defined friction models:


FRIC in Abaqus/Standard VFRIC in Abaqus/Explicit

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L5.59

Relative Sliding of Points in Contact (1/3)


Two slide distance options: Finite sliding *CONTACT PAIR

Finite sliding is the most general—used by default. Arbitrarily large sliding between surfaces and large rotations are allowed. Contact is governed by evolving contact surfaces in current configuration.

Small-sliding

Small relative sliding between surfaces. Allows large rotations of the surfaces, as long as the surfaces do not move significantly relative to each other. Contact governed by the presence of local contact planes/lines defined in the initial configuration. Computationally less expensive than finite sliding since does not require the generality of the finite-sliding algorithm. Only available for contact pairs

*CONTACT PAIR, SMALL SLIDING

L5.60


Relative Sliding of Points in Contact (2/3)

124

Some of the differences between finite and small sliding will be illustrated by example. Consider the model shown at right. The rigid punch is displaced horizontally while maintaining the clearance indicated in the figure. Afterwards, it is pushed downward into the deformable body. With finite sliding, no contact occurs while the clearance is maintained (as expected).

L5.61


Relative Sliding of Points in Contact (3/3) Now consider the case of small sliding. Recall that small sliding contact is governed by the presence of local contact planes (3D) or lines (2D/axisymmetric). In the figure at right the local contact lines are highlighted. The slave nodes highlighted in the figure will establish contact with the local contact lines as the punch is dragged horizontally even though a physical clearance is maintained between the two parts!

Contact lines

L5.62


Adjusting Initial Nodal Locations for Contact (1/6) The initial positions of the nodes on the contact surfaces can be adjusted without stress or strain prior to the analysis. Abaqus/Standard: default treatment of initially overclosed nodes depends on contact modeling approach I. General contact: By default, small initial overclosures are adjusted free of strain (i.e., nodes are adjusted prior to the analysis) such that surfaces are “just-touching;” alternatively, these can be treated as interference fits II. Contact pairs: By default, all initial overclosures are treated as interference fits; alternatively; may adjust position without strain III. For either approach may also choose to specify precise clearance or interference (not discussed here) Abaqus/Explicit: does not allow an initial overclosure of contact surfaces. I. The nodes on the contact surfaces will be adjusted automatically to remove any initial overclosure prior to the analysis. In subsequent steps the adjustments will cause strains. Gross adjustments can severely distort initial element shapes. If you see error messages that suggest this is a problem, run a datacheck analysis and look for the problem in Abaqus/Viewer.

125

L5.63

Adjusting Initial Nodal Locations for Contact (2/6) Adjusting slave nodes using general contact (Abaqus/Standard) Large initial overclosures and initial gaps can be adjusted Specify search distances above and below the surfaces I. Search above to close gaps II. Search below to increase default overclosure tolerance The adjustments are applied to surface pairs www.3ds.com | © Dassault Systèmes

*Contact Initialization Data, name=adjust-1, SEARCH ABOVE=1e-05, SEARCH BELOW=0.02

*Contact Initialization Assignment allHeads , topFlange_outer , adjust-1

L5.64

Adjusting Initial Nodal Locations for Contact (3/6)


Adjusting slave nodes using contact pairs (Abaqus/Standard) Specifying an absolute distance to adjust: *CONTACT PAIR, INTERACTION=FRIC1, ADJUST=a

126

All initially open slave nodes that fall within the adjust band (a) are moved onto the master surface.

The adjustment distance (a) is measured along the normal direction to the master surface. All initially overclosed slave nodes are relocated to the surface.

L5.65

Adjusting Initial Nodal Locations for Contact (4/6) Specifying a node set of slave nodes to adjust:

Overclosed slave nodes not in the node set will remain overclosed and will cause strains when forced back onto the contact surface during the analysis.


Example of specifying an ADJUST node set: *NSET, NSET=CONNODE, GENERATE 1, 8, 1 *CONTACT PAIR, INTERACTION=RIG, ADJUST=CONNODE

L5.66

Adjusting Initial Nodal Locations for Contact (5/6) Visualizing strain-free adjustments In Abaqus/Standard, output variable STRAINFREE is provided to visualize strain-free adjustments This output variable is written by default if any initial strain-free adjustments are made


This variable is only available in the initial output frame at t = 0

Symbol plot of STRAINFREE

Initial configuration without contact

127

L5.67

Adjusting Initial Nodal Locations for Contact (6/6) The following inconsistency exists between Abaqus/Standard and Abaqus/Explicit with respect to strain-free adjustments:

x = xo + u Abaqus/Explicit adjusts u


Abaqus/Standard adjusts xo

Desired aspect to visualize

Technique in Abaqus/CAE Abaqus/Standard model

Abaqus/Explicit model

Nodal adjustment vectors

Symbol plot of STRAINFREE at t=0

Symbol plot of U at t=0

Nodal adjustment magnitudes

Contour plot of STRAINFREE at t=0

Contour plot of U at t=0

Adjusted configuration

Undeformed shape or deformed shape at t=0

Deformed shape at t=0

Configuration prior to adjustments

Substitute -STRAINFREE for U in deformed plot (t=0)

Undeformed shape

L5.68


Contact Output (1/4)

128

Nodal contact output For both Abaqus/Standard and Abaqus/Explicit: Contact stresses: CSTRESS (contact pressure CPRESS and frictional shear stresses CSHEAR1 and CSHEAR2) Contact forces (CFORCE) For Abaqus/Standard you can also request: Contact displacements: CDISP (contact opening COPEN, relative tangential motions CSLIP1 and CSLIP2) Nodal contact areas (CNAREA) Contact status (CSTATUS) For Abaqus/Explicit you can also request: Slip velocity: FSLIPR Accumulated slip displacements: FSLIP

L5.69



Whole surface contact output Output variable

Description

CAREA

Total area of slave surface in contact

CFN CFS

Total force vector due to contact pressure and frictional shear stress of slave surface, respectively

CMN CMS

Total moment vector about the origin due to contact pressure and frictional shear stress of slave surface, respectively

CFT

Vector sum of CFN and CFS

CMT

Vector sum of CMN and CMS

XN

Coordinates of a point about which the total moment due to the contact pressure on a slave surface is equal to zero

XS

Coordinates of a point about which the total moment due to the frictional stress on a slave surface is equal to zero

XT

Coordinates of a point about which the total moment due to the contact pressure and frictional stress on a slave surface is equal to zero

L5.70



Example: two surfaces contacting at two locations

129

L5.71



Two other options exist for generating printed output relevant to Abaqus/Standard contact analyses: *PREPRINT, CONTACT=YES: I. Controls output to the printed output file during preprocessing II. Gives details of internally generated contact elements III. Recommended for small-sliding contact problems to verify master-slave node interaction IV. Use to check that surface definitions and interactions are correct *PRINT, CONTACT=YES: I. Controls output to the message file during the analysis phase II. Gives details of the iteration process III. Use to understand where difficulties are occurring during contact

Workshop 5: Seal Contact (IA)


1.

Workshop tasks 1. Evaluate a hyperelastic material model. 2. Define contact 1. Contact pairs 2. General contact 3. Apply boundary conditions 4. Perform large displacement analysis 5. Visualize the results.

1 hour

130

L5.72


Workshop 5: Seal Contact (KW)


1.

Workshop tasks 1. Evaluate a hyperelastic material model. 2. Define contact 1. Contact pairs 2. General contact 3. Apply boundary conditions 4. Perform large displacement analysis 5. Visualize the results.

L5.73


1 hour

131

132

Notes

133

Notes

134

Lesson 6: Introduction to Dynamics

L6.1


Lesson content:

What Makes a Problem Dynamic? Equations for Dynamic Problems Linear Dynamics Nonlinear Dynamics Comparing Abaqus/Standard and Abaqus/Explicit Nonlinear Dynamics Example Workshop 6: Dynamics (IA) Workshop 6: Dynamics (KW)


2 hours

L6.2

What Makes a Problem Dynamic? A problem is dynamic when the inertial forces (d’Alembert forces) are significant and vary rapidly in time.

Inertial forces are proportional to the acceleration of the mass in the structure. Solving a dynamic problem may require the integration of the equations of motion in time.


I. Direct Integration (Expensive) II. Modal Transient (Effective for Linear Problems) Many dynamic vibration problems can be studied effectively in the frequency domain. I. Frequency Response or Steady State Dynamics implies Harmonic Excitation and Response and thus does not require integration Sometimes we have large inertia loads but can do static analyses because the loads vary slowly with time (constant acceleration, centrifugal loads) I. However, centrifugal loads in flexible systems may lead to whirls (Complex Eigenvalues)

135

L6.3

Equations for Dynamic Problems Dynamic equilibrium The dynamic equilibrium equations are written for convenience with the inertial forces isolated from the other forces:

Mu  I  P  0


Assumptions:

M (the mass matrix) is constant in time. I and P may depend on nodal displacements and velocities but not on any higher-order time derivatives. I. Thus, the system is second order in time, and damping/dissipation are included in I and P. If

I  Ku  Cu where K (stiffness) and C (damping) are constant, the problem is linear.

These equilibrium equations are completely general. They apply to the behavior of any mechanical system and contain all nonlinearities. When the first term—the inertial or dynamic force—is small enough, the equations reduce to the static form of equilibrium.

L6.4


Linear Dynamics (1/12) Linear dynamics problems require the use of an implicit solution scheme (i.e., Abaqus/Standard). Several classes of linear dynamics problems can be solved with Abaqus: Natural frequency extraction * Modal superposition Implicit (direct-integration) dynamics Harmonic loading * Response spectrum analysis * Random loading * In this section we focus on natural frequency extraction and give a brief overview of modal-superposition methods.

*No integration required.

136

L6.5

Linear Dynamics (2/12) Natural frequency analysis

Studies of the vibration characteristics of a structural system often begin with a natural frequency (or eigenvalue) analysis. The *FREQUENCY procedure in Abaqus/Standard extracts eigenvalues of an undamped system: www.3ds.com | © Dassault Systèmes

Mu  Ku  0 Eigenvalues and mode shapes describe the free vibration or the frequency content of the structure. Any preload applied prior to calculation of the eigenvalues will affect the results if nonlinear geometry is used. Setting NLGEOM=YES on the *STEP option causes Abaqus to consider nonlinear geometry effects, including preloads (preloads contribute to K).

L6.6

Linear Dynamics (3/12) Three eigensolvers are available for symmetric real eigenvalue extraction problems.

Automatic multi-level substructuring (AMS) I. Most efficient solver when a large number of eigenvalues are required


Lanczos (default) I. For very large models, use SIM architecture* Subspace iteration The structure may be unconstrained or constrained. If constrained, preload effects may be included.

*SIM is a high-performance linear dynamics architecture.

137

L6.7

Linear Dynamics (4/12) Example: Frequency extraction of an engine block

Modeled with 10-node tetrahedral elements (C3D10) Linear elastic material model


Steel The structure is unrestrained.

L6.8

Linear Dynamics (5/12) Step definition


# modes requested

Natural frequency extraction procedure

Invokes SIM-based architecture.

*STEP *FREQUENCY,EIGENSOLVER=LANCZOS, SIM 100, 1., , Set equal to LANCZOS to invoke the LANCZOS eigensolver.

Specify minimum frequency to exclude rigid body modes. *OUTPUT, FIELD *NODE OUTPUT U *END STEP

Leave maximum frequency blank to be sure you get all 100 modes Output is restricted to nodal displacements for the purpose of visualizing mode shapes.

Note: It is not necessary to specify the number of modes; simply specify a maximum frequency of interest

138

L6.9

Linear Dynamics (6/12)


The first 10 nonrigid body eigenmodes are shown below

Mode 1

Mode 2

Mode 4

Mode 7

Mode 3

Mode 5

Mode 8

Mode 6

Mode 9

Mode 10

L6.10

Linear Dynamics (7/12) Modal superposition

The eigenmodes of a structure can be used in several different mode-based procedures to study its linear dynamic response: Modal dynamics


I. Calculates linear dynamic response in time domain II. Direct integration also available Steady-state dynamics I. Calculates dynamic response due to harmonic excitation

II. Direct solution or modal Response spectrum I. Estimates peak response to dynamic motion

Random response I. Predicts response to random continuous excitation

139

L6.11

Linear Dynamics (8/12) Steady-state dynamics

When a damped structure is excited with a harmonic load, it has a transient response that disappears rather quickly and is rarely of much interest.


Eventually the structure reaches a steady state that is characterized by a harmonic response. The STEADY STATE DYNAMICS procedure provides the solution to the linear dynamic equations of motion when the loading is harmonic. Three options are available for steady-state dynamic analysis: Direct Mode-based Subspace projection

L6.12

Linear Dynamics (9/12) Example: Harmonic excitation of a tire

Investigating the frequency response of a tire about a static footprint solution.


The excitation is due to a harmonic vertical load that is applied to the reference point of the road.

The rim of the tire is held fixed. Reference: “Subspace-based steady-state dynamic tire analysis,” Section 3.1.3 of the Abaqus Example Problems Manual.

The road is modeled as a rigid surface.

140

L6.13


Linear Dynamics (10/12) Step definitions *STEP, NLGEOM=YES *STATIC *BOUNDARY RIM, 1, 3 ROAD, 1, 2 ROAD, 4, 6 *DSLOAD INSIDE, P, 200.E3 *CLOAD ROAD, 3, 3300. *END STEP

Static preload (“footprint” step)

L6.14



Frequency extraction

Frequency range

*STEP *FREQUENCY,EIGENSOLVER=LANCZOS 20 Subspace-based steady-state *END STEP dynamics procedure *STEP,NLGEOM=YES *STEADY STATE DYNAMICS, SUBSPACE PROJECTION=ALL FREQUENCIES, INTERVAL=EIGENFREQUENCY, FREQUENCY SCALE=LINEAR 80, 130, 3 *CLOAD The load is purely inROAD, 3, 200. phase: *END STEP

Fz  200cos t

141

L6.15



Results

Contour of displacement magnitude

Vertical displacement of the road’s reference point

L6.16


Nonlinear Dynamics (1/8)

142

Overview Abaqus/Standard Uses implicit time integration to calculate the transient dynamic or quasi-static response of a system. Three application types: I. dynamic responses requiring transient fidelity and involving minimal energy dissipation; II. dynamic responses involving nonlinearity, contact, and moderate energy dissipation; and III. quasi-static responses in which considerable energy dissipation provides stability and improved convergence behavior for determining an essentially static solution. Abaqus/Explicit Uses explicit time integration scheme to calculate the transient dynamic or quasi-static response of a system.

L6.17

Nonlinear Dynamics (2/8) Time integration of the equations of motion

Nonlinear dynamics problems require direct integration of the equations of motion.


The spatial discretization (finite element approximation) turns the partial differential equations describing dynamic equilibrium into a set of coupled, nonlinear, ordinary differential equations in time. Time integration is needed to solve this system of ordinary differential equations. The methods used to integrate these equations through time distinguish Abaqus/Standard and Abaqus/Explicit.

L6.18

Nonlinear Dynamics (3/8) Abaqus/Standard

Uses a second-order accurate, implicit scheme called the Hilber-Hughes-Taylor (HHT) rule unless the application type is quasi-static.


I. This is a generalization of the Newmark method. Second-order accurate means the scheme integrates a constant acceleration exactly. The method is unconditionally stable: any size time increment can be used and the solution will remain bounded. Abaqus/Explicit Uses a second-order accurate, explicit integration scheme to calculate the transient dynamic or quasi-static response of a system. The method is conditionally stable—it gives a bounded solution only when the time increment is less than a critical value.

143

L6.19


Nonlinear Dynamics (4/8) Automatic time incrementation in Abaqus/Standard Incrementation scheme depends on dynamic application type Transient fidelity applications (default for models without contact) I. *DYNAMIC, APPLICATION=TRANSIENT FIDELITY II. Require minimal energy dissipation III. Small time increments required to accurately resolve the vibrational response of the structure, and numerical energy dissipation is kept at a minimum Moderate dissipation (default for models with contact) I. *DYNAMIC, APPLICATION= MODERATE DISSIPATION II. A moderate amount of energy is dissipated by plasticity, viscous damping, or other effects III. Accurate resolution of high-frequency vibrations is usually not of interest IV. Improved convergence for analyses involving contact Quasi-static I. *DYNAMIC, APPLICATION=QUASI-STATIC II. These problems typically show monotonic behavior, and inertia effects are introduced primarily to regularize unstable static behavior

L6.20


Application


Transient fidelity

Default incrementation scheme

Default half-increment residual tolerance*

Time integration method HHT

a 0.05 b 0.275625 g 0.55

Not considered unless use conservative incrementation

HHT

a 0.41421 b 0.5 g 0.91421

Not considered

Backward Euler

N/A

Conservative: a. Same rules as for static analyses b. Dtmax0.01*Tstep c. Limit on half increment residual

1000*time average force (no contact)

Moderate dissipation

a. Same rules as for static analyses b. Dtmax0.1*Tstep

Quasi-static

Aggressive: a. Same rules as for static analyses

10000*time average force (with contact)

*The half-increment residual is the out-of-balance force that exists halfway through a time increment.

144

Integration parameters

L6.21

Nonlinear Dynamics (6/8) Automatic time incrementation in Abaqus/Explicit The time increment size is controlled by the stable time increment. The explicit dynamics procedure gives a bounded solution only when the time increment is less than a critical or stable time increment.


The stability limit is given in terms of the highest eigenvalue in the model max and the fraction of critical damping ( ) in the highest mode:

Dtmin 

2

max

( 1   2   ).

Damping reduces the stable time increment! Not feasible to compute max, so easy-to-compute conservative estimates are used instead.

L6.22



The concept of a stable time increment is explained easily by considering a one-dimensional problem.

One-dimensional problem

The stable time increment is the minimum time that a dilatational wave takes to move across any element in the model. A dilatational wave consists of volume expansion and contraction. The dilatational wave speed, cd , can be expressed for a one-dimensional problem as

cd 

E



,

where E is the Young's modulus and  is the current material density. Based on the current geometry each element in the model has a characteristic length, Le.

145

L6.23

Nonlinear Dynamics (8/8) Thus, the stable time increment can be expressed as

Dt 

Le . cd

Decreasing Le and/or increasing cd will reduce the size of the stable time increment. www.3ds.com | © Dassault Systèmes

Decreasing element dimensions reduces Le. Increasing material stiffness increases cd. Decreasing material compressibility increases cd. Decreasing material density increases cd. Abaqus/Explicit monitors the finite element model throughout the analysis to determine a stable time increment.

L6.24

Comparing Abaqus/Standard and Abaqus/Explicit (1/3)


Abaqus/Standard

146

Abaqus/Explicit

Time increment size is not limited: generally fewer time increments required to complete a given simulation.

Time increment size is limited: generally many more time increments are required to complete a given simulation.

Each time increment is relatively expensive since the solution for a set of simultaneous equations is required for each.

Each time increment is relatively inexpensive because the solution of a set of simultaneous equations is not required. Most of the computational expense is associated with element calculations (forming and assembling I).

L6.25

Comparing Abaqus/Standard and Abaqus/Explicit (2/3) Abaqus/Standard


Ideal for problems where the response period of interest is long compared to the vibration frequency of the model. Difficult to use explicit dynamics effectively because of the limit on the time increment size. Use for problems that are mildly nonlinear and where the nonlinearities are smooth (e.g., plasticity). With a smooth nonlinear response Abaqus/Standard will need very few iterations to find a converged solution.

Abaqus/Explicit Ideal for high-speed dynamic simulations Require very small time increments; implicit dynamics inefficient. Usually more reliable for problems involving discontinuous nonlinearities. Contact behavior is discontinuous and involves impacts, both of which cause problems for implicit time integration. Other sources of discontinuous behavior include buckling and material failure.

L6.26


Comparing Abaqus/Standard and Abaqus/Explicit (3/3) Example of a problem well suited for Abaqus/Explicit Pipe whip This example simulates a pipe-on-pipe impact resulting from the rupture of a high-pressure line in a power plant. A sudden release of fluid causes one segment of the pipe to rotate about its support and strike a neighboring pipe.

147

L6.27

Nonlinear Dynamics Example (1/3)


Reference: “Double cantilever elastic beam under point load,” Section 1.3.2 in the Abaqus Benchmarks Manual.

L6.28



Abaqus/Standard input file

148

*HEADING NONLINEAR ELASTIC BEAM *NODE 1, 0. 6, 10. *NGEN 1, 6 *NSET, NSET=NFIL 6, *ELEMENT, TYPE=B23 1, 1, 2 *ELGEN, ELSET=BEAM 1, 5 *BEAM SECTION, ELSET=BEAM, SECTION=RECT, MATERIAL=A1 1., .125 0., 0., -1. 3 *MATERIAL, NAME=A1 *ELASTIC 30.E6, *DENSITY 2.5362E-4, *RESTART, WRITE, FREQUENCY=10

*STEP, INC=400, NLGEOM=YES *DYNAMIC 25.E-6, 5.E-3 *BOUNDARY 1, 1, 2 1, 6 6, 1 6, 6 *CLOAD 6, 2, 320. *END STEP

L6.29



Comparing the Abaqus/Standard and Abaqus/Explicit results The results obtained with the default incrementation schemes show excellent agreement. Using a tighter half-increment residual tolerance for the implicit analysis further improves the agreement.

*DYNAMIC, HALFINC SCALE FACTOR=0.05

In the non-default case shown here, the half-increment scale factor was set to 0.05 (the default value is 1000)

Workshop 6: Dynamics (IA)

Interactive version. Choose either the interactive Workshop tasks or keywords version of this workshop. 1. Complete the model and perform a frequency extraction analysis. 2. Examine the printed output for relevant frequency results. 3. View the eigenmodes in Abaqus/Viewer. 4. Evaluate the effects of mesh density and element dimension and order. 5. Perform a free-vibration analysis using the implicit dynamics method.


1.

L6.30

1 hour

149

Workshop 6: Dynamics (KW)

Keywords version. Choose either the interactive Workshop tasks or keywords version of this workshop. 1. Modify an existing input file, and perform a frequency extraction analysis. 2. Examine the printed output for relevant frequency results. 3. View the eigenmodes in Abaqus/Viewer. 4. Evaluate the effects of mesh density and element dimension and order. 5. Perform a free-vibration analysis using the implicit dynamics method.


1.

1 hour

150

L6.31

Notes

151

Notes

152

Lesson 7: Using Abaqus/Explicit

L7.1


Lesson content:

Overview of the Explicit Dynamics Procedure Abaqus/Explicit Syntax Rigid Bodies Workshop 7: Contact with Abaqus/Explicit (IA) Workshop 7: Contact with Abaqus/Explicit (KW)


2 hours

L7.2

Overview of the Explicit Dynamics Procedure (1/6) The explicit dynamics procedure is often complimentary to an implicit solver such as Abaqus/Standard.

From a user standpoint the distinguishing characteristics of the explicit and implicit methods are: Explicit methods require a small time increment size. Depends solely on the highest natural frequencies of the model.


Independent of the type and duration of loading. Simulations generally take on the order of 104 to 106 increments, but the computational cost per increment is relatively small. Implicit methods do not place an inherent limitation on the time increment size. Increment size is generally determined from accuracy and convergence considerations. Implicit simulations typically take orders of magnitude fewer increments than explicit simulations. However, since a global set of equations must be solved in each increment, the cost per increment of an implicit method is far greater than that of an explicit method. Knowing these characteristics of the two procedures can help you decide which methodology is appropriate for your problems.

153

L7.3

Overview of the Explicit Dynamics Procedure (2/6)


Stress wave propagation This stress wave propagation example illustrates how the explicit dynamics solution procedure works without iterating or solving sets of linear equations. We consider the propagation of a stress wave along a rod modeled with three elements. We study the state of the rod as we increment through time. Mass is lumped at the nodes.

Initial configuration of a rod with a concentrated load, P, at the free end

L7.4



u1 

 u P  u1  u1dt  el1  1  d el1  el1dt M1 l



  el1   0  d el1   el1  E el1 Configuration at the end of Increment 1

154



L7.5



u1 

P  Fel1  u1  u1old  u1dt M1

u2 

Fel1  u 2  u2 dt M2





el1 

u 2  u1  d el1  el1dt l   el1  1  d el1



  el1  E el1

Configuration of the rod at the beginning of Increment 2

Configuration of the rod at the beginning of Increment 3

L7.6


Overview of the Explicit Dynamics Procedure (5/6) Example of a problem well suited for Abaqus/Explicit Pipe whip This example simulates a pipe-on-pipe impact resulting from the rupture of a high-pressure line in a power plant. A sudden release of fluid causes one segment of the pipe to rotate about its support and strike a neighboring pipe.

155

L7.7



Hydroforming Uses fluid pressure to form a component. Abaqus/Explicit captures the unstable wrinkling of excess blank material.

A draw cap is added to decrease the wrinkling effects.

L7.8

Abaqus/Explicit Syntax (1/3) The basic input structure and options for an Abaqus/Explicit model are the same as those for an Abaqus/Standard model. This allows users to leverage their knowledge of Abaqus/Standard toward learning Abaqus/Explicit.


An Abaqus/Explicit analysis is performed when the input file contains the *DYNAMIC, EXPLICIT procedure option.

156

In the majority of Abaqus/Explicit analyses you provide just the total step time and the time increment size is chosen automatically so that it always satisfies the stability limit. *STEP *DYNAMIC, EXPLICIT , 70.E-3 Options for controlling the time increment size are available for special circumstances.

L7.9

Abaqus/Explicit Syntax (2/3) Unlike Abaqus/Standard, Abaqus/Explicit uses a finite-strain, large-displacement, large-rotation formulation by default. The NLGEOM parameter is not needed on the *STEP option.


Geometrically linear analysis (small-deformation analysis) can be obtained by setting NLGEOM=NO. The numerics of the explicit dynamic procedure require that elements with lumped mass matrices be used. Since solution efficiency is usually an important factor when using Abaqus/Explicit, only first-order reducedintegration elements are generally available. Exceptions: Modified triangles and tetrahedrals (CPS6M, CPE6M, C3D10M), second-order beam elements (B22 and B32), fully-integrated membrane element (M3D4), fully-integrated shell elements (S4, S4T), and fully-integrated first-order hex elements (C3D8, C3D8I, C3D8T).

L7.10

Abaqus/Explicit Syntax (3/4) Some options unique to Abaqus/Explicit The following model definition and history options are available only in Abaqus/Explicit (output and control options are not listed):


Analysis procedures

*DYNAMIC, EXPLICIT: This procedure specifies an explicit dynamics step and that Abaqus/Explicit will be the solver program. *DYNAMIC TEMPERATURE-DISPLACEMENT, EXPLICIT: This procedure specifies a coupled thermal-mechanical step. *ANNEAL: This procedure sets all nodal velocities to zero and sets all state variables, such as stress and plastic strain, to zero.

Material

*EOS: The equation of state material model can be used to model a hydrodynamic (explosive) material or a nearly incompressible fluid. *EXTREME VALUE: This option specifies critical variables whose extreme values will be monitored every increment. *TRACER PARTICLE: This option defines tracer particles that track material points in an adaptive mesh domain.

157

L7.11

Rigid Bodies As noted previously, Abaqus has a general rigid body capability.

Two additional points are relevant when using this capability with Abaqus/Explicit. The elements in a rigid body do not affect the stable time increment.


It is possible to define the thickness and density of rigid elements on the *RIGID BODY option. *RIGID BODY, REF NODE=node, ELSET=element set, DENSITY=#

thickness A constant thickness can be specified as a value on the data line following the *RIGID BODY option. A variable thickness can be specified by using the NODAL THICKNESS parameter on the *RIGID BODY option.

Workshop 7: Contact with Abaqus/Explicit (IA)


1. Workshop tasks a. Define general contact between the two pipes. b. Assign boundary conditions and initial velocities. c. Perform impact analysis. d. View deformation and energy histories.

1 hour

158

L7.12


Workshop 7: Contact with Abaqus/Explicit (KW)



1. Workshop tasks a. Define general contact between the two pipes. b. Assign boundary conditions and initial velocities. c. Perform impact analysis. d. View deformation and energy histories.

L7.13

1 hour

159

160

Notes

161

Notes

162

Lesson 8: Quasi-Static Analysis in Abaqus/Explicit

L8.1


Lesson content:

Introduction Solution Strategies Quasi-Static Simulations Using Explicit Dynamics Energy Balance Example: Load Rates Example: Mass Scaling Adaptive Meshing Summary Workshop 8: Quasi-Static Analysis (IA) Workshop 8: Quasi-Static Analysis (KW)


2 hours

L8.2


Introduction (1/3) In the previous lectures we discussed how to solve nonlinear static and dynamic problems using Abaqus. We now revisit the subject of nonlinear static problems with a particular focus on problems involving: Very complex contact conditions Very large deformations I. Mesh distortion possible Typical application: metal forming simulations Bulk forming (drawing, rolling, extrusion, upsetting, etc.) Sheet metal forming (stretching, drawing)

163

L8.3

Introduction (2/3) Upsetting


Rolling

Rolling of a symmetric I-section

Upsetting of a cylindrical billet

L8.4

Introduction (3/3)


Hydroforming Uses fluid pressure to form a component. Unstable wrinkling of excess blank material.

A draw cap is added to decrease the wrinkling effects.

164

L8.5


Solution Strategies (1/3) Two solvers: Implicit solver (Abaqus/Standard) Solves for either true static or true dynamic equilibrium. Explicit solver (Abaqus/Explicit) Solves for true dynamic equilibrium. At first glance it appears the implicit solver would be the appropriate choice for modeling highly nonlinear static problems. However, explicit solvers are more efficient for this class of problems. This is especially true for three-dimensional problems involving contact and very large deformations.

L8.6


Solution Strategies (2/3) Example: Simulation of a deep drawing process used to form an oil pan The pan is formed by displacing the punch downward while holding the die and blank holder fixed. The blank is modeled with shell elements; the tools are assumed rigid. Analysis performed with both implicit (Abaqus/Standard) and explicit (Abaqus/Explicit) solvers.

blank holder punch die blank

165

L8.7


Solution Strategies (3/3) The final deformed configuration is shown at right. Near the end of the punch stroke, the blank pulls through the blank holder and begins to wrinkle. The Abaqus/Standard job was about 20 times more expensive (in terms of CPU cost) than the Abaqus/Explicit job. Abaqus/Standard fails to converge at the point where the blank begins to wrinkle.

L8.8


Quasi-Static Simulations Using Explicit Dynamics (1/10) Introduction The explicit dynamics procedure is a true dynamic procedure. It was originally developed to model highspeed impact events. Explicit dynamics solves for the state of dynamic equilibrium where inertia can play a dominant role in the solution. Application of explicit dynamics to model quasi-static events, such as metal forming processes, requires special consideration: It is computationally impractical to model the process in its natural time period. I. Recall that stability considerations limit the size of the allowable increment:

t 

Le . cd

II. Literally millions of time increments would be required. Artificially increasing the speed of the process in the simulation is necessary to obtain an economical solution.

166

L8.9


Quasi-Static Simulations Using Explicit Dynamics (2/10) Two approaches to obtaining economical quasi-static solutions with an explicit dynamics solver Increased load rates Artificially reduce the time scale of the process by increasing the loading rate. Material strain rates calculated in the simulation are artificially high by the same factor applied to increase the loading rate. I. This is irrelevant if the material is rate insensitive. Mass scaling If strain rate sensitivity is being modeled, erroneous solutions can result if the load rates are increased. Mass scaling allows you to model processes in their natural time scale when considering rate-sensitive materials. I. Artificially increasing the material density by a factor of f 2 increases the stable time increment by a factor of f.

L8.10


Quasi-Static Simulations Using Explicit Dynamics (3/10) How much can I increase the load rate or scale the mass? Increased load rates and mass scaling achieve the same effect. Increased load rates reduce the time scale of the simulation. Mass scaling increases the size of the stable time increment. With both approaches, fewer increments are needed to complete the job. As the speed of the process is increased, a state of static equilibrium evolves into a state of dynamic equilibrium. Inertia forces become more dominant. The goal is to model the process in the shortest time period (or with the most mass scaling) in which inertia forces are still insignificant.

167

L8.11


Quasi-Static Simulations Using Explicit Dynamics (4/10) Suggested approach Run a series of simulations in the order from the fastest load rate to the slowest (or largest mass scaling to the smallest), since the analysis time is greater for slower load rates (or smaller mass scaling). Examine the results (deformed shapes, stresses, strains, energies) to get an understanding for the effects of varying the model. For example, excessive tool speeds in explicit sheet metal forming simulations tend to suppress wrinkling and to promote unrealistic localized stretching. Excessive tool speeds in explicit bulk forming simulations cause ―jetting‖—hydrodynamic-type response.

L8.12

Quasi-Static Simulations Using Explicit Dynamics (5/10) Jetting Consider the following bulk forming process (180 section of an axisymmetric model). When the tool speed is too large, highly localized deformation develops (jetting).


jetting

tool speed = 10 m/s

tool speed = 500 m/s

Effect of tool speed on deformed shape

168

L8.13

Quasi-Static Simulations Using Explicit Dynamics (6/10)


Example: sheet metal This figure shows a simple model of a standard door beam intrusion test for an automobile door. The circular beam is fixed at each end, and the beam is deformed by a rigid cylinder. The actual test is quasi-static.

Rigid cylinder impacting a deformable beam

L8.14


Quasi-Static Simulations Using Explicit Dynamics (7/10) At an extremely high impact velocity, 400 m/sec, there is highly localized deformation and no structural response by the beam. The dominant response in a static test will be in the first structural mode of the beam. The frequency of this mode is used to estimate the impact velocity. The frequency of the first mode is approximately 250 Hz. This rate corresponds to a period of 4 milliseconds. Using a velocity of 25 m/sec, the cylinder will be pushed into the beam 0.1 m in 4 milliseconds.

V

Velocity 400 m/s:

Localized effect

V

0.1 m

Velocity 25 m/s:

Good global result

169

L8.15

Quasi-Static Simulations Using Explicit Dynamics (8/10) Why is the velocity 25 m/sec appropriate? The frequency ( f ) of the first mode is approximately 250 Hz.

This corresponds to a period t = 0.004 seconds.


During this period, the rigid cylinder is pushed into the beam d = 0.1 m. Thus, the velocity v is estimated to be v = d / t = 0.1/0.004 = 25 m/sec. Recall, the wave speed of metals is about 5000 m/sec, so the impact velocity 25 m/sec is about 0.5% of the wave speed. The impact velocity should be limited to less than 1% of the wave speed of the material. A more accurate solution could be obtained by ramping up the velocity smoothly from zero over the analysis step.

L8.16


Quasi-Static Simulations Using Explicit Dynamics (9/10)

170

Use the SMOOTH STEP amplitude curve A quasi-static solution is also promoted by applying loads gradually: A constant velocity condition applied to a tool results in a sudden impact load onto the metal blank. This may induce propagation of a stress wave through the blank, producing undesired results. Ramping up the tool velocity gradually from zero minimizes these adverse effects. Ramping down the tool velocity to zero as the tool is moved to its final position is also recommended for the same reasons.

L8.17


Quasi-Static Simulations Using Explicit Dynamics (10/10) The SMOOTH STEP amplitude definition creates a fifth-order polynomial transition between two amplitude values such that the first and second time derivatives are zero at the beginning and the end of the transition. When the displacement time history is defined using the SMOOTH STEP definition, the velocity and the acceleration will be zero at every amplitude value specified.

*AMPLITUDE, NAME=SSTEP, DEFINITION=SMOOTH STEP 0.0, 0.0, 1.0E-5, 1.0 *BOUNDARY, TYPE=DISPLACEMENT, AMP=SSTEP 12, 2, 2, 2.5

L8.18

Energy Balance (1/4) An energy balance equation can be used to help evaluate whether a simulation is yielding an appropriate quasistatic response. In Abaqus/Explicit this equation is written as

EKE  EI  EV  EFD   EW  EPW  ECW  EMW  ETOT  constant,


where

Work done by contact and constraint penalties, and by propelling added mass due to mass scaling

EKE

is the kinetic energy,

EI

is the internal energy (both elastic and plastic strain energy and the artificial energy associated with hourglass control),

EV

is the energy dissipated by viscous mechanisms,

EFD

is the frictional dissipation energy,

EW

is the work due to loads and boundary conditions, and

ETOT

is the total energy in the system.

171

L8.19

Energy Balance (2/4)


Consider a pull test applied to a uniaxial tensile specimen. If the physical test is quasi-static, the work applied by the external forces in stretching the specimen equals the internal energy in the specimen.

Uniaxial pull test

L8.20


Energy Balance (3/4)

172

The energy history for the quasi-static test would appear as shown in the figure at right: Inertia forces are negligible. The velocity of material in the test specimen is very small. Kinetic energy is negligible. As the speed of the test increases: The response of the specimen becomes less static, more dynamic. Material velocities and, therefore, kinetic energy become more significant. Energy history for quasi-static pull test

L8.21


Energy Balance (4/4) Hence, examination of the energy content provides another measure to evaluate whether the results from an Abaqus/Explicit metal forming simulation reflect a quasi-static solution. The kinetic energy of the deforming material should not exceed a small fraction of its internal energy throughout the majority of the forming process. A small fraction typically means 1–5%. I. It is generally not possible to achieve this in early stages of the process since the blank will be moving before it develops any significant deformation. II. Use smooth step amplitude curves to improve early response. Not interested in kinetic energy of the tools. I. Subtract their contribution from global model kinetic energy or restrict energy output to deforming components.

L8.22

Example: Load Rates (1/4) Cylindrical cup deep drawing The quarter-symmetric finite element model is shown in the figure. Friction is modeled along all contact interfaces: Punch and blank: m = 0.25.


Die and blank: m = 0.125. Blank holder and blank: m = 0. The deep drawing simulation is conducted by applying a downward force of 22.87 kN to the blank holder, then displacing the punch downward 36 mm.

Initial configuration for cylindrical cup deep drawing

173

L8.23

Example: Load Rates (2/4)


We examine three different punch speeds: 3 m/s 30 m/s 150 m/s The computation cost of each cylindrical cup deep drawing simulation is summarized in the following table:

Punch speed (m/s)

Time increments

Normalized CPU time

3 (1X)

27929

1.0

30 (10X)

2704

0.097

150 (50X)

529

0.019

L8.24


Example: Load Rates (3/4) Contours of blank thickness in final formed configuration Excessive punch speeds lead to results that do not correspond to the physics. At 150 m/s unrealistic thinning of the blank is predicted. Results obtained at 30 m/s and 3 m/s are very similar, even though the difference in computation cost is a factor of 10.

Vpunch = 30 m/s

Vpunch = 3 m/s

Vpunch = 150 m/s

174

L8.25

Example: Load Rates (4/4) Comparison of internal and kinetic energies At a punch speed of 150 m/s the kinetic energy of the blank is a significant fraction of its internal energy.


At punch speeds of 3 m/s and 30 m/s the kinetic energy is only a small fraction of the internal energy over the majority of the forming process history.

L8.26

Example: Mass Scaling (1/2) Uniaxial tension test

The figure shows the problem definition for a tension test on a plane strain bar with the material properties of a mild steel.


It is modeled with quarter symmetry.

Mass scaling is available through the *FIXED MASS SCALING option. Mass scaling applied at the beginning of a step. Syntax: *FIXED MASS SCALING, ELSET=name, FACTOR= f 2 The density of every element in the specified element set is increased by f 2, thus increasing each element’s stable time increment by f .

Uniaxial tension test

175

L8.27


Example: Mass Scaling (2/2) This figure shows the results of three different analyses. The results on the left and in the center are almost identical. The solution for the results in the center requires one-fifth the computer time of the first solution. The solution on the right gives an essentially meaningless result compared to the original static solution.

Mass scaling factor

1

25

10000

Contours of PEEQ

L8.28

Adaptive Meshing (1/8)


Motivation In many nonlinear simulations the material in the structure or process undergoes very large deformations. These deformations distort the finite element mesh, often to the point where the mesh is unable to provide accurate results or the analysis terminates prematurely for numerical reasons. In such simulations it is necessary to use adaptive meshing tools to minimize the distortion in the mesh periodically.

176

Note: In this course we restrict our attention to the ALE adaptive meshing capability available in Abaqus/Explicit. The adaptive remeshing capability available in Abaqus/Standard and the Coupled Eulerian-Lagrangian capability available in Abaqus/Explicit are not discussed here.

L8.29


Adaptive Meshing (2/8) Adaptive meshing is useful in a broad range of applications: Can be used as a continuous adaptive meshing tool for transient analysis problems undergoing large deformations, such as: I. Dynamic impact II. Penetration III. Sloshing IV. Forging Can be used as a solution technique to model steady-state processes, such as: I. Extrusion II. Rolling Can be used as a tool to analyze the transient phase in a steady-state process.

L8.30


Adaptive Meshing (3/8) Adaptive meshing basics Adaptive meshing is performed in Abaqus/Explicit using the arbitrary Lagrangian-Eulerian (ALE) method. The primary characteristics of the adaptive meshing capability are: The mesh is smoothed at regular intervals to reduce element distortion and to maintain good element aspect ratios. The same mesh topology is maintained—the number of elements and nodes and their connectivity do not change. It can be used to analyze Lagrangian (transient) problems and Eulerian (steady-state) problems.

177

L8.31



Arbitrary Lagrangian-Eulerian (ALE) method Lagrangian Nodes move exactly with material points. description It is easy to track free surfaces and apply boundary conditions. The mesh will become distorted with high strain gradients; default description in Abaqus. Eulerian description

Nodes stay fixed while material flows through the mesh It is more difficult to track free surfaces. No mesh distortion because mesh is fixed. Available using the Coupled Eulerian-Lagrangian (CEL) capability.

ALE

Mesh motion is constrained to the material motion only where necessary (at free boundaries), but otherwise material motion and mesh motion are independent.

L8.32



Motion of mesh and material with various methods

178

L8.33

Adaptive Meshing (6/8) ALE simulation of an axisymmetric forging problem


Undeformed model

Deformed meshes at 70% of die travel

L8.34



By using the adaptive meshing capability, a high-quality mesh can be maintained throughout the entire forging process.

Nodes along the free boundary move with the material in the direction normal to the material’s surface. They are allowed to adapt (adjust their position) tangent to the free surface.

Interior nodes adaptively adjust in all directions ALE simulation: deformed mesh at 100% of die travel

179

L8.35



In a transient (Lagrangian-type) problem, such as this forging simulation, minimal additional input is required to invoke the adaptive meshing capability.

*HEADING .... *ELSET, ELSET=BLANK .... *STEP *DYNAMIC, EXPLICIT .... *ADAPTIVE MESH, ELSET=BLANK [, FREQUENCY=..., MESH SWEEPS=...] .... *END STEP Adaptive meshing is available for all first-order, reduced-integration continuum elements. Other element types may exist in the model.

L8.36


Summary

180

Excessive loading rates can produce solutions with significant inertia effects. A general guideline is to restrict loading rates so that, for example, tool speeds are less than 1% of the material wave speed. Ramping loads up from zero also promotes a quasi-static response. Use the SMOOTH STEP amplitude definition. Mass scaling can be used for problems with rate-dependent material behavior, allowing the process to be modeled in its natural time period. The energy balance can be used to assist in evaluating whether a given solution represents a quasistatic response to applied loads. Since results can depend strongly on the process speed (real or artificially adjusted by mass scaling), it is vital to ensure that unrealistic results are not being generated by excessive artificial process speed scaling. To confirm that the Abaqus/Explicit results are realistic, it may be useful to study a simplified version of the problem as a static analysis in Abaqus/Standard for comparison. The easiest way to create a suitable simplified test case for this purpose is often to define a twodimensional version of part of the problem. Adaptive meshing is used to maintain a high-quality mesh in the presence of very large deformations.

Workshop 8: Quasi-Static Analysis (IA) 1.


2.

L8.37

Interactive version. Choose either the interactive Exercise simulates the deep drawing of a or keywords version of this workshop. can bottom Workshop tasks include: This workshop is optional. 1. Perform a frequency extraction analysis to determine an appropriate analysis time for this quasi-static process. 2. Complete the geometry definition of the rigid tools, and include contact and material definitions. 3. Include a SMOOTH STEP amplitude definition to improve quasi-static behavior. 4. Include mass scaling to reduce the analysis time without degrading the results. 5. Perform the analysis, and determine whether or not the results are acceptable.

1 hour

Workshop 8: Quasi-Static Analysis (KW) 1.


2.

L8.38

Keywords version. Choose either the interactive Exercise simulates the deep drawing of a or keywords version of this workshop. can bottom Workshop tasks include: This workshop is optional. 1. Perform a frequency extraction analysis to determine an appropriate analysis time for this quasi-static process. 2. Complete the geometry definition of the rigid tools, and include contact and material definitions. 3. Include a SMOOTH STEP amplitude definition to improve quasi-static behavior. 4. Include mass scaling to reduce the analysis time without degrading the results. 5. Perform the analysis, and determine whether or not the results are acceptable.

1 hour

181

182

Notes

183

Notes

184

Lesson 9: Combining Abaqus/Standard and Abaqus/Explicit

L9.1


Lesson content:

Introduction Abaqus Usage Springback Calculation Using Abaqus/Standard Workshop 9: Import Analysis (IA) Workshop 9: Import Analysis (KW)


1 hour

L9.2

Introduction (1/3) Abaqus provides a capability to transfer a deformed mesh and an associated state between an Abaqus/Explicit analysis and an Abaqus/Standard analysis.


This capability provides great flexibility, for example, in modeling springback in metal forming processes. The deformed model can be transferred from Abaqus/Explicit to Abaqus/Standard to, for example: Obtain the final static configuration after a dynamic event. Simulate springback after a metal forming operation. Perform eigenvalue or buckling simulations on a formed part. Simulate the movement of rigid tools more efficiently. The deformed model can be transferred from Abaqus/Standard to Abaqus/Explicit to, for example: Simulate additional forming steps after an intermediary springback phase. Simulate forming processes that occur after a part cools down from a heat treatment phase (thermal stresses are calculated in Abaqus/Standard). Continue a simulation following a phase of the analysis that was done more efficiently in Abaqus/Standard. Follow the steady-state rolling of a tire in Abaqus/Standard with a transient rolling along a bumpy road in Abaqus/Explicit.

185

L9.3

Introduction (2/3)


Import summary The ability to import the material state and the nodal positions is the main requirement of importing results between the analysis modules. The following table summarizes the import capabilities:

Can be imported

Need to be respecified

Cannot be imported

Material state *

Boundary conditions

Some materials *

Nodal positions

Loads

Elements, element sets

Contact definitions

Nodes, node sets

Output requests

Temperatures

Multi-point constraints Nodal transformations Amplitude definitions

L9.4


Introduction (3/3)

186

Comments regarding material states Only the material states for the some materials are imported correctly for further analysis. These include: Linear elastic Hyperelastic Mullins effect Hyperfoam Mises plasticity (including the kinematic hardening models) Viscoelastic User-defined materials (UMAT and VUMAT) See Section 9.2.1 of the Abaqus Analysis User's Manual for a complete list of supported materials

L9.5

Abaqus Usage (1/4) Performing an import analysis requires the following:

A restart (.res) file containing the current state of the model.


If transferring from Abaqus/Standard to Abaqus/Explicit, also require the I. analysis database (.mdl and .stt), II. part (.prt), and III. output database (.odb) files. If transferring from Abaqus/Explicit to Abaqus/Standard, also require the I. state (.abq), II. analysis database (.stt), III. package (.pac), IV. part (.prt), and V. output database (.odb) files. The additional files noted above are written by default; do not delete them if planning on performing a restart analysis. A new input (.inp) file for the next analysis stage that contains: The *IMPORT option directly after the *HEADING option Any additional model data History data for the next stage of the simulation

L9.6

Abaqus Usage (2/4) Executing an import analysis

During an Abaqus/Explicit or Abaqus/Standard simulation, a restart file must be written at the time when transfer of the model’s state is desired.


Using the Abaqus driver, set the job parameter to the new job name and set the oldjob parameter to the job name associated with the restart file from the previous analysis stage. abaqus job=new_jobname oldjob=previous_jobname

Specifying the analysis increment for import Importing from Abaqus/Explicit into an Abaqus/Standard model: The *IMPORT option specifies the STEP and INTERVAL of the restart file from which the model state is to be imported: *IMPORT, STEP=step number, INTERVAL=interval number Importing from Abaqus/Standard into an Abaqus/Explicit model: The *IMPORT option specifies the STEP and INCREMENT of the restart file from which the model state is to be imported: *IMPORT, STEP=step number, INC=increment number

187

L9.7

Abaqus Usage (3/4) Elements and nodes

Specify the element sets that are to be imported on the data line of the *IMPORT option. *IMPORT, STEP=step

number, INTERVAL=interval number


elset_1, elset_2, elset_3 Each element set name specified on the data line of the *IMPORT option must have been used in a section definition option (e.g., *SOLID SECTION) in the original analysis. The current thickness of shell and membrane elements is imported automatically and becomes the initial thickness for the element if UPDATE=YES. All nodes attached to imported elements are imported. Additional nodes and elements can be defined in the new analysis.

L9.8

Abaqus Usage (4/4) Material state and reference configuration


By default, the material state (for supported materials) is imported in an import analysis (STATE=YES on the *IMPORT option). For the analysis to continue without resetting the reference configuration, set UPDATE=NO on the *IMPORT option: *IMPORT, UPDATE=NO In some cases it may be desirable to obtain springback displacements and strains relative to the geometry at the start of the springback analysis (reset to zero at the start of the springback step). Set UPDATE=YES on the *IMPORT option: *IMPORT, UPDATE=YES

UPDATE=YES should not be used if additional forming stages will follow because the reference configuration will not be consistent. Other combinations of the STATE and UPDATE parameters are available but are not discussed here. The setting of NLGEOM is imported and becomes the setting for the new analysis.

188

L9.9

Springback Calculation Using Abaqus/Standard (1/7) The blank shown in the figure at right undergoes large deformations during the sheet metal forming process.


Once the forming process is complete and the confining tools are removed, the blank will attempt to recover its elastic deformation. This springback phenomenon may lead to unacceptable warping of the formed product. Forming tools must be designed to compensate for springback effects.

L9.10

Springback Calculation Using Abaqus/Standard (2/7) For the calculation of springback associated with sheet metal forming processes:

Generally, the forming process is simulated using Abaqus/Explicit because it is more efficient for such analyses.


The deformed mesh of the blank and its associated material state at the end of the forming process are imported into an Abaqus/Standard model to analyze springback.

The springback calculation is performed more efficiently in Abaqus/Standard than in Abaqus/Explicit. The displacements that Abaqus/Standard calculates are the totals from the forming and springback stages if UPDATE=NO is used on the *IMPORT option.

189

L9.11

Springback Calculation Using Abaqus/Standard (3/7) Equilibrium

Upon importing the deformed blank and its current state into Abaqus/Standard, the model is not in static equilibrium. Dynamic forces, contact forces, and boundary conditions that exist in Abaqus/Explicit but not in Abaqus/Standard contribute to this condition:


Dynamic forces:

The forming process is simulated using a dynamic procedure, so the deformed blank is in a state of dynamic equilibrium. Inertia and damping forces are present. In a quasi-static forming simulation the state of dynamic equilibrium is relatively close to a state of static equilibrium.

Boundary and contact conditions: Contact forces are not imported. Boundary conditions can be modified in the import analysis.

L9.12

Springback Calculation Using Abaqus/Standard (4/7) Achieving static equilibrium during springback analysis

When the deformed blank is imported with the material state into Abaqus/Standard, a set of artificial internal stresses are automatically applied that equilibrate the imported stresses so that static equilibrium is obtained at the start of the analysis.


These artificial stresses are ramped off during the springback calculation step.

190

As these stresses are removed, the blank deforms further (referred to as springback) as a result of redistribution of internal forces. The final configuration following springback is achieved after complete removal of the artificial stresses or initial out-of-balance forces.

L9.13

Springback Calculation Using Abaqus/Standard (5/7) Example: Springback calculation for cylindrical cup


The following input in Abaqus/Standard is used to define the springback analysis:

*HEADING Springback Calculation *IMPORT, STEP=1, INTERVAL=10, UPDATE=YES, STATE=YES BLANK, *STEP, NLGEOM *STATIC 0.1, 1. *BOUNDARY NodeX, XSYMM Must have sufficient boundary conditions to NodeY, YSYMM 1, 3, 3, 0.0 prevent rigid body motion *RESTART, WRITE, FREQUENCY=5 *EL PRINT, ELSET=BLANK, FREQUENCY=99 S, *END STEP

L9.14

Springback Calculation Using Abaqus/Standard (6/7) Element set BLANK is the only element set whose state is imported into Abaqus/Standard.

Node set definitions NodeX and NodeY are imported and subsequently used to define symmetry boundary conditions.


The z-translation of node 1 is restrained to preclude rigid body motion of the deformed blank. The NLGEOM parameter must be used with the *STEP option, since Abaqus/Explicit includes nonlinear geometry by default. The *STATIC procedure is carried out incrementally. The initial out-of-balance forces are ramped down in accordance with the time incrementation.

191

L9.15

Springback Calculation Using Abaqus/Standard (7/7)


The configuration after springback is shown in the figure. A magnification factor of 10 is applied to the displacements for visualization purposes.

Deformed configuration after springback

L9.16

Workshop 9: Import Analysis (IA) 1.

This exercise simulates the springback of a formed can bottom

2.

Workshop tasks include:

Interactive version. Choose either the interactive or keywords version of this workshop. This workshop is optional.

Import the results into an Abaqus/Standard analysis to examine springback.


1.

30 minutes

192

L9.17

Workshop 9: Import Analysis (KW) 1.

This exercise simulates the springback of a formed can bottom

2.

Workshop tasks include:

Keywords version. Choose either the interactive or keywords version of this workshop. This workshop is optional.

Import the results into an Abaqus/Standard analysis to examine springback.


1.

30 minutes

193

194

Notes

195

Notes

196

Appendix 1: Element Selection Criteria

A1.1


Lesson content:

Elements in Abaqus Structural (Shells and Beams) vs. Continuum Elements Modeling Bending Using Continuum Elements Stress Concentrations Contact Incompressible Materials Mesh Generation Solid Element Selection Summary

1.5 hours

A1.2


Elements in Abaqus (1/8) The wide range of elements in the Abaqus element library provides flexibility in modeling different geometries and structures. Each element can be characterized by considering the following: Family Number of nodes Degrees of freedom Formulation Integration

197

A1.3

Elements in Abaqus (2/8)


Family A family of finite elements is the broadest category used to classify elements. Elements in the same family share many basic features. There are many variations within a family.

shell elements

continuum (solid elements)

membrane elements

rigid elements

beam elements

truss elements

special-purpose elements like springs, dashpots, and masses

infinite elements

A1.4



Number of nodes (interpolation) An element’s number of nodes determines how the nodal degrees of freedom will be interpolated over the domain of the element. Abaqus includes elements with both first- and second-order interpolation.

First-order interpolation

198

Second-order interpolation

A1.5


Elements in Abaqus (4/8) Degrees of freedom The primary variables that exist at the nodes of an element are the degrees of freedom in the finite element analysis. Examples of degrees of freedom are: Displacements Rotations Temperature Electrical potential Some elements have internal degrees of freedom that are not associated with the user-defined nodes.

A1.6



Formulation The mathematical formulation used to describe the behavior of an element is another broad category that is used to classify elements. Examples of different element formulations: Plane strain

Small-strain shells

Plane stress

Finite-strain shells

Hybrid elements

Thick-only shells

Incompatible-mode elements

Thin-only shells

Integration The stiffness and mass of an element are calculated numerically at sampling points called ―integration points‖ within the element. The numerical algorithm used to integrate these variables influences how an element behaves.

199

A1.7



Abaqus includes elements with both ―full‖ and ―reduced‖ integration. Full integration: I. The minimum integration order required for exact integration of the strain energy for an undistorted element with linear material properties. Reduced integration: I. The integration rule that is one order less than the full integration rule.

Full integration

Reduced integration

Firstorder interpolation 2x2

1x1

3x3

2x2

Secondorder interpolation

A1.8

Elements in Abaqus (7/8) Element naming conventions: examples


B21: Beam, 2-D, 1st-order interpolation

CAX8R: Continuum, AXisymmetric, 8-node, Reduced integration

DC3D4: Diffusion (heat transfer), Continuum, 3-D, 4-node

200

S8RT: Shell, 8-node, Reduced integration, Temperature

CPE8PH: Continuum, Plane strain, 8-node, Pore pressure, Hybrid

DC1D2E: Diffusion (heat transfer), Continuum, 1-D, 2-node, Electrical

A1.9

Elements in Abaqus (8/8) Comparing Abaqus/Standard and Abaqus/Explicit element libraries

Both programs have essentially the same element families: continuum, shell, beam, etc.


Abaqus/Standard includes elements for many analysis types besides stress analysis: heat transfer, soils consolidation, acoustics, etc. Acoustic elements are also available in Abaqus/Explicit. Abaqus/Standard includes many more variations within each element family. Abaqus/Explicit includes mostly first-order reduced-integration elements. Exceptions: second-order triangular and tetrahedral elements; second-order beam elements; first-order fully-integrated brick (including incompatible mode version), shell, and membrane elements. Many of the same general element selection guidelines apply to both programs.

A1.10

Structural (Shells and Beams) vs. Continuum Elements (1/3) Continuum (solid) element models can be large and expensive, particularly in three-dimensional problems.

If appropriate, structural elements (shells and beams) should be used for a more economical solution.


A structural element model typically requires far fewer elements than a comparable continuum element model. For structural elements to produce acceptable results, the shell thickness or the beam cross-section dimensions should be less than 1/10 of a typical global structural dimension, such as: The distance between supports or point loads The distance between gross changes in cross section The wavelength of the highest vibration mode

201

A1.11

Structural (Shells and Beams) vs. Continuum Elements (2/3) Shell elements

Shell elements approximate a threedimensional continuum with a surface model.


Model bending and in-plane deformations efficiently. If a detailed analysis of a region is needed, a local three-dimensional continuum model can be included using multi-point constraints or submodeling.

3-D continuum

surface model

shell model of a hemispherical dome subjected to a projectile impact

A1.12

Structural (Shells and Beams) vs. Continuum Elements (3/3) Beam elements

Beam elements approximate a threedimensional continuum with a line model.


Model bending, torsion, and axial forces efficiently.

Many different cross-section shapes are available.

3-D continuum

line model

Cross-section properties can also be specified by providing engineering constants.

framed structure modeled using beam elements

202

A1.13

Modeling Bending Using Continuum Elements (1/10)


Physical characteristics of pure bending

xx

Plane cross-sections remain plane throughout the deformation. The axial strain xx varies linearly through the thickness. The strain in the thickness direction yy is zero if  = 0. No membrane shear strain. Implies that lines parallel to the beam axis lie on a circular arc.

A1.14



Modeling bending using second-order solid elements (CPE8, C3D20R, …) Second-order full- and reduced-integration solid elements model bending accurately: The axial strain equals the change in length of the initially horizontal lines. The thickness strain is zero. The shear strain is zero. lines that are initially vertical do not change length (implies yy= 0).

Because the element edges can assume a curved shape, the angle between the deformed isoparametric lines remains equal to 90o (implies xy= 0).

203

A1.15

Modeling Bending Using Continuum Elements (3/10) Modeling bending using first-order fully-integrated solid elements (CPS4, CPE4, C3D8) These elements detect shear strains at the integration points. Nonphysical; present solely because of the element formulation used. Overly stiff behavior results from energy going into shearing the element rather than bending it (called ―shear locking‖).


integration point

Because the element edges must remain straight, the angle between the deformed isoparametric lines is not equal to 90º (implies  xy  0 ).

Do not use these elements in regions dominated by bending!

A1.16



Modeling bending using first-order reduced-integration elements (CPE4R, …) These elements eliminate shear locking. However, hourglassing is a concern when using these elements. Only one integration point at the centroid. A single element through the thickness does not detect strain in bending. Deformation is a zero-energy mode (deformation but no strain; called ―hourglassing‖).

Change in length is zero (implies no strain is detected at the integration point).

Bending behavior for a single first-order reduced-integration element

204

A1.17



Hourglassing can propagate easily through a mesh of first-order reduced-integration elements, causing unreliable results. Hourglassing is not a problem if you use multiple elements—at least four through the thickness. Each element captures either compressive or tensile axial strains but not both. The axial strains are measured correctly. The thickness and shear strains are zero. Cheap and effective elements.

A1.18



Detecting and controlling hourglassing Hourglassing can usually be seen in deformed shape plots. Example: Coarse and medium meshes of a simply supported beam with a center point load. Abaqus has built-in hourglass controls that limit the problems caused by hourglassing. Verify that the artificial energy used to control hourglassing is small (<1%) relative to the internal energy.

Same load and displacement magnification (1000)

205

A1.19



Use the X–Y plotting capability in Abaqus/CAE to compare the energies graphically.

internal energy

internal energy

artificial energy

Two elements through the thickness: Ratio of artificial to internal energy is 2%

artificial energy

Four elements through the thickness: Ratio of artificial to internal energy is 0.1%

A1.20



206

Modeling bending using incompatible mode elements (CPS4I, …) Perhaps the most cost-effective solid continuum elements for bending-dominated problems. Compromise in cost between the first- and second-order reduced-integration elements, with many of the advantages of both. Model shear behavior correctly—no shear strains in pure bending. Model bending with only one element through the thickness. No hourglass modes, and work well in plasticity and contact problems. The advantages over reduced-integration first-order elements are reduced if the elements are severely distorted; however, all elements perform less accurately if severely distorted.

A1.21



Example: Cantilever beam with distorted elements

Parallel distortion

Trapezoidal distortion

A1.22

Modeling Bending Using Continuum Elements (10/10) Summary

xx

yy

xy

Physical behavior

0

0

0

Second-order

0

0

0

First-order, full integration

0

0

0

0

0

0

Hourglassing if too few elements through thickness

0

0

0

OK if enough elements through the thickness

0

0

0

OK if not overly distorted


Element type

First-order, reduced integration

Incompatible mode

Notes

OK

Shear locking

207

A1.23

Stress Concentrations (1/6)


Second-order elements clearly outperform first-order elements in problems with stress concentrations and are ideally suited for the analysis of (stationary) cracks. Both fully-integrated and reduced-integration elements work well. Reduced-integration elements tend to be somewhat more efficient—results are often as good or better than full integration at lower computational cost.

A1.24



Second-order elements capture geometric features, such as curved edges, with fewer elements than first-order elements.

Physical model

Model with first-order elements—element faces are straight line segments.

208

Model with second-order elements— element faces are quadratic curves.

A1.25



Both first- and second-order quads and bricks become less accurate when their initial shape is distorted. First-order elements are known to be less sensitive to distortion than second-order elements and, thus, are a better choice in problems where significant mesh distortion is expected. Second-order triangles and tetrahedra are less sensitive to initial element shape than most other elements; however, well-shaped elements provide better results.

ideal

undistorted

okay

bad

distorted

A1.26

Stress Concentrations (4/6) A typical stress concentration problem, a NAFEMS benchmark problem, is shown at right. The analysis results obtained with different element types follow.


P

elliptical shape

209

A1.27



First-order elements (including incompatible mode elements) are relatively poor in the study of stress concentration problems.

Element s yy at D (Target=100.0) type Coarse mesh Fine mesh CPS3 55.06 76.87 CPS4 71.98 91.2 CPS4I 63.45 84.37 CPS4R 43.67 60.6 CPS6 96.12 101.4 CPS8 91.2 100.12 CPS8R 92.56 97.16

A1.28



Second-order elements such as CPS6, CPS8, and CPS8R give much better results. Well-shaped, second-order, reduced-integration quadrilaterals and hexahedra can provide high accuracy in stress concentration regions. Distorted elements reduce the accuracy in these regions.

210

A1.29


Contact If the surface-to-surface contact discretization is used: No fundamental issues or element type restrictions Abaqus/Standard always uses this formulation for general contact If the node-to-surface contact discretization is used: Best to avoid having second-order tetrahedral elements (C3D10, C3D10I) underlying the slave surface with this contact discretization Susceptible to poor convergence and extreme contact pressure noise Use ―modified‖ versions of these elements (C3D10M) instead Sometimes C3D10 or C3D10I elements work fine if penalty enforcement of contact is specified Abaqus automatically activates supplementary constraints for this combination of features But the extra (supplementary) constraints can be another source of convergence problems

A1.30

Incompressible Materials (1/3)


Many nonlinear problems involve incompressible materials ( = 0.5) and nearly incompressible materials ( > 0.475). Rubber Metals at large plastic strains Conventional finite element meshes often exhibit overly stiff behavior due to volumetric locking, which is most severe when these materials are highly confined.

overly stiff behavior of an elasticplastic material with volumetric locking

correct behavior of an elastic-plastic material

Example of the effect of volumetric locking

211

A1.31


Incompressible Materials (2/3) For an incompressible material each integration point’s volume must remain almost constant. This overconstrains the kinematically admissible displacement field and causes volumetric locking For example, in a refined three-dimensional mesh of 8-node hexahedra, there is—on average—1 node with 3 degrees of freedom per element. The volume at each integration point must remain fixed. Fully integrated hexahedra use 8 integration points per element; thus, in this example, we have as many as 8 constraints per element, but only 3 degrees of freedom are available to satisfy these constraints. The mesh is overconstrained—it ―locks.‖ Volumetric locking is most pronounced in fully integrated elements. Reduced-integration elements have fewer volumetric constraints. Reduced integration effectively eliminates volumetric locking in many problems with nearly incompressible material.

A1.32

Incompressible Materials (3/3)


Fully incompressible materials modeled with solid elements must use the ―hybrid‖ formulation (elements whose names end with the letter ―H‖). In this formulation the pressure stress is treated as an independently interpolated basic solution variable, coupled to the displacement solution through the constitutive theory. Hybrid elements introduce more variables into the problem to alleviate the volumetric locking problem. The extra variables also make them more expensive. The Abaqus element library includes hybrid versions of all continuum elements (except plane stress elements, where this is not needed).

212

Hybrid elements are only necessary for: All meshes with strictly incompressible materials, such as rubber. Refined meshes of reduced-integration elements that still show volumetric locking problems. Such problems are possible with elastic-plastic materials strained far into the plastic range. Even with hybrid elements a mesh of first-order triangles and tetrahedra is overconstrained when modeling fully incompressible materials. Hence, these elements are recommended only for use as ―fillers‖ in quadrilateral or brick-type meshes with such material.

A1.33

Mesh Generation (1/5)


Meshes Typical element shapes are shown at right. Most elements in Abaqus are topologically equivalent to these shapes. For example, CPE4 (stress), DC2D4 (heat transfer), and AC2D4 (acoustics) are topologically equivalent to a linear quadrilateral.

A1.34



Quad/hex vs. tri/tet elements Of particular importance when generating a mesh is the decision regarding whether to use quad/hex or tri/tet elements. Quad/hex elements should be used wherever possible. They give the best results for the minimum cost. When modeling complex geometries, however, the analyst often has little choice but to mesh with triangular and tetrahedral elements.

Turbine blade with platform modeled with tetrahedral elements

213

A1.35


Mesh Generation (3/5) First-order tri/tet elements (CPE3, CPS3, CAX3, C3D4, C3D6) are poor elements; they have the following problems: Poor convergence rate. I. They typically require very fine meshes to produce good results. Volumetric locking with incompressible or nearly incompressible materials, even using the ―hybrid‖ formulation. These elements should be used only as fillers in regions far from any areas where accurate results are needed. Second-order tri/tet elements (C3D10, C3D10I, etc.) Suitable for general usage Less sensitive to initial element shape that quads/hex but convergence rate is slower Guidelines for contact analysis I. Surface-to-surface contact discretization » No restriction on element type (use C3D10, C3D10I, C3D10M, etc.) II. Node-to-surface contact discretization » Restrict usage to modified second-order elements (e.g., C3D10M)

A1.36



214

Mesh refinement and convergence Use a sufficiently refined mesh to ensure that the results from your Abaqus simulation are adequate. Coarse meshes tend to yield inaccurate results. The computer resources required to run your job increase with the level of mesh refinement. It is rarely necessary to use a uniformly refined mesh throughout the structure being analyzed. Use a fine mesh only in areas of high gradients and a coarser mesh in areas of low gradients. Can often predict regions of high gradients before generating the mesh. Use hand calculations, experience, etc. Alternatively, you can use coarse mesh results to identify high gradient regions. Some recommendations: Minimize mesh distortion as much as possible. A minimum of four quadratic elements per 90o should be used around a circular hole. A minimum of four elements should be used through the thickness of a structure if first-order, reduced integration solid elements are used to model bending. Other guidelines can be developed based on experience with a given class of problem.

A1.37



It is good practice to perform a mesh convergence study. Simulate the problem using progressively finer meshes, and compare the results. I. The mesh density can be changed very easily using Abaqus/CAE since the definition of the analysis model is based on the geometry of the structure. When two meshes yield nearly identical results, the results are said to have ―converged.‖ I. This provides increased confidence in your results.

A1.38


Solid Element Selection Summary (1/2)

Class of problem

Best element choice

Avoid using

General contact between deformable bodies

First-order quad/hex

Second-order elements with the node-tosurface contact discretization

Contact with bending

Incompatible mode

First-order fully integrated quad/hex or second-order elements with the node-tosurface contact discretization

Bending (no contact)

Second-order quad/hex

First-order fully integrated quad/hex

Stress concentration

Second-order

First-order

Nearly incompressible ( >0.475 or large strain plasticity pl >10%)

First-order elements or secondorder reduced integration elements

Second-order fully integrated

215

A1.39


Solid Element Selection Summary (2/2)

216

Class of problem

Best element choice

Completely incompressible (rubber  = 0.5)

Hybrid quad/hex, first-order if large deformations are anticipated

Bulk metal forming (high mesh distortion)

First-order reduced integration quad/hex

Complicated model geometry (linear material, no contact)

Second-order quad/hex if possible (if not overly distorted) or second-order tet/tri (because of meshing difficulties)

Complicated model geometry (nonlinear problem or contact)

First-order quad/hex if possible (if not overly distorted). If meshing requirements dictate, use second-order tet/tri (modified form; use regular form only with surface-to-surface contact discretization)

Natural frequency (linear dynamics)

Second-order

Nonlinear dynamic (impact)

First-order

Avoid using

Second-order quad/hex

Second-order

Notes

217

Notes

218

A2.1

Appendix 2: Contact Issues Specific to Abaqus/Standard Lesson content:


Contact as Part of the Model Definition Mesh Density Considerations Contact Logic in Abaqus/Standard

30 minutes

A2.2

Contact as Part of the Model Definition For Abaqus/Standard the entire contact definition is model data (it must appear before the first *STEP option). Contact pairs can be activated or deactivated during the analysis history using the *MODEL CHANGE option. *MODEL CHANGE, TYPE=CONTACT PAIR, [ADD | REMOVE]


surface_1, surface_2

219

A2.3

Mesh Density Considerations (1/2)


Contact pairs: Mesh density considerations of the (default) strict master/slave approach The slave surface should be meshed more finely than the master surface. If mesh densities are equal, the slave surface usually should be the surface with the softer underlying material.

A2.4

Mesh Density Considerations (2/2)


General contact: Master-slave roles are assigned automatically Largely based on mesh refinement.

Internal, component surfaces ranked by suitability as master

220

Overall general contact surface

A2.5

Contact Logic in Abaqus/Standard (1/10) Contact requires the imposition of constraints between the points that are in contact. Different ways of imposing constraints. For most of the contact algorithms, Abaqus/Standard uses the Lagrange multiplier method by default. For each potential contact point the contact condition is described by a single, often nonlinear, inequality constraint: h(u1 , u 2 , u3 , ...)  0, www.3ds.com | © Dassault Systèmes

where h is the “penetration” and uN are degrees of freedom.

A2.6

Contact Logic in Abaqus/Standard (2/10) Schematic of (default) behavior within an increment


Begin increment

1

Identify initially active contact constraints

2

Form and solve system of equations

Newton iterations

Yes

5 No (Reduce increment size and try again)

Identify changes in 3 contact constraint status

Determine if tending toward convergence

Check if solution 4 has converged

End increment

No

Yes

(At least one convergence criterion is not satisfied)

(Within convergence tolerances)

221

A2.7

Contact Logic in Abaqus/Standard (3/10)


Default contact algorithm (refer to flowchart on previous page): 1

Determine the initial contact state at each point (closed or open). For first increment of a step, based on initial model state; otherwise, based on solution extrapolation (if any)

2

Calculate the stiffness, imposing contact constraints accordingly. Form the system of equations and pass through the equation solver.

3

Are contact pressures and clearances consistent with the assumed contact state? Contact status changes (open/closed or stick/slip) often cause significant changes to the system of equations Iterations with contact status changes are flagged as severe discontinuity iterations (SDIs)

A2.8

Contact Logic in Abaqus/Standard (4/10)


4

222

5

Has convergence been achieved? By default, Abaqus quantifies the contact incompatibilities associated with SDIs. These incompatibilities must be sufficiently small to achieve convergence with respect to the contact state. Also have to ensure that the force residuals and solution corrections are sufficiently small to achieve equilibrium. If the contact state and equilibrium conditions satisfy their respective convergence criteria, the increment is complete. If convergence is not achieved, is it likely to be achieved? Abaqus evaluates trends, such as the number of contact status changes in successive iterations, to determine whether or not to continue iterating or cut back the increment size. If convergence is likely, update the contact constraints based on 3 and the stiffness, and resolve the system of equations; otherwise, try again with a smaller increment size.

A2.9

Contact Logic in Abaqus/Standard (5/10) Contact printout example Reference: Example Problem 1.3.4, “Deep drawing of a cylindrical cup” Status (.sta) file:


SUMMARY OF JOB INFORMATION: MONITOR NODE: 200 DOF: 2 STEP INC ATT SEVERE EQUIL TOTAL DISCON ITERS ITERS RIKS ITERS 1 1 1 1 1 2 2 1 1 0 1 1 3 1 1 10 0 10 3 2 1 7 1 8 3 3 1U 10 0 10 3 3 2 5 0 5 3 4 1 3 1 4 3 5 1 2 3 5 3 6 1 4 1 5 3 7 1 4 1 5 3 8 1 6 1 7 3 9 1U 8 0 8 3 9 2 4 3 7 3 10 1 2 3 5 3 11 1 4 2 6 . . .

TOTAL TIME/ FREQ 1.00 2.00 2.01 2.02 2.02 2.02 2.03 2.04 2.05 2.07 2.10 2.10 2.11 2.12 2.15

STEP TIME/LPF

INC OF TIME/LPF

DOF MONITOR

IF

1.00 1.00 0.0100 0.0200 0.0200 0.0238 0.0294 0.0378 0.0505 0.0695 0.0979 0.0979 0.109 0.125 0.149

1.000 1.000 0.01000 0.01000 0.01500 0.003750 0.005625 0.008438 0.01266 0.01898 0.02848 0.04271 0.01068 0.01602 0.02403

0.000 0.000 -0.000600 -0.00120 -0.00120 -0.00142 -0.00176 -0.00227 -0.00303 -0.00417 -0.00588 -0.00588 -0.00652 -0.00748 -0.00892

A2.10

Contact Logic in Abaqus/Standard (6/10) Message file, Step 3, Increment 6: INCREMENT


1, TIME INCREMENT

1.266E-02

CONTACT PAIR (ASURF,BSURF) NODE 167 IS NOW SLIPPING. CONTACT PAIR (ASURF,BSURF) NODE 171 IS NOW SLIPPING. :


: :

*PRINT, CONTACT=YES causes this detailed printout.

Slave nodes that slip; stick/slip messages cause SDIs only if Lagrange friction is used or if slip reversal occurs.

(Useful for troubleshooting)

: CONTACT PAIR (ASURF,BSURF) NODE 153 OPENS. CONTACT PRESSURE/FORCE IS -845822..

Incompatibilities detected in the assumed contact state  SDI

CONTACT PAIR (ASURF,BSURF) NODE 161 OPENS. CONTACT PRESSURE/FORCE IS -1.50656E+006. CONTACT PAIR (ASURF,BSURF) NODE 163 OPENS. CONTACT PRESSURE/FORCE IS -108355.. CONTACT PAIR (ASURF,BSURF) NODE 165 OPENS. CONTACT PRESSURE/FORCE IS -620880.. CONTACT PAIR (CSURF,DSURF) NODE 363 OPENS. CONTACT PRESSURE/FORCE IS -3.5893E+006. CONTACT PAIR (ESURF,FSURF) NODE 309 IS NOW SLIPPING. 6 SEVERE DISCONTINUITIES OCCURRED DURING THIS ITERATION. 5 POINTS CHANGED FROM CLOSED TO OPEN

Due to slip reversal

1 POINTS CHANGED FROM STICKING TO SLIPPING

223

A2.11

Contact Logic in Abaqus/Standard (7/10) Message file, Step 3, Increment 6 (cont'd): CONVERGENCE CHECKS FOR SEVERE DISCONTINUITY ITERATION

1

MAX. PENETRATION ERROR -8.16193E-009 AT NODE 331 OF CONTACT PAIR (ESURF,FSURF)

Convergence checks for contact state

MAX. CONTACT FORCE ERROR -4369.44 AT NODE 363 OF CONTACT PAIR (CSURF,DSURF) www.3ds.com | © Dassault Systèmes

THE ESTIMATED CONTACT FORCE ERROR IS LARGER THAN THE TIME-AVERAGED FORCE.

AVERAGE FORCE

5.393E+03

TIME AVG. FORCE

3.147E+03

LARGEST RESIDUAL FORCE

-1.110E+04

AT NODE

333

DOF

2

LARGEST INCREMENT OF DISP.

-7.782E-04

AT NODE

329

DOF

2

LARGEST CORRECTION TO DISP.

-1.737E-05

AT NODE

337

DOF

2

FORCE

EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE.

AVERAGE MOMENT ALL MOMENT

114.

TIME AVG. MOMENT

Convergence checks for equilibrium

Not only is the contact incompatibility too large, but force equilibrium has not been achieved either 89.8

RESIDUALS ARE ZERO

LARGEST INCREMENT OF ROTATION

1.853E-33

AT NODE

100

DOF

6

LARGEST CORRECTION TO ROTATION

6.489E-34

AT NODE

300

DOF

6

THE MOMENT

EQUILIBRIUM EQUATIONS HAVE CONVERGED

A2.12

Contact Logic in Abaqus/Standard (8/10) Four additional iterations are required; the first three are SDIs (involve contact incompatibilities). In the final iteration both the contact and equilibrium checks pass and the increment converges.


CONVERGENCE CONVERGENCE CONVERGENCE CONVERGENCE

CHECKS CHECKS CHECKS CHECKS

FOR FOR FOR FOR

SEVERE DISCONTINUITY ITERATION SEVERE DISCONTINUITY ITERATION SEVERE DISCONTINUITY ITERATION EQUILIBRIUM ITERATION 1

2 ... 3 ... 4 ...

MAX. PENETRATION ERROR -1.38869E-014 AT NODE 331 OF CONTACT PAIR (ESURF,FSURF) MAX. CONTACT FORCE ERROR -0.00111133 AT NODE 331 OF CONTACT PAIR (ESURF,FSURF) THE CONTACT CONSTRAINTS HAVE CONVERGED. AVERAGE LARGEST LARGEST LARGEST

FORCE 5.244E+03 TIME AVG. FORCE RESIDUAL FORCE -9.24 AT NODE 367 INCREMENT OF DISP. -7.809E-04 AT NODE 129 CORRECTION TO DISP. 4.229E-08 AT NODE 137 THE FORCE EQUILIBRIUM EQUATIONS HAVE CONVERGED

3.123E+03 DOF 1 DOF 2 DOF 2

AVERAGE MOMENT 109. TIME AVG. MOMENT 89.0 ALL MOMENT RESIDUALS ARE ZERO LARGEST INCREMENT OF ROTATION 1.925E-33 AT NODE 100 DOF 6 LARGEST CORRECTION TO ROTATION 2.049E-35 AT NODE 100 DOF 6 THE MOMENT EQUILIBRIUM RESPONSE WAS LINEAR IN THIS INCREMENT

224

No SDIs in this iteration

A2.13

Contact Logic in Abaqus/Standard (9/10) Increment summary:

ITERATION SUMMARY FOR THE INCREMENT: 5 TOTAL ITERATIONS, OF WHICH 4 ARE SEVERE DISCONTINUITY ITERATIONS AND 1 ARE EQUILIBRIUM ITERATIONS.


CURRENT VALUE OF MONITOR NODE TIME INCREMENT COMPLETED STEP TIME COMPLETED

1.266E-02, 5.047E-02,

200 D.O.F.

2 IS

-3.028E-03


5.047E-02 2.05

A2.14

Contact Logic in Abaqus/Standard (10/10) Contact diagnostics in Abaqus/Viewer


Constrained nodes want to open: incompatible contact state

Toggle on to see the locations in the model where the contact state is changing.

225

226

Notes

227

Notes

228

Appendix 3: Contact Issues Specific to Abaqus/Explicit

A3.1

Lesson content:


Contact Pairs as Part of the History Data Enforcing the Contact Constraints Double-Sided Contact Initial Kinematic Compliance

30 minutes

A3.2


Contact Pairs as Part of the History Data (1/2) For Abaqus/Explicit the contact pair definition is part of the history data in the input file. *HEADING . . *STEP *DYNAMIC, EXPLICIT , 200E-3 Contact pairs are defined, or *CONTACT PAIR removed, on a step-by-step basis as ASURF, BSURF needed. . . . *STEP *DYNAMIC, EXPLICIT , 200E-3 *CONTACT PAIR ASURF, DSURF

229

A3.3

Contact Pairs as Part of the History Data (2/2)


The *CONTACT PAIR option has the OP parameter, which can have the value ADD or DELETE. Example:

*STEP *DYNAMIC, EXPLICIT . . *CONTACT PAIR ASURF, BSURF *END STEP *STEP . . *CONTACT PAIR, OP=DELETE ASURF, BSURF *CONTACT PAIR, OP=ADD BSURF, CSURF *END STEP

Delete the contact pair involving surfaces ASURF and BSURF. Add a contact pair involving surfaces BSURF and CSURF.

A3.4

Enforcing the Contact Constraints (1/3) Contact constraints can be enforced with one of the following algorithms:

Kinematic compliance (only available for contact pair algorithm)


Penalty

230

In most cases the kinematic and penalty algorithms will produce nearly the same results; however, in some cases one method may be preferable to the other.

A3.5

Enforcing the Contact Constraints (2/3) Kinematic compliance contact

The default kinematic contact formulation achieves precise compliance with the contact conditions.


It works well in most cases, but some problems with chattering contact may work more easily using penalty contact. Cannot model rigid-to-rigid contact. Available only for the contact pair algorithm.

A3.6


Enforcing the Contact Constraints (3/3) Penalty contact The penalty contact algorithm provides less stringent enforcement of contact constraints than the kinematic algorithm. The penalty algorithm allows for treatment of more general types of contact; for example, contact between two rigid bodies. Since the penalty algorithm introduces additional stiffness behavior into a model, this stiffness can influence the stable time increment. Penalty contact is used with the general contact algorithm. To invoke penalty contact for the contact pair algorithm: Set the MECHANICAL CONSTRAINT parameter to PENALTY on the *CONTACT PAIR option. The “spring” or “penalty” stiffness that relates the contact force to the penetration distance is chosen automatically by Abaqus/Explicit. Conflicting criteria must be considered: The effect on the maximum stable time increment should be minimal. The allowed penetration must not be significant in most analyses. For the general contact algorithm: The penalty stiffness can be scaled using the *CONTACT CONTROLS ASSIGNMENT, TYPE=SCALE PENALTY option. For the contact pair algorithm: You can specify a factor by which to scale the default penalty stiffnesses by using the SCALE PENALTY parameter on the *CONTACT CONTROLS option.

231

A3.7

Double-Sided Contact (1/3)


A single surface defined on shell, membrane, and rigid elements can include both the top (SPOS) and bottom (SNEG) faces of these elements. The general contact algorithm automatically uses double-sided surfaces. For the contact pair algorithm: Define a double-sided surface by omitting the face identifier from the *SURFACE option. Consistent element normals are not required. Contact can occur on either face of the elements forming the double-sided surface. For example, a slave node can start out on one side of a double-sided surface and then pass around the perimeter to the other side during the analysis. Double-sided surfaces are often necessary in such situations. The additional computational cost when performing an analysis with double-sided contact is minimal.

A3.8

Double-Sided Contact (2/3) Example: Compression of nested cylindrical shells

deformable cylinders


rigid lid

rigid box Front view

232

Oblique view (front and side of box removed)

A3.9

Double-Sided Contact (3/3)


General contact *HEADING : *CONTACT *CONTACT INCLUSIONS, ALL EXTERIOR : *STEP *DYNAMIC, EXPLICIT : *END STEP

Contact pairs *HEADING : *SURFACE, NAME=RING1 RING1 *SURFACE, NAME=RING2 RING2 *SURFACE, NAME=RING3 RING3 *SURFACE, NAME=BOX BOX *SURFACE, NAME=LID LID : *STEP *DYNAMIC, EXPLICIT : *CONTACT PAIR RING1, RING2 RING1, RING3 RING2, RING3 RING1, BOX RING2, BOX RING3, BOX RING1, LID : *END STEP

Double-sided contact allows simple definition of complex contact conditions when using contact pairs. Since the shell thickness is not shown in plots, the displaced shape indicates gaps between the contacting surfaces (recall shell thickness is accounted for in contact calculations).

A3.10

Initial Kinematic Compliance Abaqus/Explicit does not allow an initial overclosure of contact surfaces.


The nodes on the contact surfaces will be adjusted to remove any initial overclosure prior to the analysis: Only nodes on the contact surface are moved. The displacements associated with adjusting the surface do not cause any initial strain or stress for contact pairs defined in the first step of the analysis. In subsequent steps : The initial overclosures are ignored with the general contact algorithm. The adjustments will cause strains with the contact pair algorithm. Both surfaces will be adjusted if the contact pair is a balanced master/slave pair. Detailed information regarding resolution of initial overclosures can be written to the message (.msg) file using the *DIAGNOSTICS option.

233

234

Notes

235

Notes

236

Workshop 1 Basic Input and Output Interactive Version Note: This workshop provides instructions in terms of the Abaqus GUI interface. If you wish to use the Abaqus Keywords interface instead, please see the “Keywords” version of these instructions. Please complete either the Keywords or Interactive version of this workshop.

Goals     

Learn to use Abaqus utilities and documentation. Understand the basic structure of an Abaqus/CAE model, and be able to make simple modifications to it. Learn how to perform a datacheck analysis and how to submit an analysis job in Abaqus/CAE. Gain familiarity with the Visualization module. Explore the structure and contents of the printed output (.dat) file.

Abaqus utilities and documentation Abaqus provides various utilities for obtaining information on usage, system configuration, example problems, and environment settings for the analysis package. 1. At the prompt, enter the command abaqus information=system

to obtain information on the system. Note that abaqus is a generic command that may have been renamed on your system. For example, if more than one version is installed on the system, the command might include the version number, as in abq6121. In the remainder of this workshop as well as all subsequent workshops, use the appropriate command for your system.

© Dassault Systèmes, 2012


237

W1.2

Question W1–1: What is the processor on your machine? Question W1–2: What is the operating system (OS) level?

2. Open the online documentation with the command abaqus doc

Open the Abaqus Analysis User’s Manual, and search for the string DSLOAD to find information on the DSLOAD option. You can find information related to the data line syntax in the Abaqus Keywords Reference Manual (use the hyperlink for the DSLOAD option, or open the Keywords Manual directly). The online documentation graphical user interface is shown in Figure W1–1.

Figure W1–1. Online documentation 3. Open the online Abaqus Example Problems Manual. Search for plate buckling to find example problems that discuss plate buckling.

Question W1–3: What are the four example problems that fit the search

criteria?

4. Go to Example Problem 1.1.14 in the online Abaqus Example Problems Manual. In the left panel of the window, display the subtopics of the problem and click


238


W1.3

Input files. In the right panel of the window, the list of input files associated with

this problem appears. You can select any input filename from the list; a separate window will open containing that file. 5. All example problem input files are included in the Abaqus release and can be obtained using the abaqus fetch utility. In your terminal window, enter abaqus fetch job=damagefailcomplate_cps4

at the command line prompt. 6. Use the online documentation to determine the input syntax for some options. followed directly by the keyword option. Parameters and their associated values appear on the keyword line, separated by commas. Many options require data lines, which follow directly after their associated keyword line and contain the data specified in the Abaqus Keywords Reference Manual for each option. Data items are separated by commas. Refer to the discussions of keyword line and data line syntax in Lecture 1, as necessary. Question W1–4:

How would you run a script from within the Abaqus/CAE environment? Hint: Search for “run script” in the Abaqus/CAE

User’s Manual Question W1–5:

In the space provided, write which Category option you would choose to define a displacement/rotation boundary condition in Abaqus/CAE. Hint: Search displacement/rotation boundary condition in

the Abaqus/CAE User’s Manual.



239

W1.4

Analyzing a connecting lug

Figure W1–2. Sketch of the connecting lug In this workshop you will model the connecting lug shown in Figure W1–2. The lug is welded to a massive structure at one end, so we assume that this end is fixed. The other end contains a hole through which a bolt is placed when the lug is in service. You have to calculate the deflection of the lug when a load of 30 kN is applied to the bolt along the negative 2-direction. To model this problem, you will use three-dimensional continuum elements and perform a linear analysis with elastic materials. You will model the load transmitted to the lug through the bolt as a uniform pressure load applied to the bottom half of the hole, as shown in Figure W1–2. In this workshop SI units (N, m, and s) will be used.

Preliminaries 1. Enter the working directory for this workshop: ../abaqus_solvers/interactive/lug

2. Run the script ws_solver_lug.py using the following command: abaqus cae startup=ws_solver_lug.py

The above command creates an Abaqus/CAE database named Lug.cae in the current directory. The geometry, mesh, and step definitions for the lug are included in a model named standard.


240


W1.5

Before completing the model, view the contents of the model using the Model Tree on the left hand side of the main window. Question W1–6: How many steps are there in this analysis?

Use the Query information tool

(or select Tools→Query from the main menu bar)

to query element information of the lug. Switch to the Mesh module and click . In the Query dialog box, select Element in the General Queries field. Select one element of the lug in the viewport. Read the query results reported in the message area at the bottom of the main window. Question W1–7: What element type is used to model the lug?

Completing the model You will now add the material definition, and create the boundary conditions and the pressure load to complete the lug model. 1. Note that a dummy material named Steel has already been created and assigned to the part Lug. Add the steel material properties to this material. a. In the Model Tree, expand the Materials container and double-click Steel. The material editor appears. b. From the material editor’s menu bar, select Mechanical→Elasticity→Elastic. Enter the following elastic material properties: Elastic modulus E = 200.E9 Pa and Poisson’s ratio  = 0.3. Question W1–8: Do you need to define a density to complete the material

definition? Material density is necessary for what types of analyses? 2. In the Model Tree, double-click the BCs container to create an ENCASTRE boundary condition on the flat end as highlighted in Figure W1–3. The ENCASTRE boundary condition constrains all active structural degrees of freedom. a. In the Create Boundary Condition dialog box, name the boundary condition Fix left end, choose the category Mechanical and the type Symmetry/Antisymmetry/Encastre, and click Continue. b. Select the flat end of the lug as shown in Figure W1–3. Use [Shift]+Click to select both regions. Adjust your view, if necessary, to see the model geometry more clearly. c. Click mouse button 2 in the viewport or click Done in the prompt area to confirm the selections. The boundary condition editor appears.



241

W1.6

d. The Edit Boundary Condition dialog box, choose ENCASTRE (U1=U2=U3=UR1=UR2=UR3=0) and click OK to exit the boundary condition editor. The arrow symbols appear on the flat end indicating the constrained degrees of freedom. Question W1–9: How else could you define a completely constrained boundary

condition?

Fully constrain this end

Figure W1–3. Region for fully constrained boundary condition 3. In the Model Tree, double-click the Loads container to create a distributed pressure load with a magnitude of 50 MPa on the highlighted surfaces shown in Figure W1–4. a. In the Create Load dialog box, name the load Pressure Load, select the step LugLoad, choose the category Mechanical and the type Pressure, and click Continue. b. Select the surfaces highlighted in Figure W1–4. c. Click mouse button 2 in the viewport or click Done in the prompt area to confirm the selections. The load editor appears. d. In the Edit Load dialog box, accept the Uniform distribution, enter a value of 50E6 for the Magnitude, and click OK to exit the load editor.


242


W1.7

Note that the magnitude of the applied uniform pressure is determined by dividing the total load by the projected horizontal area of the hole, where 30kN  50MPa . 2  0.015m  0.02m

Region for Pressure Load

Figure W1–4. Region for distributed pressure load

Submitting a datacheck analysis You will first perform a datacheck analysis and then a full analysis. 1. In the Model Tree, double-click the Jobs container. In the Create Job dialog box, name the job lug and click Continue. In the Edit Job dialog box, accept all default settings and click OK to exit the job editor. 2. Save your model database. 3. In the Model Tree, expand the Jobs container. Click mouse button 3 on the job lug and select Data Check from the menu that appears. 4. Click mouse button 3 on the job lug and select Monitor from the menu that appears to monitor any warnings or errors that may occur during the datacheck analysis. 5. In the job monitor, open the Data File tabbed page. Search for the string P R O B L E M to see the summary of the problem size. Include spaces between the letters of the search string. Question W1–10: How many elements are there in the model? How many

variables are there?



243

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Running a full analysis 1. In the Model Tree, expand the Jobs container. Click mouse button 3 on the job lug and select Continue from the menu that appears. If Abaqus/CAE asks if you want to overwrite old job files, click OK. This means that output files with the same job name that exist from a previous analysis will be overwritten. 2. Monitor the job’s progress.

Postprocessing the results When the analysis is complete, use the following procedure to view the analysis results in the Visualization module: 1. In the Model Tree, click mouse button 3 on the job lug and select Results from the menu that appears to open the file lug.odb in the Visualization module. 2. When the output database is opened in the Visualization module, the undeformed model shape is displayed by default. To change the plot mode, you can use either the Plot menu or the toolbox icons displayed on the left side of the viewport (see Figure W1–5). You can identify the function of each tool in the toolbox by positioning your cursor above the icon for that tool; a label for the icon pop-ups describing its function. 1. To plot the deformed shape, click the Plot Deformed Shape tool toolbox or select Plot→Deformed Shape from the main menu bar.

in the

3. Open the Common Plot Options dialog box by clicking in the toolbox. Turn on the node and element numbers, and make the nodes visible. 4. Use the display option tools (see Figure W1–5) to switch to hidden line, filled, or wireframe display.


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W1.9

View manipulation tools

Display option tools

Results Tree

Toolbox

Figure W1–5. Abaqus/Viewer main window 5. Note the displacement magnification factor shown in the bottom of the title. By default, Abaqus/CAE automatically scales the displacement according to the maximum model dimensions for a small-displacement analysis. Displacements are scaled so that the deformed shape will be clear. For a large-displacement analysis the scale factor is 1.0 by default. Set the displacement magnification factor to 1.0 so that you can see the actual displacement, and redraw the displaced shape plot. Hint: You will have to use the Common Plot Options dialog box.

6. Create a contour plot of the Mises stress by clicking the Plot Contours on Deformed Shape tool

. 7. Frequently users want to remove all annotations that are written on the plots, especially when they are creating hard-copy images or animations. From the main menu bar, select Viewport→Viewport Annotation Options to suppress the annotations used in the plots.



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W1.10

The annotations are divided into three categories: legend, title block, and state block. Each category can be controlled separately. The title block contains information about which Abaqus version was used and when the analysis was performed. The state block contains the step title, the increment and step time of the data being displayed, and information on the variable and magnification factor used to calculate the shape of the model. 8. Probe the displacement of the nodes around the hole in the lug. a. Click the Query information tool . In the Query dialog box that appears, select Probe values in the Visualization Module Queries field. b. In the Probe Values dialog box that appears, click to change the default field output variable to the displacement component U2. c. In the Field Output dialog box that appears, select U as the output variable and U2 as the component and click OK to save the selection and exit the Field Output dialog box. d. In the Probe Values dialog box, select Nodes as the item to probe. e. Select a node in viewport to obtain its displacement along the 2-direction. Click on a node to query its displacement value along the 2 direction. 9. Use a similar procedure to probe the Mises stress in the elements around the hole in the lug.

Modifying the model and understanding changes in the results 1. Switch to the Load module. 2. Reduce the amplitude of the distributed pressure load to 25 MPa. 3. Create a new job named lugmod and submit the analysis. 4. View the results in the Visualization module. Question W1–11: How have the displacement and stress results changed after

the load reduction? Do the results reflect the reduction in loading? Note: A script that creates the complete model described in these instructions is available for your convenience. Run this script if you encounter difficulties following the instructions or if you wish to check your work. The script is named ws_solver_lug_answer.py and is available using the Abaqus fetch utility.


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Answers Question W1–1: What is the processor on your machine? Answer:

It depends on the system you are using.

Question W1–2: What is the operating system (OS) level? Answer:


Question W1–3: What are the four example problems that fit the search Answer:

criteria? Problem 1.1.14, ―Damage and failure of a laminated composite plate‖ Problem 1.2.2, ―Laminated composite shells: buckling of a cylindrical panel with a circular hole‖ Problem 1.2.5, ―Unstable static problem: reinforced plate under compressive loads‖ Problem 9.1.8, ―Deformation of a sandwich plate under CONWEP blast loading‖

Question W1–4: Answer:

How would you run a script from within the Abaqus/CAE environment? From the main menu bar, select File→Run Script.

Question W1–5: In the space provided, write which Category option you

Answer:

would choose to define a displacement/rotation boundary condition in Abaqus/CAE. You would choose the Mechanical category option.

Question W1–6: How many steps are there in this analysis? Answer:

Not including the initial step which is automatically created by Abaqus/CAE, there is only one step in this analysis.

Question W1–7: What element type is used to model the lug? Answer:


C3D20R elements—i.e., 20-node brick elements (threedimensional, quadratic, hexahedral continuum elements) with reduced integration—are used to model the lug. Introduction to Abaqus/Standard and Abaqus/Explicit

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W1.12

Question W1–8: Do you need to define a density to complete the material

Answer:

definition? Material density is necessary for what types of analyses? No. The density is necessary for analysis procedures that consider inertia effects. In a static analysis inertia effects are not considered.

Question W1–9: How else could you define a completely constrained boundary Answer:

condition? You could have chosen to fix all six degrees of freedom separately by choosing the Displacement/Rotation type boundary condition and specifying zero values for all degrees of freedom from 1 through 6.

Question W1–10: How many elements are there in the model? How many Answer:

variables are there? The model has 288 elements. The total number of variables, including degrees of freedom plus any Lagrange multiplier variables, is 5211.

Question W1–11: How have the displacement and stress results changed after

Answer:


248

the load reduction? Do the results reflect the reduction in loading? The displacements and stresses have decreased by a factor of two, since this is a linear analysis and our load was decreased by a factor of two.


Notes

249

Notes

250

Workshop 2 Linear Static Analysis of a Cantilever Beam: Multiple Load Cases Interactive Version Note: This workshop provides instructions in terms of the Abaqus GUI interface. If you wish to use the Abaqus Keywords interface instead, please see the “Keywords” version of these instructions. Please complete either the Keywords or Interactive version of this workshop.

Introduction In this workshop you will become familiar with using load cases in a linear static analysis. You will model a cantilever beam. The left end of the beam is encastred while a series of loads are applied to the free end. Six load cases are considered: unit forces in the global X-, Y-, and Z-directions as well as unit moments about the global X-, Y-, and Zdirections. The model is shown in Figure W2–1. You will solve the problem using a single perturbation step with six load cases and (optionally) using six perturbation steps with a single load case in each step.

Figure W2–1. Cantilever beam model



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W2.2

Preliminaries 1. Enter the working directory for this workshop ../abaqus_solvers/interactive/load_cases

2. Run the script ws_solver_load_cases.py using the following command: abaqus cae startup=ws_solver_load_cases.py.

The above command creates an Abaqus/CAE database named Beam.cae in the current directory. The geometry, mesh and boundary condition definitions for the beam are included in the model named LoadCases. You will add the step, load, and load case definitions to complete the model.

Defining a linear perturbation static step 1. In the Model Tree, double-click the Steps container. 2. In the Create Step dialog box, name the step BeamLoadCases, choose the Linear perturbation procedure type, and select Static, Linear perturbation from the list of procedures, and click Continue. The step editor appears. 3. In the Basic tabbed page of the step editor, type Six load cases applied to right end of beam in the Description field. 4. Click OK to create the step and to exit the step editor.

Defining loads and load cases As indicated in Figure W2–1, we wish to apply forces and moments to the right end of the beam. However, the beam is modeled with solid C3D8I elements which possess only displacement degrees of freedom. Thus, only forces may be directly applied to the model. Rather than applying force couples to the model, we will apply concentrated moments to the end of the beam. To this end, all loads will be transmitted to the beam through a rigid body constraint. This approach is adopted to take advantage of the fact that the rigid body reference node possesses six degrees of freedom in three-dimensions: 3 translations and 3 rotations and thus allows direct application of concentrated moments. Rigid bodies and constraints will be discussed further in Lecture 5. Note that a rigid body constraint named Constraint-1 has been created to constrain the free end of the beam with a predefined reference point named RP-1; therefore, the forces and moments which you will specify on RP-1 will be transmitted to the beam through this rigid body constraint (see Figure W2–2).


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W2.3

Apply all forces and moments here.

Figure W2–2. Rigid body reference point To define loads: 1. In the Model Tree, double-click the Loads container. 2. In the Create Load dialog box, name the load Force-X, select the step BeamLoadCases, choose the category Mechanical and the type Concentrated force, and click Continue. 3. Select the reference point RP-1 as the point to which the load will be applied. 4. Click mouse button 2 in the viewport or click Done in the prompt area to accept the selection. 5. In the Edit Load dialog box, enter a value of 1.0 for CF1. 6. Click OK to complete the load definition. 7. Using a similar procedure, create two additional Concentrated force loads named Force-Y and Force-Z and three Moment loads named Moment-X, Moment-Y, and Moment-Z, with the definitions as listed in Table W2–1. Tip: To define the additional forces, simply copy Force-X into a new name and edit its definition; to define the moments, first create Moment-X and then

copy/edit it to define the additional loads. Abaqus/CAE displays arrows at the reference point indicating the loads applied to the model.



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Table W2–1. Load definitions Load name Definition Force-X

CF1 = 1.0

Force-Y

CF2 = 1.0

Force-Z

CF3 = 1.0

Moment-X

CM1 = 1.0

Moment-Y

CM2 = 1.0

Moment-Z

CM3 = 1.0

To define load cases: 1. In the Model Tree, expand the branch of the step BeamLoadCases underneath the Steps container and double-click Load Cases to create a load case in the step. 2. In the Create Load Case dialog box, name the load case LC-Force-X, accept BeamLoadCases as the step, and click Continue. The load case editor appears. 3. Click at the bottom of the Edit Load Case dialog box. 4. In the Load Selection dialog box that appears, select Force-X and click OK to confirm the selection and to return to the load case editor. 5. Click OK to exit the Edit Load Case dialog box. 6. Create five additional load cases: one for each of the remaining loads. Name the load cases LC-Force-Y, LC-Force-Z, LC-Moment-X, LC-Moment-Y, and LC-Moment-Z and add the corresponding load to each. Tip: Copy/edit LC-Force-X to define the additional load cases.

Note that the fixed-end boundary conditions were defined in the initial step, and as such, are active in each load case of the analysis step.

Creating and submitting the analysis job To create and submit the analysis job: 1. Create a job named LoadCases for this linear static perturbation analysis. Tip: To create a job, double-click Jobs in the Model Tree.

2. Save your model database file and submit the job for analysis. In the Model Tree, click mouse button 3 on the job name and select Submit from the menu that appears. From the same menu, you can select Monitor to monitor the job’s progress.


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W2.5

Viewing the analysis results When the job is complete, click mouse button 3 on the job LoadCases in the Model Tree and select Results from the menu that appears. Abaqus/CAE switches to the Visualization module and opens the output database LoadCases.odb. Examine the results of the analysis. Note that load case output is stored in separate frames in the output database. Use the Frame Selector (click in the context bar) to choose which load case is displayed (alternatively, open the Step/Frame dialog box by selecting Result→Step/Frame). Figure W2–3 shows contour plots of the Mises stress for each of the load cases.

Force-X

Force-Y

Force-Z

Moment-X

Moment-Y

Moment-Z

Figure W2–3. Mises stress contours



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W2.6

Combining results from the load cases and envelope plots You will now linearly combine the results of each load case to plot the stress and deformation in the beam under a given load combination. Recall that each load case is based on a unit load; the results of each load case will be scaled relative to those obtained for LC-Force-Y when combining the data. 1. From the main menu bar, select Tools→Create Field Output→From Frames. 2. In the dialog box that appears, accept Sum values over all frames as the operation. 3. In the Frames tabbed page, click . In the Add Frames dialog box that appears, choose BeamLoadCases as the step from which to obtain the data. Click Select All and then click OK to close the dialog box. 4. Remove the initial frame; for the remaining frames, enter the scale factors shown in Figure W2–4.

Figure W2–4 Scale factors for linear combination of load cases. 5. Switch to the Fields tabbed page to examine the data that will be combined. Accept the default selection (all available field data) and click OK to close the dialog box. 6. From the main menu bar, select Result→Step/Frame.


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W2.7

7. In the Step/Frame dialog box, select Session Step as the active step for output and click OK. 8. Plot the Mises stress as shown in Figure W2–5. Note that this figure has been customized to overlay the undeformed model shape on the contour plot and a deformation scale factor of 5e4 has been used.

Figure W2–5 Mises stress due to combined loading. 9. Now create an envelope plot of the maximum stress in the beam: a. From the main menu bar, select Tools→Create Field Output→From Frames. b. In the dialog box that appears, select Find the maximum value over all frames as the operation. c. In the Frames tabbed page, click . In the Add Frames dialog box that appears, choose BeamLoadCases as the step from which to obtain the data. Select all but the initial frame then click OK to close the dialog box. d. Switch to the Fields tabbed page. Unselect all output and then select only S and U. e. Click OK to close the dialog box. f. From the main menu bar, select Result→Step/Frame. g. In the Step/Frame dialog box, select Session Step as the active step for output and The maxmum value over all selected frames as the frame, as shown in Figure W2–6.



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W2.8

Figure W2–6 Frame selection for envelope plot. h. In the Field Output dialog box (Result→Field Output), select S_max as the primary variable and U_max as the deformed variable. i. Plot the Mises stress as shown in Figure W2–7. Note that this figure has been customized to overlay the undeformed model shape on the contour plot and a deformation scale factor of 5e4 has been used.

Figure W2–7 Envelope plot of maximum Mises stress.


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W2.9

Using Multiple Perturbation Steps (Optional) Now perform the same analysis using multiple perturbation steps rather than multiple load cases. 1. In the Model Tree, click mouse button 3 on the model LoadCases and select Copy Model from the menu that appears. Name the new model MultiSteps. 2. For the model MultiSteps, delete the step BeamLoadCases. Note that all of the loads and load cases will be deleted when you delete the step BeamLoadCases. 3. Create six new linear perturbation static steps named Step-FX, Step-FY, StepFZ, Step-MX, Step-MY, and Step-MZ. 4. In the Model Tree, double-click the Loads container for the model MultiSteps and define a concentrated force load called Force-X in the step Step-FX with CF1=1.0 at the reference point. 5. Similarly, create loads named Force-Y, Force-Z, Moment-X, Moment-Y, and Moment-Z in steps Step-FY, Step-FZ, Step-MX, Step-MY, and Step-MZ, respectively. Here CF2=1.0, CF3=1.0, CM1=1.0, CM2=1.0, and CM3=1.0 at the reference point in the respective loads. Note that the fixed-end boundary conditions were defined in the initial step, and therefore, are active in each analysis step. 6. Create a new job named MultiSteps for the model MultiSteps and make sure to select the new model for the source. Submit the new job for analysis and monitor the job’s status. 7. When the job is complete, open the output database MultiSteps.odb in the Visualization module and compare the results obtained using both modeling approaches. You will find that the results are identical.

Comparing solution times Next, open the message (.msg) file for each job in the job monitor. Scroll to the bottom of the file and compare the solution times. You will notice that the multiple step analysis required 2.5 times as much CPU time as the multiple load case analysis. For a small model such as this one, the overall analysis time is small so speeding up the analysis by a factor of three may not appear significant. However, it is clear that for large jobs, the speedup offered by multiple load cases will play a significant role in reducing the time required to obtain a solution for a given problem.



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W2.10

Multiple load case analysis: ANALYSIS SUMMARY: TOTAL OF 1 0 1 1 : :

INCREMENTS CUTBACKS IN AUTOMATIC INCREMENTATION ITERATIONS PASSES THROUGH THE EQUATION SOLVER OF WHICH

THE SPARSE SOLVER HAS BEEN USED FOR THIS ANALYSIS. JOB TIME SUMMARY USER TIME (SEC) SYSTEM TIME (SEC) TOTAL CPU TIME (SEC) WALLCLOCK TIME (SEC)

= = = =

0.10000 0.10000 0.20000 1

Multiple perturbation step analysis: ANALYSIS SUMMARY: TOTAL OF 6 0 6 6 : :



= = = =

0.4000 0.1000 0.5000 1

Note: A script that creates the complete models described in these instructions is available for your convenience. Run this script if you encounter difficulties following the instructions or if you wish to check your work. The script is named ws_solver_load_cases_answer.py and is available using the Abaqus fetch utility.


260


Notes

261

Notes

262

Workshop 3 Nonlinear Statics Interactive Version Note: This workshop provides instructions in terms of the Abaqus GUI interface. If you wish to use the Abaqus Keywords interface instead, please see the “Keywords” version of these instructions. Please complete either the Keywords or Interactive version of this workshop.

Goals    

Define alternate nodal and material directions. Include nonlinear geometric effects by adding the NLGEOM parameter. Include nonlinear material effects by defining plastic material behavior. Become familiar with the output for an incremental analysis.

Introduction In this workshop you will model the plate shown in Figure W3–1. It is skewed at 30 to the global X-axis, built-in at one end, and constrained to move on rails parallel to the plate axis at the other end. You will determine the midspan deflection when the plate carries a uniform pressure. You will modify the model to include alternate nodal and material directions as well as nonlinear effects.



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W3.2

All degrees of freedom at this end are constrained except along the axis of the plate.

Figure W3–1. Sketch of skewed plate

Preliminaries 1. Enter the working directory for this workshop ../abaqus_solvers/interactive/skew

2. Run the script ws_solver_skew_plate.py using the following command: abaqus cae startup=ws_solver_skew_plate.py.

The above command creates an Abaqus/CAE database named SkewPlate.cae in the current directory. A model named linear includes the geometry, mesh and material definitions for the plate. You will first add the necessary data to complete the linear analysis model. You will later perform the simulation considering both geometrically and material nonlinear effects. In a subsequent workshop a restart analysis will be performed to study the unloading of the plate.

Defining the local material directions The orientation of the structure in the global coordinate system is shown in Figure W3–1. The global Cartesian coordinate system defines the default material directions, but the plate is skewed relative to this system. It will not be easy to interpret the results of the simulation if you use the default material directions because the direct stress in the material 1-direction (i.e., global X-direction), 11, will contain contributions from both the axial stress, produced by the bending of the plate, and the stress transverse


264


W3.3

to the axis of the plate. It will be easier to interpret the results if the material directions are aligned with the axis of the plate and the transverse direction. Therefore, a local rectangular coordinate system is needed in which the local x-direction lies along the axis of the plate (i.e., at 30º to the global X-axis) and the local y-direction is also in the plane of the plate. You will define the datum coordinate system (CSYS) and then assign the material orientation. 1. Switch to the Property module and define a rectangular datum coordinate system as shown in Figure W3–2 using the Create Datum CSYS: 2 Lines tool . a. Note the small black triangles at the base of the toolbox icons. These triangles indicate the presence of hidden icons that can be revealed. Click the Create Datum CSYS: 3 Points tool but do not release the mouse button. When additional icons appear, release the mouse button. b. Select the Create Datum CSYS: 2 Lines tool . It appears in the toolbox with a white background indicating that you selected it. c. In the Create Datum CSYS dialog box, name the datum CSYS Skew, select the Rectangular coordinate system type, and click Continue. Make the next two selections as indicated in Figure W3–2.

Select this edge to be in the local x-y plane

Select this edge to be along the local x-direction

Figure W3–2. Datum coordinate system used to define local directions 2. Assign the material orientations to the plate. a. In the toolbox, click the Assign Material Orientation tool . b. Select the entire part as the region to be assigned a local material orientation.



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W3.4

c. Click mouse button 2 in the viewport or click Done in the prompt area to confirm the selection. d. Click Datum CSYS List in the prompt area. e. In the Datum CSYS List dialog box, select skew and click OK. In the material orientation editor, select Axis 3 for the direction of the approximate shell normal. No additional rotation is needed about this axis. f. Click OK to confirm the input. Tip: To verify that the local material directions have been assigned correctly, select Tools→Query from the main menu bar and perform a property query on the material orientations. Once the part has been meshed and elements have been created in the model, all element variables will be defined in this local coordinate system.

Prescribing boundary conditions and applied loads As shown in Figure W3–1, the left end of the plate is completely fixed; the right end is constrained to move on rails that are parallel to the axis of the plate. Since the latter boundary condition direction does not coincide with the global axes, you must define a local coordinate system that has an axis aligned with the plate. You can use the datum coordinate system that you created earlier to define the local directions. 1. In the Model Tree, double-click the BCs container and define a Displacement/Rotation mechanical boundary condition named Rail boundary condition in the Apply Pressure step. In this example you will assign boundary conditions to sets rather than to regions selected directly in the viewport. Thus, when prompted for the regions to which the boundary condition will be applied, click Sets in the prompt area of the viewport. 2. From the Region Selection dialog box that appears, select the set Plate-1.EndB. Toggle on Highlight selections in viewport to make sure the correct set is selected. The right edge of the plate should be highlighted. Click Continue. 3. In the Edit Boundary Condition dialog box, click to specify the local coordinate system in which the boundary condition will be applied. In the viewport, select the datum CSYS Plate-1.Skew. The local x-direction is aligned with the plate axis. Note that Plate-1.Skew is the assembly-level datum CSYS generated by the part-level datum CSYS Skew. 4. In the Edit Boundary Condition dialog box, fix all degrees of freedom except for U1 by toggling them on and entering a value of 0 for each. The right edge of the plate is now constrained to move only in the direction of the plate axis. Once the plate has been meshed and nodes have been generated in the model, all printed nodal output quantities associated with this region


266


W3.5

(displacements, velocities, reaction forces, etc.) will be written in this local coordinate system. 5. Create another boundary condition named Fix left end to fix all degrees of freedom at the left edge of the plate (set Plate-1.EndA). Use the default global directions for this boundary condition. 6. Define a uniform pressure load named Pressure across the top of the shell in the Apply Pressure step. Select both regions of the part using [Shift]+Click, and choose the top side of the shell (Brown) as the surface to which the pressure load will be applied. You may need to rotate the view to more clearly distinguish the top side of the plate. Specify a load magnitude of 2.0E4 Pa.

Running the job and postprocessing the results 1. Create a job named SkewPlate with the following description: Linear Elastic Skew Plate, 20 kPa Load. 2. Save your model database file. 3. Submit the job for analysis and monitor the solution progress. When the analysis is complete, use the following procedure to postprocess the analysis results. 4. In the Model Tree, click mouse button 3 on the job SkewPlate and select Results from the menu that appears to open the file SkewPlate.odb in the Visualization module. 5. Click the Plot Deformed Shape tool

to plot the deformed shape.

6. Use the the Query information tool to probe the value of the midspan deformation. a. In the Query dialog box, select Probe values in the Visualization Module Queries field. b. Change the displayed field variable to the displacement along the 3direction. In the Probe Values dialog box, click to change the default field output variable to U3. In the Field Output dialog box that appears, select U as the output variable and U3 as the component and click OK. c. In the Probe Values dialog box, select Nodes as the item to probe. d. Click on a node (as indicated in Figure W3–3) along the midespan to probe its displacement along the 3-direction. Enter this value in the “Linear” column of Table W3–1.



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W3.6

Figure W3–3. Midspan node

Adding geometric nonlinearity Now perform the simulation considering geometrically nonlinear effects. Copy the model named linear to a new model named nonlinear. You will add geometric nonlinearity into the model nonlinear; the changes required for this model are described next. 1. In the Model Tree, expand the Steps container and double-click Apply Pressure to edit the step definition. a. In the Basic tabbed page of the Edit Step dialog box, toggle on Nlgeom to include geometric nonlinearity effects and set the time period for the step to 1.0. b. In the Incrementation tabbed page, set the initial increment size to 0.1. Note that the default maximum number of increments is 100; Abaqus may use fewer increments than this upper limit, but it will stop the analysis if it needs more. You may wish to change the description of the step to reflect that it is now a nonlinear analysis step. 2. Create a job named NlSkewPlate for the model nonlinear and give it the description Nonlinear Elastic Skew Plate. Save your model database file. 3. Submit the job for analysis and monitor the solution progress. The Job Monitor is particularly useful in nonlinear analyses. It gives a brief summary of the automatic time incrementation used in the analysis for each increment. The information is written as soon as the increment is completed, so you can monitor the analysis as it is running. This facility is useful in large, complex problems. The information given in the Job Monitor is the same as that given in the status file (NlSkewPlate.sta). 4. When the job is complete, open the output database NlSkewPlate.odb in the Visualization module and plot the deformed model shape.


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W3.7

5.

Query the vetical displacement (U3) of the same midspan node as discribed earlier and enter the displacement result in the “Nlgeom” column of Table W3–1. Table W3–1. Midspan displacements Load (kPa)

Linear (m)

Nlgeom (m)

20 60

6. Triple the pressure in both the linear and nonlinear analysis models. Create new jobs and run each of these analyses 7. Upon job completion, look at the results and enter the vertical displacement of the same node in Table W3-1. Question W3–1: How does tripling the load affect the midspan displacement in

the linear analyses? Question W3–2: How do the results of the nonlinear analyses compare to each other and to those from the linear analyses?

Adding Plasticity You will now include another source of nonlinearity: plasticity. The material data are shown in Figure W3–4 (in terms of true stress vs. total log strain). Abaqus, however, requires the plastic material data be defined in terms of true stress and plastic log strain. Thus, you will need to determine the plastic strains corresponding to each data point (see the hint below). The changes described below are to be made to the nonlinear model. 1. In the Model Tree, expand the Materials container and double-click Steel. 2. In the Edit Material dialog box, add plasticity by choosing Mechanical→Plasticity→ Plastic. 3. Enter the data lines corresponding to points A and B on the stress-strain curve as shown in Figure W3–4. The Young’s modulus for this material is 30E9 Pa. Hint: The total strain tot at any point on the curve is equal to the sum of the

elastic strain el and plastic strain pl. The elastic strain at any point on the curve can be evaluated from Young’s modulus and the true stress:el= / E. Use the following relationship to determine the plastic strains to include on the plastic option:

 pl   tot   el   tot   E .



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W3.8

You can use the command line interface (CLI) of Abaqus/CAE as a simple calculator. For example, to compute the plastic strain at B, type 0.02-(3e7/3e10) in the command line interface and hit [Enter]. The value of the plastic strain is printed (in this case the plastic strain at B is 0.019). Note that the command line interface is hidden by default, but it uses the same space that is occupied by the message area at the bottom of the main window. To access the command line interface, click the yellow prompt button the bottom left corner of the main window.

in

Question W3–3: Why is the second entry on the first data line of the plasticity

option equal to 0.0? 4. Change the pressure to 10 kPa. a. In the Model Tree, double-click Pressure underneath the Loads container. b. In the Edit Load dialog box that appears, enter a value of 10000 for Magnitude. 5. Request restart output every increment in the step named Apply Pressure (switch to the Step module; select Output→Restart Requests). Note that the step name is important for the restart analysis to be performed later. 6. Create a new job named PlSkewPlate and give it the description Nonlinear Plastic Skew Plate. 7. Save your model database file. 8. Submit the job for analysis and monitor the solution progress.

Figure W3–4. Stress versus strain curve


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W3.9

Postprocessing an incremental analysis When the job is complete, visualize the output database PlSkewPlate.odb in the Visualization module. 1. By default, the last increment of the last step is selected. Use the Frame Selector in the context bar to select other steps or increments; alternatively, use the Step/Frame dialog box (Result→Step/Frame). 2. Use the view manipulation tools to position the model as you wish. Turn perspective on or off by clicking the Turn Perspective On tool Perspective Off tool

or the Turn

in the toolbar.

3. Plot the deformed shape by clicking the Plot Deformed Shape tool

.

A sample deformed shape plot is shown in Figure W3–5. Your plot may look different if you have positioned your model differently

Figure W3–5. Final deformed shape 4. Create a contour plot of variable S11 by following this procedure: a. b. c. d. e.

Click the Plot Contours tool in the toolbox. Select Result→Field Output. In the Field Output dialog box, select S11 as the stress component. Click Section Points to select a section point. In the Section Points dialog box that appears, select Top and bottom as the active locations and click OK. Your contour plot should look similar to Figure W3–6. Abaqus plots the contours of the Mises stress on both the top and bottom faces of each shell element. To see this more clearly, rotate the model in the viewport.



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Figure W3–6. Contour plot of S11: SPOS, top image; SNEG, bottom image Question W3–4: Where do the peak displacements and stresses occur in the

model?

5. Click the Animate: Time History tool to animate the results. You can stop the animation and move between frames and steps by using the arrow buttons in the context bar. 6. Render the shell thickness (View→ODB Display Options; toggle on Render shell thickness). The plot appears as shown in Figure W3–7. Note that for the purpose of visualization, a linear interpolation is used between the contours on the top and bottom surfaces of the shell.


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Figure W3–7 Contour plot with shell thickness visible. 7. Create a displacement history plot of U3 of the midspan node you tracked in the previous analyses: a. In the Results Tree, expand the History Output container underneath the output database named PlSkewPlate.odb. b. Click History Output and press F2; filter the container according to *U3*. c. Double-click the data object for the node tracked in the previous analyses. Your plot should look similar to Figure W3–8. Note this figure has been customized.

Figure W3–8. History of displacement at the midspan



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Note: A script that creates the complete models described in these instructions is available for your convenience. Run this script if you encounter difficulties following the instructions or if you wish to check your work. The script is named ws_solver_skew_plate_answer.py

and is available using the Abaqus fetch utility.


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Answers Question W3–1: How does tripling the load affect the midspan displacement in Answer:

the linear analyses? The midspan displacement is tripled in the linear analysis.

Question W3–2: How do the results of the nonlinear analyses compare to each Answer:

other and to those from the linear analyses? The midspan displacement is not tripled in the nonlinear analysis when the load is tripled. At the higher load, the value of the displacement predicted by the nonlinear analysis is less than the value predicted by the linear analysis.

Question W3–3: Why is the second entry on the first data line of the plastic Answer:

option equal to 0.0? The first data line of the plastic option defines the initial yield point. The plastic strain at this point is zero.

Question W3–4: Where do the peak displacements and stresses occur in the Answer:


model? The peak value of vertical displacement occurs at the midspan. The supports of the plate are likely to be heavily stressed; this is confirmed by contour plots of S11.


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Workshop 4 Unloading Analysis of a Skew Plate Interactive Version Note: This workshop provides instructions in terms of the Abaqus GUI interface. If you wish to use the Abaqus Keywords interface instead, please see the “Keywords” version of these instructions. Please complete either the Keywords or Interactive version of this workshop.

Introduction You will now continue the analysis of the plate shown in Figure W4–1. Recall our analysis includes geometric and material nonlinearity. We previously determined the plate exceeded the material yield strength and therefore has some plastic deformation. Since we requested restart output, we can resume the analysis to determine the residual stress state. In this workshop we will remove the load in order to recover the elastic deformation; the plastic deformation will remain.


Figure W4–1 Sketch of the skew plate. © Dassault Systèmes, 2012


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Adding a restart model Open the database ../abaqus_solvers/interactive/skew/SkewPlate.cae created in the previous workshop and copy the model named nonlinear to a new model named restart. The changes required for this model are described next. Model Attributes 1. In the Model Tree, double-click the model restart to edit the attributes for the restart analysis model. (Alternatively, from the main menu bar, select Model→Edit Attributes→restart.) 2. On the Restart tab of the Edit Model Attributes dialog box: a. Click the checkbox to indicate the (previous) job where the restart data was saved (recall this job was named PlSkewPlate). b. Indicate the step from which to restart the analysis (recall this step was named Apply Pressure) and that the restart analysis will commence from the end of the step. Step definition 1. In the Model Tree, double-click the Steps container to add a new general static step after the Apply Pressure step. 2. Name the step Unload. 3. In the Basic tabbed page of the Edit Step dialog box, Nlgeom should already be on to include geometric nonlinearity effects. 4. Set the time period for the step to 1.0. 5. As before, in the Incrementation tabbed page, set the initial increment size to 0.1. Loads 1. Use the Load Manager to deactivate the pressure load in the step named Unload. Alternatively, you could simply edit the load magnitude (for example, to examine the effect of a load reversal). Job definition 1. Create a new job named PlSkewPlate-unload using the model restart and enter the following job description: Unload Plastic Skew Plate. Note that the job type is set to Restart. 2. Save your model database file. 3. Submit the job for analysis, and monitor the solution progress. 4. Correct any modeling errors, and investigate the source of any warning messages.


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Postprocessing In the Visualization module, contour the U3 displacement component in the plate: 1. Click the Plot Contours tool in the toolbox. 2. From the list of variable types on the left side of the Field Output toolbar, select Primary (if it is not already selected). 3. From the list of available output variables in the center of the toolbar, select output variable U (spatial displacement at nodes). 4. From the list of available components and invariants on the right side of the Field Output toolbar, select U3. 5. Compare to the results at the end of the Apply Pressure step. Note that in this output database file, the results for frame 0 correspond to the results at the end of the Apply Pressure step (use the Frame Selector to switch to a different frame). The difference between the final state of the model and its initial state is due to the elastic springback that has occurred. The deformation that remains is permanent and unrecoverable. Note: A script that creates the complete models described in these instructions is available for your convenience. Run this script if you encounter difficulties following the instructions or if you wish to check your work. The script is named ws_solver_skew_plate_answer.py and is available using the Abaqus fetch utility.



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Workshop 5 CLD Analysis of a Seal using Abaqus/Standard Interactive Version Note: This workshop provides instructions in terms of the Abaqus GUI interface. If you wish to use the Abaqus Keywords interface instead, please see the “Keywords” version of these instructions. Please complete either the Keywords or Interactive version of this workshop.

Goals    

Evaluate a hyperelastic material. Define contact interactions using contact pairs and general contact. Perform a large displacement analysis with Abaqus/Standard. Use the Visualization module to create a compression load-deflection curve.

Introduction In this workshop, a compression analysis of a rubber seal is performed to determine the seal’s performance. The goal is to determine the seal’s compression load-deflection (CLD) curve, deformation and stresses. The analysis will be performed using Abaqus/Standard. Two analyses are performed: one using contact pairs and the other using general contact. As shown in Figure W5–1, the top outer surface of the seal is covered with a polymer layer, and the seal is compressed between two rigid surfaces (the upper one is displaced along the negative Y-direction; the lower one is fixed). During compression, the cover contacts the top rigid surface; the outer surface of the seal is in contact with the cover and the bottom rigid surface; in addition the inner surface of the seal may come into contact with itself.



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U2

Cover

Rigid Surfaces Seal fixed

Figure W5–1. Seal model: meshed assembly

Preliminaries 1. Enter the working directory for this workshop ../abaqus_solvers/interactive/seal

2. Run the script ws_solver_seal.py using the following command: abaqus cae startup=ws_solver_seal.py.

The above command creates an Abaqus/CAE database named seal.cae in the current directory. The geometry, mesh, and material definitions are included in the model named Seal. You will first perform a material evaluation to evaluate the stability of the hyperelastic material model, add the necessary data to complete the model, run the job, and finally postprocess the results.

Material Evaluation It is important to determine whether the material model of the seal will be stable during the analysis. Before completing the model, evaluate the material definition used for the seal. 1. Review the material definition. In the Model Tree, double-click Santoprene underneath the Materials container. It is a hyperelastic material with a first-order polynomial strain energy potential. The coefficients are already chosen for the analysis. 2. Evaluate the material definition. Abaqus/CAE provides a convenient Evaluate option that allows you to view the behavior predicted by a hyperelastic material by performing standard tests to choose a suitable material formulation. You will use this option to view the behavior predicted by the material Santoprene.


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a. From the main menu bar in the Property module, choose Material→Evaluate→Santoprene. b. The Evaluate Material dialog box appears. Notice that you can choose either the Coefficients or Test data source for evaluating the material.

Typically the test data are used to define a material model; you can use the Evaluate option to view the predicted behavior and adjust the material definition as necessary. In this workshop you will only evaluate the stability of the material model for the given coefficients. c. In the Evaluate Material dialog box, accept all defaults and click OK. Abaqus/CAE creates and submits a job to perform the standard tests using the material Santoprene; at the same time, Abaqus/CAE switches to the Visualization module and displays the evaluation results when the job is complete. Figure W5–2 shows the Material Parameters and Stability Limit Information dialog box; Figure W5–3 shows three stress vs. strain plots from uniaxial, biaxial, and planar tests. Question W5–1: What do the plots indicate about the stability of the material?

Based on these results, you can have confidence that your material will remain stable.

Figure W5–2. Material parameters and stability limit information



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Figure W5–3. Material evaluation results for uniaxial, biaxial, and planar tests After evaluating the material, you will now complete the model definition. Close the viewports and dialog box displaying the material evaluation results, if necessary, to view the model for the subsequent procedure.


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Part 1: Analysis using contact pairs Defining the step and the contact pairs 1. In the Model Tree, double-click the Steps container to create a static, general step named PushDown. a. In the Basic tabbed page of the step editor, set the time period to 1 and turn on Nlgeom. b. In the Incrementation tabbed page, enter a value of 0.005 for Initial Increment size and 200 for Maximum number of increments. c. In the Other tabbed page, select Unsymmetric as the matrix storage

scheme (it is recommended when the surface-to-surface contact discretization method is used). 2. Define a contact pair between the seal and the bottom rigid surface. a. In the Model Tree, double-click the Interactions container. In the Create Interaction dialog box, name the interaction BotSeal and select the step PushDown and Surface-to-surface contact (Standard). Click Continue. b. You will be prompted to select a master surface. In the prompt area, click Surfaces. In the Region Selection dialog box that appears, select the predefined surface Bottom and toggle on Highlight selections in viewport to view this surface. Click Continue. c. In the prompt area, select Surface as the slave surface type. In the Region Selection dialog box that appears, select the predefined surface SealOuter and visualize this surface. Click Continue. The interaction editor appears. d. In the Edit Interaction dialog box accept all defaults and click OK. Note that Abaqus/CAE automatically assigns the predefined (also the only available) interaction property frictionless to this interaction. 3. Using a similar procedure, define the following contact pairs as listed in Table W5–1 with the interaction property frictionless. Table W5–1. Contact pairs Interaction Name

Master Surface

Slave Surface

TopCover

Top

Cover

SealCover

Cover

SealOuter

Question W5–2: In the interaction SealCover, why do we choose SealOuter

as the slave surface?



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4. Create a self-contact interaction for the inner surface of the seal. a. In the Model Tree, double-click the Interactions container. In the Create Interaction dialog box, name the interaction SealSelf and select the step PushDown and Self-contact (Standard). Click Continue. b. In the Region Selection dialog box that appears, select the predefined surface SealInner and visualize this surface. Click Continue.

The interaction editor appears. c. In the Edit Interaction dialog box accept all defaults and click OK. Defining boundary conditions and output requests Asymmetric lateral sliding of the model is prevented by constraining the seal and the cover along their vertical symmetry axes in the X-direction. The bottom rigid surface is fixed, and a displacement of –6 units is applied to the top rigid surface along the Ydirection to compress the seal between the two surfaces. To complete these boundary conditions: 1. In the Model Tree, double-click the BCs container to create a Displacement/Rotation type boundary condition named Fix1 in the step PushDown. a. When prompted to select the region, click Sets in the prompt area (if

necessary). b. In the Region Selection dialog box, select the predefined set Fix1, toggle on Highlight selections in viewport to visualize the selection, and click Continue. c. In the Edit Boundary Condition dialog box, toggle on U1, accept the default value of 0, and click OK. 2. Create a Symmetry/Antisymmetric/Encastre type boundary condition named FixBot to encastre the predefined set BotRP (the reference node of the bottom

rigid surface). 3. Create a Displacement/Rotation type boundary condition named PushDown in the step PushDown to define the displacement of the top rigid surface. a. Select the predefined set TopRP (the reference node of the top rigid

surface). b. Specify a value of 0 for U1 and UR3, and -6 for U2. 4. Edit the field output request named F-Output-1 to include the nominal strain, NE. 5. Create a new history output request in the step PushDown for the set TopRP to write the history of the variables Displacements: U and Forces: RF to the output

database file.


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Running the job and postprocessing the results 1. Create a job named seal for the model Seal. 2. Save your model database, submit the job for analysis, and monitor the job’s

process. When the job is complete, open the output database file seal.odb in the Visualization module and postprocess the results. 3. Plot the undeformed and the deformed model shapes. To distinguish between the different instances, color code the model based on part instances. Tip: From the toolbar, select Part instances from the color-coding pull down menu, as shown in Figure W5–4 (or use the Color Code Dialog tool customize the color for each part instance).

to

Figure W5–4. Color-coding pull down menu 4. Use the Animate: Time History tool

to animate the deformation history. 5. Display only the seal. In the Results Tree, expand the Instances container underneath the output database file named seal.odb. Click mouse button 3 on the instance SEAL-1 and select Replace from the menu that appears. Abaqus/CAE now displays only this instance. 6. Contour the Mises stress of the seal on the deformed shape. If necessary, use the frame selector in the context bar to select the final increment. The contour plot is shown in Figure W5–5.



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Figure W5–5. Mises contour plot 7. Contour the minimum and maximum principal nominal strains. Elastic strains can

be very high for hyperelastic materials. Because of this, the linear elastic material model is not used because it is not appropriate for elastic strains greater than approximately 5%. 8. Display the reaction force history at the reference node of the top rigid surface: In the Results Tree, expand the History Output container underneath the output database file named seal.odb and double-click Reaction force: RF2 PI: TOP-1 Node 3 in NSET TOPRP. 9. You will now create the CLD curve. a. In the History Output container, click mouse button 3 on Reaction force: RF2 PI: TOP-1 Node 3 in NSET TOPRP and select Save As from the menu that appears. Save the data as Force. b. Click mouse button 3 on Spatial displacement: U2 PI: TOP-1 Node 3 in NSET TOPRP and select Save As from the menu that appears. Save the data as Disp. c. In the Results Tree, double-click XYData. In the Create XY Data dialog box that appears, select the Operate on XY data source and click Continue.

The Operate on XY Data dialog box appears. d. From the Operators listed in the Operate on XY Data dialog box, select combine(X, X) and then abs(A). Note that the abs(A) operator is used to obtain the absolute values. In the XY Data field, double-click the curve Disp. The current expression reads combine(abs("Disp")). Move the cursor before the far-right bracket, enter a comma, and then select the operator abs(A). In the XY Data field, double-click the curve Force. The final expression reads combine(abs("Disp"), abs("Force") ). Click Plot Expression to plot this expression. Save this plot as CLD.


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10. Customize the plot as follows:

a. From the main menu bar, select Options→XY Options→Plot.  In the Plot Options dialog box, fill the plot background in white. b. Double-click anywhere on the chart to open the Chart Options dialog box. 

In the Grid Display tabbed page, toggle on the major X- and Ygrid lines. Set the line color to blue and the line style to dashed.



Change the fill color using the following RGB values: red: 175; green: 250; blue: 185.



In the Grid Area tabbed page, select Square as the size and drag the slider to 80. From the list of auto-alignments, choose the one that places the chart in the center of the viewport c. Double-click the legend to open the Chart Legend Options dialog box. 

In the Contents tabbed page, click font size to 10.



In the Area tabbed page, toggle on Inset.



Toggle on Fill to flood the legend with a white background.

to increase the legend text

 In the viewport, drag the legend over the chart. d. Double-click either axis to open the Axis Options dialog box. 

In the X Axis region of the dialog box, select the displacement axis.



In the Scale tabbed page, place 4 major tick marks on the X-axis at (use the By count method).



In the Title tabbed page, change the X-axis title to Displacement (inch).



In the Y Axis region of the dialog box, select the force axis.



In the Scale tabbed page, specify that the Y-axis should extend from 0 (the Y-axis minimum) to 250 (the Y-axis maximum).



Increase the number of Y-axis minor tick marks per increment to 4.



In the Title tabbed page, change the Y-axis title to Force (lbf).



In the Axes tabbed page, change the font size for both axes to 10.

 e. Expand the list of plot option icons in the toolbox:



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f. Examine the remaining options. Add the following plot title: CLD Diagram. Double-click the plot title to open the Plot Title Options dialog box. 

In the Title tabbed page, click bold.






In the viewport, drag the plot title above the chart.

to change the legend text style to

g. Click in the toolbox to open the Curve Options dialog box. Change the legend text to Top Surface Ref Point and toggle on Show symbol. Set the color for both the line and symbols to red. Use large filled squares for the symbols. Reposition the legend as necessary. The final plot appears as shown in Figure W5–6.

Figure W5–6. Compression load deflection diagram Question W5–3:


294

What does the inverted peak near 4 inches of deflection represent?


W5.11

Part 2: Analysis using general contact 1. Copy the model named Seal to one named Seal_gc.

Make all subsequent modifications to the new model. 2. In the Model Tree, expand the Interactions container and select the 4 interactions defined earlier. 3. Click mouse button 3 and select Delete from the menu that appears, as shown in Figure W5–7.

Figure W5–7. Contact pairs to be deleted 4. In the Model Tree, double-click Interactions (or select Interaction→Create). 5. In the Create Interaction dialog box that appears, set the step to Initial and choose General contact (Standard) as the type. Click Continue. 6. In the interaction editor, select frictionless from the list of available Global property assignment options, as shown in Figure W5–8.



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Figure W5–8. General contact interaction 7. Click OK to complete the operation. 8. Create a job named seal_gc for the model Seal_gc. 9. Save your model database, submit the job for analysis, and monitor the job’s

process. When the job is complete, open the output database file seal_gc.odb in the Visualization module and postprocess the results. 10. Compare the results with those obtained using contact pairs. A comparison of the stress state in the seal is shown in Figure W5–9 while a comparison of the forcedisplacement curve is shown in Figure W5–10. The agreement between the two approaches is excellent. The general contact approach, however, provides a much simpler user interface since the entire contact domain is defined automatically and properties are assigned globally.


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Figure W5–9. Comparison of the stress state in the seal (general contact, top; contact pairs, bottom)

Figure W5–10. Comparison of force-displacement curves



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Note: A script that creates the complete seal model is available for your convenience. Run this script if you encounter difficulties following the instructions or if you wish to check your work. The script is named ws_solver_seal_answer.py



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Answers Question W5–1: What do the plots indicate about the stability of the material? Answer:

The plots never have a negative slope, indicating that the material is stable throughout the entire strain range.

Question W5–2: In the interaction SealCover, why do we choose SealOuter

as the slave surface? Answer:

SealOuter has a more refined mesh and should therefore be

specified as the slave surface.

Question W5–3: What does the inverted peak near 4 inches of deflection Answer:


represent? This peak represents the inward buckling that occurs at the bottom corners of the seal during compression. If you look at the deformed shape at the time corresponding to approximately 3.7 inches of displacement, you will observe this phenomenon.


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Workshop 6 Dynamics Interactive Version Note: This workshop provides instructions in terms of the Abaqus GUI interface. If you wish to use the Abaqus Keywords interface instead, please see the “Keywords” version of these instructions. Please complete either the Keywords or Interactive version of this workshop.

Goals   

Become familiar with the Abaqus/CAE procedures for frequency extraction and implicit dynamic analyses. Become more familiar with monitoring job status. Learn how to plot eigenmodes and create history plots using Abaqus/CAE.

Introduction In this workshop the dynamic response of the cantilever beam shown in Figure W6–1 is investigated. A frequency extraction is performed to determine the 10 lowest vibration modes of the beam. The effects of mesh refinement, element interpolation order, and element dimension will be considered. The problem is also solved by performing a direct integration dynamic analysis to simulate the vibration of the beam upon removal of the tip load. The frequency of the vibration predicted by the transient analysis will be compared with the natural frequency results.

Figure W6–1. Problem description © Dassault Systèmes, 2012


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Preliminaries 1. Enter the working directory for this workshop ../abaqus_solvers/interactive/dynamics

2. Run the script ws_solver_beam.py using the following command: abaqus cae startup=ws_solver_beam.py.

The above command creates an Abaqus/CAE database named Beam.cae in the current directory. The model named static includes the beam model for a static, general analysis. Currently 5 B21 elements are used to discretize the beam. You will edit this model further as described below.

Part 1: Frequency extraction analysis Perform a frequency extraction analysis to determine the 10 lowest eigenmodes of the structure. In the current model do the following. 1. Add a density of 2.3E6 unit to the beam material definition named MATEA. 

In the Model Tree, expand the Materials container and double-click the material MATEA.



In the material editor, select General→Density from the menu bar.



Enter the value 2.3E-6 for Mass Density in the Density field.

2. The frequency analysis procedure will be used instead of the general static one. Thus, suppress the general static step named Displace (do not delete it since it will be used later). a. In the Model Tree, expand the Steps container and click mouse button 3 on the step Displace and select Suppress from the menu that appears. b. Create a new step named Frequency; select Linear perturbation as the procedure type and Frequency from the list of available perturbation steps. c. Click Continue. d. In the step editor, accept the default Lanczos eigensolver and enter a value of 10 for Number of eigenvalues requested. e. Click OK to save the change and exit the step editor. 3. Create a job named frequency. 4. Save your model database, submit the job for analysis, and monitor the job’s process.


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Visualizing results When the analysis is complete, use the following procedure to view the eigenmodes and eigenvalues from the frequency analysis in the Visualization module: 1. In the Model Tree, click mouse button 3 on the job frequency and select Results from the menu that appears to open the file frequency.odb in the Visualization module. 2. Plot the first eigenmode (plot the deformed model shape and use the Frame or the Step/Frame dialog box to choose the frame corresponding to Mode 1). 3. Using the arrow keys in the context bar, select different mode shapes. 4. The results for modes 1 and 4 are shown in Figure W6–2. These correspond to the first and fourth transverse modes of the structure. Selector

5. Figure W6–2. First and fourth transverse modes (coarse mesh; 2D linear beam elements)

Question W6–1: Are there modes of the physical system that cannot be

captured by your model because of limitations in element type or mesh? (Remember that the elements are planar and the mesh is somewhat coarse.) Question W6–2: Do any of the mode shapes for your model look non-physical?



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Effect of mesh on extracted modes From Figure W6–2 it is apparent that such a coarse mesh of linear-interpolation elements is unable to adequately represent the mode shapes associated with the higher modes. In fact the current mesh is unable to represent anything beyond the fifth mode. To obtain accurate results for all extracted modes, a sufficiently refined mesh is required. Thus, increase the mesh refinement. Also, switch to quadratic interpolation elements since these provide superior accuracy for frequency extraction analysis. 1. Remesh the part using a global seed size of 5. 2. Change the element type to B22. 3. Create a new job, run it, and compare the results with those obtained previously. The results for modes 1 and 4 are shown in Figure W6–3.

Figure W6–3. First and fourth transverse modes (fine mesh; 2D quadratic beam elements)

The results indicate that the refined mesh is able to represent all extracted modes. The natural frequency of the first mode predicted by the fine-mesh model is within 2% of that predicted by the coarse mesh model. The difference in results for the fourth mode is more significant: there is an 8% difference in the predicted natural frequency for this mode. Note that all modes with the exception of modes 6 and 10 are transverse modes. Modes 6 and 10 are longitudinal modes. To see the longitudinal modes more clearly, superimpose the undeformed model shape on the deformed model shape.


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Torsional and out-of-plane modes The current model, given that it uses two-dimensional beam elements, is unable to capture any torsional or out-of-plane modes. For this a three-dimensional model is required (using either beam, solid, or shell elements). With three-dimensional beam elements, however, it is not possible to visualize the modes. Thus, in what follows, shell elements are used to capture the out-of-plane modes. A predefined model named shell is available that uses three-dimensional quadratic shell elements to represent the beam structure. The shell part is 200 units long by 50 units wide. The part mesh consists of 40 S8R elements along the length of the structure and 10 along its width. Homogeneous shell section properties with the same material properties used earlier and a thickness of 5 units are assigned to the part. 1. Create a job for the shell model, run it, and compare the results with those obtained previously. 2. The results for the first and fourth transverse modes are shown in Figure W6–4. The agreement in terms of both mode shape and natural frequency between the (refined) beam and shell models is excellent (compare with Figure W6–3).

Figure W6–4. First and fourth transverse modes (3D shell model)



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W6.6

3. The three-dimensional model captures the torsional and out-of-plane modes that are suppressed by the two-dimensional model. The first three of these modes are shown in Figure W6–5.

Figure W6–5. Torsional and out-of-plane modes (3D shell model)


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Part 2: Transient dynamic analysis You will now investigate the free vibration of the beam upon removal of the tip load, using an implicit dynamic procedure (Abaqus/Standard). 1. Copy the model named static to a model named dynamic. Make the following changes to the dynamic model. 2. Delete the frequency extraction step. 3. Resume the static, general step named Displace. 4. Create a dynamic, implicit step after the static, general step. a. In the Model Tree, double-click the Steps container. b. In the Create Step dialog box, name the step Release. c. Select Dynamic, Implicit from the list of available General procedure types, and click Continue. d. In the Edit Step dialog box, accept the default step time 1. e. In the Incrementation tabbed page, choose Automatic time incrementation, enter a value of 200 for the maximum number of increments, and 0.01 for the initial increment size. f. Click OK to save the data and exit the step editor. 5. Deactivate the load in the step named Release. a. In the Model Tree, expand the branch of the load DisplaceTip underneath the Loads container, as shown in Figure W6–6a. b. Click mouse button 3 on Release (propagated) under the States subcontainer and select Deactivate from the menu that appears. Note that Release (propagated) is changed into Release (Inactive), as shown in Figure W6–6b, to indicate that the load is deactivated in this step.

(a)

(b) Figure W6–6. Loads container in the Model Tree



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A part-level set named TIP has been predefined. This set will be used for writing the displacement history of the tip node to the output database file and also to monitor the solution progress. This set is indicated in Figure W6–3. TIP

Figure W6–3. Part-level node set 6. Add a history output request to write the displacement history every increment for the set TIP to the output database file. a. In the Model Tree, double-click the History Output Requests container. In the Create History dialog box, select the step Displace and click Continue. b. In the Edit History Output Request dialog box, select the domain Set and the set Beam-1.TIP. c. Expand the Displacement/Velocity/Acceleration branch in the Output Variables field and toggle on U, Translations and rotations. d. Click OK to exit the history output editor. 7. It is useful to be able to monitor the progress of an analysis by tracking the value of one degree of freedom. a. From the main menu bar of the Step module, select Output→DOF Monitor to open the DOF Monitor dialog box. b. Activate the stippled entries by toggling on Monitor a degree of freedom throughout the analysis. c. Click to select the set Beam-1.TIP as the Region. Tip: Click Points in the prompt area to select the set Beam-1.TIP from the Region Selection dialog box. d. Enter 2 as the Degree of freedom. e. Click OK to exit the DOF Monitor dialog box. 8. Create a job named dynamic for the model dynamic. 9. Save your model database, submit the job for analysis, and monitor the job’s process.


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Visualizing results When the analysis is complete, plot the transverse displacement history (U2) at the tip node. 1. Open the file dynamic.odb in the Visualization module. 2. Plot the history of the displacement component U2 at the tip node. In the Results Tree, expand the History Output container underneath the output database named dynamic.odb and double-click Spatial displacement: U2 at Node … in NSET TIP. The tip response is shown in Figure W6–7. From this plot, you can estimate the frequency of the first vibration mode. Note that there are nearly 6 cycles in a 1 second time period. This is in agreement with the results obtained earlier using the natural frequency extraction procedure (5.95 Hz).

Figure W6–7. Tip node displacement history Question W6–3: How does this compare with the frequency calculated in the

eigenvalue analysis?

Note: A script that creates the complete model described in these instructions is available for your convenience. Run this script if you encounter difficulties following the instructions outlined here or if you wish to check your work. The script is named ws_solver_beam_answer.py and is available using the Abaqus fetch utility.



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W6.10

Answers


Answer:

captured by your model because of limitations in element type or mesh? (Remember that the elements are planar and the mesh is somewhat coarse). Because the model is two-dimensional, it cannot capture the modes that occur out of the plane of the model, including torsional modes. The mesh is too coarse to capture modes other than the first five. Use more elements to look at all 10 requested modes.

Question W6–2: Do any of the mode shapes for your model look nonphysical? Answer:

No.

Question W6–3: How does this compare with the frequency calculated in the Answer:


312

eigenvalue analysis? The frequency calculated from the history plot of the tip displacement is approximately 5.9, which agrees very closely with the frequency calculated in the eigenvalue analysis.


Notes

313

Notes

314

Workshop 7 Contact with Abaqus/Explicit Interactive Version Note: This workshop provides instructions in terms of the Abaqus GUI interface. If you wish to use the Abaqus Keywords interface instead, please see the “Keywords” version of these instructions. Please complete either the Keywords or Interactive version of this workshop.

Goals     

Define a rigid body constraint. Define a general contact interaction. Apply boundary and initial conditions. Perform an impact analysis. Use Abaqus/Viewer to view results.

Introduction This workshop involves the simulation of a pipe-on-pipe impact resulting from the rupture of a high-pressure line in a power plant. It is assumed that a sudden release of fluid could cause one segment of the pipe to rotate about its support and strike a neighboring pipe. The goal of the analysis is to determine strain and stress conditions in both pipes and their deformed shapes. The simulation will be performed using Abaqus/Explicit.



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W7.2

fixed end

impacting pipe axis of rotation

Figure W7–1. Pipe whip model assembly Both pipes have a mean diameter of 6.5 inches with a 0.432 inch wall thickness and a span of 50 inches between supports. The fixed pipe is assumed to be fully restrained at both ends, while the impacting pipe is allowed to rotate about a fixed pivot located at one of its ends, with the other end free. We exploit the symmetry of the structure and the loading and thus model only the geometry on one side of the central symmetry plane, as shown in Figure W7–1.

Preliminaries 1. Enter the working directory for this workshop: ../abaqus_solvers/interactive/pipe_whip

2. Run the script ws_solver_pipe_whip.py using the following command: abaqus cae startup=ws_solver_pipe_whip.py

The above command creates an Abaqus/CAE database named pipeWhip.cae in the current directory. A model named contact consists of the geometry and mesh definitions for the pipes. You will add necessary data to complete the model for the impact analysis.

Defining material and section properties Both pipes are made of steel. A von Mises elastic, perfectly plastic material model is used, with a yield stress of 45,000 psi. 1. In the Model Tree, double-click Materials to create a material named Steel with the following properties: Modulus of elasticity: 30.0E6 psi Poisson’s ratio: 0.3 Yield Stress: 45.0E3 psi Density: 7.324E–4 lb-sec2/in4


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W7.3

Question W7–1: Why is density required in the material model definition? Can

you comment on the units of density used in this problem? 2. In the Model Tree, double-click Sections to create a homogeneous shell section named PipeSection. In the Basic tabbed page of the Edit Section dialog box, select During analysis for the section integration, specify a shell thickness of 0.432 in, select the Gauss thickness integration rule, and view and accept all other default settings. Click OK to exit the section editor. 3. In the Model Tree, expand the branch of each part underneath the Parts container and double-click Section Assignments to assign this shell section to both parts. Question W7–2: Why are only three integration points used through the

thickness?

Defining rigid body constraint You will define a rigid body constraint between the nodes at the pivot end of the impacting pipe and the reference point, as shown in Figure W72. 1. In the Model Tree, double-click Constraints. 2. In the Create Constraint dialog box, select Rigid body as the constraint type and click Continue. 3. In the Edit Constraint dialog box, select the region type Tie (nodes) and click in the right side of the dialog box. 4. Select the edge(s) shown in Figure W7–2 as the tie region for the rigid body. 5. Similarly, select the reference point RP-1 in the viewport as the rigid body reference point. 6. In the Edit Constraint dialog box, click OK to apply the constraint.

tie region

Figure W7–2. Rigid body constraint



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W7.4

Question W7–3: In order to drive both the translations and rotations of the pipe

edge nodes, what type of node set needs to be used in the rigid body constraint?

Defining step and output requests Because of the high-speed nature of the event, the simulation is performed using a single explicit dynamics step. 1. In the Model Tree, double-click Steps to create a Dynamic, Explicit step with a time period of 0.015 seconds. Accept all defaults for the time incrementation and other parameters. 2. In the Model Tree, expand the Field Output Requests container and doubleclick F-Output-1. In the Edit Field Output Requests dialog box, review the preselected field output variables. Change the frequency at which the output is written to 12 evenly spaced time intervals. 3. In the Model Tree, double-click History Output Requests to create a history output request for reaction forces at the constrained end of the fixed pipe. In the Edit History Output Request dialog box: a. Select Set in the Domain field and select RefPt from the Set drop down list. Note that the set RefPt contains the reference point. b. Request history output at 100 evenly spaced time intervals during the analysis. c. From the list of available output variables, click the arrow next to Forces/Reactions and toggle on RF, Reaction forces and moments from the list that appears. d. Click OK.

Defining contact interaction 1. In the Model Tree, double-click Interaction Properties. 2. In the Create Interaction Property dialog box, accept Contact as the interaction type and click Continue. 3. In the Edit Contact Property dialog box, select Mechanical→Tangential Behavior and choose the Penalty friction formulation. Specify a friction coefficient of 0.2. Click OK to close the dialog box. 4. In the Model Tree, double-click Interactions. 5. In the Create Interaction dialog box, accept Step-1 as the step in which the interaction will be created and General contact (Explicit) as the interaction type. Click Continue. 6. In the Edit Interaction dialog box, accept the All* with self contact domain. 7. Choose the contact property defined earlier and click OK to close the dialog box.


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W7.5

Defining Initial conditions The impacting pipe is given an initial angular velocity of 75 radians/sec about its supported (pinned) end. Question W7–4: How can you use the coordinates of the reference point to

define the axis of rotation?

1. Perform a Point/Node query ( ) to determine the coordinates of two end points on the axis of rotation at the pivot end of impacting pipe, as shown in Figure W7–3.

first point

second point

Figure W7–3. Points on axis of rotation The coordinates will be printed out to the message area as shown in Figure W7–4.

Figure W7–4. Point coordinates 2. In the Model Tree, double-click Predefined Fields. 3. In the Create Predefined Field dialog box, select the Initial step, the Mechanical category, and the Velocity type. Click Continue to proceed. 4. Select the impacting pipe as the region to which the initial velocity will be assigned, and click Done.



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W7.6

5. In the Edit Predefined Field dialog box, change the field definition to Rotational only. Enter a value of 75 for the Angular velocity. Use the coordinates of the first point indicated in Figure W7–3 to define Axis point 1 and the coordinates of the second point indicated in Figure W7–3 to define Axis point 2. Tip: Copy and paste the coordinates from the message area into the dialog box. Question W7–5: What keyword was added to the input file when you created

the angular velocity field? Search the Abaqus Keywords Reference Manual and read the documentation on this keyword. Hint: You can see how Abaqus/CAE creates the input file for a given model by selecting Model→Edit Keywords from the main menu bar and viewing its contents. In order to find what keyword was added in a given step, check the keyword editor before and after the step in Abaqus/CAE and note the changes.

Defining boundary conditions The edges located on the symmetry plane must be given appropriate symmetry boundary conditions. One end of the impacting pipe and both ends of the fixed pipe are fully restrained. 1. In the Model Tree, double-click BCs. 2. In the Create Boundary Condition dialog box, accept Symmetry/ Antisymmetry/Encastre as the boundary condition type and click Continue to create the boundary conditions shown in Figure W7–5.

• • •

Symmetry boundary conditions: Select the edges shown in Figure W7–5; and in the Edit Boundary Condition dialog box, choose the ZSYMM (U3=UR1=UR2=0) boundary condition. Fully constrained boundary conditions: Select the edge shown in Figure W7–5; and in the Edit Boundary Condition dialog box, choose the ENCASTRE (U1=U2=U3=UR1=UR2=UR3=0) boundary condition. Pinned Boundary condition: Select RP-1 in the viewport. In the Edit Boundary Condition dialog box, choose the PINNED (U1=U2=U3=0) boundary condition.


320


W7.7 fully constrained end: ENCASTRE BC

symmetry: ZSYMM BC (all edges on this plane)

PINNED BC

Figure W7–5. Boundary conditions Question W7–6: Would the results of this analysis differ if both halves of the

pipe were modeled instead of using symmetry boundary conditions?

Running the job and postprocessing the results 1. Save your model database file. 2. A job named pipe-whip has been already been created for you. Submit the job for analysis, and monitor its progress. 3. When the analysis has completed, open the output database file pipe-whip.odb in the Visualization module. 4. Plot the undeformed and the deformed model shapes. Use the Color Code Dialog tool

to customize the color for each instance, as shown in Figure W7–6.

Figure W7–6. Deformed model shape



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W7.8

5. Use the Animate: Time History tool to animate the deformation history. 6. Contour the Mises stress and equivalent plastic strain (PEEQ) on the deformed shape, as shown in Figure W7–7. MISES

PEEQ

Figure W7–7. Contour plots 7. Create X–Y plots of the model’s kinetic energy (ALLKE), internal energy (ALLIE), and plastic dissipated energy (ALLPD). The energy plot is shown in Figure W7–8. Note this figure has been customized for clarity. Tip: Expand the History Output container in the Results Tree and select the three curves noted above. Click mouse button 3 and select Plot from the menu that appears.

Figure W7–8. Energy histories Question W7–7: What do the energy history plots indicate?


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W7.9

8. Select the pinned node reaction force components RF1, RF2, and RF3. The reaction force plot is shown in Figure W7–9. Note this figure has been customized for clarity.

Figure W7–9. Reaction force histories

Note: A script that creates the complete pipe assembly model is available for your convenience. Run this script if you encounter difficulties following the instructions or if you wish to check your work. The script is named ws_solver_pipe_whip_answer.py and is available using the Abaqus fetch utility.



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Answers Question W7–1: Why is density required in the material model definition? Can Answer:

you comment on the units of density used in this problem? All Abaqus/Explicit analyses require a density value because Abaqus/Explicit solves for dynamic equilibrium (i.e., inertia effects are considered). The units for all material parameters must be consistent; in this problem, the English system is used with pounds and inches as the units for force and length, respectively. Thus, the consistent unit for density is lb-sec2/in4.

Question W7–2: Why are only three integration points used through the Answer:

thickness? Three section points are used to reduce the run time of the job.


Answer:

edge nodes, what type of node set needs to be used in the rigid body constraint? A tie node set needs to be used.

Question W7–4: How can you use the coordinates of the reference point to Answer:

define the axis of rotation? The axis passes through the reference point and is parallel to the 3-direction. Thus, define the axis using two points. Each of the “axis” points must have the same 1- and 2-coordinates as the reference point; the values of the 3-coordinates of the “axis” points will dictate the sense of positive rotation.

Question W7–5: What keyword was added to the input file when you created

the angular velocity predefined field? Search the Abaqus Keywords Manual and read the documentation on this keyword. Answer:


324

Abaqus/CAE adds the keyword *INITIAL CONDITIONS, TYPE=ROTATING VELOCITY, which imposes a rigid body type initial rotation on the chosen geometry about a defined axis.


W7.11

Question W7–6: Would the results of this analysis differ if both halves of the

Answer:

pipe were modeled instead of using symmetry boundary conditions? As long as the model of the pipe whip (including loads, boundary conditions, and mesh) is symmetric about the symmetry plane defined, the results from the full model and the halved model will not differ.

Question W7–7: What do the energy history plots indicate? Answer:


Near the end of the simulation, the impacting pipe is beginning to rebound, having dissipated the majority of its kinetic energy by inelastic deformation in the crushed zone.


325

326

Notes

327

Notes

328

Workshop 8 Quasi-Static Analysis Interactive Version Note: This workshop provides instructions in terms of the Abaqus GUI interface. If you wish to use the Abaqus Keywords interface instead, please see the “Keywords” version of these instructions. Please complete either the Keywords or Interactive version of this workshop.

Goals  

Approximate a quasi-static solution using Abaqus/Explicit. Understand the effects of mass scaling.

Introduction In this workshop you will examine the deep drawing of a can bottom. A one-stage forming process is simulated in Abaqus/Explicit; the springback analysis is performed in Abaqus/Standard. The final deformed shape of the can bottom is shown in Figure W8–1. In a subsequent workshop the import capability is used to transfer the results between Abaqus/Explicit and Abaqus/Standard in order to perform a springback analysis. One of the advantages of using Abaqus/Explicit for metal forming simulations is that, in general, Abaqus/Explicit resolves complicated contact conditions more readily than Abaqus/Standard.



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W8.2

Figure W8–1. Final deformed shape

Preliminaries 1. Enter the working directory for this workshop: ../abaqus_solvers/interactive/forming

2. Run the script ws_solver_can_bottom.py using the following command: abaqus cae startup=ws_solver_can_bottom.py

The above command creates an Abaqus/CAE database named canBottom.cae in the current directory. It includes two models. The one named frequency will be used to determine the first eigenmode of the blank to establish the step time for the subsequent Abaqus/Explicit analysis. The one named stamp will initially be used to perform the metal forming analysis and will later be edited for the springback analysis. Figure W8–2 shows the components of the model—the punch, the die, and the blank—in their initial positions. The blank is modeled using axisymmetric shell elements (SAX1). The shell reference surface lies at the shell midsurface.


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W8.3

(0.032, 0.03025)

(0.0, 0.00025)

Origin (0.0, 0.0)

Figure W8–2. Model geometry

Part 1: Establishing the Abaqus/Explicit analysis time In this section you will determine the first eigenmode of the blank and use it to establish the step time for the subsequent Abaqus/Explicit analysis. 1. Using the Model Tree, review the model definitions of the model frequency. Question W8–1: What analysis procedure is used in this model? Question W8–2: In Abaqus a distinction is made between linear perturbation

analysis steps and general analysis steps. What type of procedure is the analysis procedure in this model? Question W8–3: In an analysis with more than one step in the same model, what influence does the result of a linear perturbation step have on the base state of the model for the following analysis step? 2. Create a job named frequency for the model frequency. 3. Save your model database file, submit the job for analysis, and monitor its progress. 4. When the analysis is complete, open the output database file frequency.odb in the Visualization module.



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W8.4

5. Plot the deformed model shape. The deformed shape for the first eigenmode will be displayed in the viewport. The corresponding eigenvalue will be reported in the state block. The fundamental frequency, f, of the blank is 304 Hz, corresponding to a time period of 0.0033 s ( T  1/ f ). This time period provides a lower bound on the step time for the first forming stage. Choosing the step time to be 10 times the time period of the fundamental natural frequency, or 0.033 s, should ensure a quality quasi-static solution. This time period corresponds to a constant punch velocity of 0.45 m/s, which is typical for metal forming.

Part 2: Metal Forming Analysis You will now complete the model stamp to perform the metal forming analysis using ABAUS/Explicit. Make the following changes to the model stamp. Completing the assembly In this section you will complete the assembly definition of the can bottom forming model (Figure W8–2) by instancing the part representing the punch (PUNCH1). 1. Make current the model stamp. If necessary, set this model to be the root of the tree. 2. In the Model Tree, expand the Assembly container and double-click Instances to create an instance of the analytical rigid part PUNCH1. In the Create Instance dialog box, select part PUNCH1, accept all other default settings, and click OK. Use the Translate Instance tool in the toolbox to offset the punch from the blank by the half thickness of the blank (0.00025 m). The viewport displays the assembly with the geometry as shown in Figure 8–2. Defining displacement history output In this section you will add a history output request to write the displacement history at the reference point of the punch to the output database file. 1. Create a geometry-based set including the punch reference point. a. In the Model Tree, expand the branch of the part PUNCH1 underneath the Parts container and double-click Sets. b. Name the set PunchRP. c. From the viewport, select the reference point RP of the part PUNCH1. 2. In the Model Tree, double-click History Output Requests to create an additional history output request to output the displacement (translation and rotation) history for the set PUNCH1-1.PunchRP. Note that PUNCH1-1.PunchRP is an assemblylevel set generated from the previously-created part-level set PunchRP by Abaqus/CAE.


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W8.5

Defining contact In this section you will define contact of the blank with the die and the punch. 1. Define a contact property. a. In the Model Tree, double-click Interaction Properties. b. In the Create Interaction Property dialog box, select the type Contact and click Continue. c. From the menu bar of the contact property editor, select Mechanical→Tangential Behavior. d. Select the Penalty friction formulation and enter 0.1 for the friction coefficient. e. Click OK to exit the contact property editor. 2. Define a contact pair between the blank and the die. a. In the Model Tree, double-click the Interactions container. In the Create Interaction dialog box, name the interaction blank_die, select Step-1 as the step and the Surface-to-surface contact (Explicit) type, and click Continue. b. You will be prompted to select the first surface. In the viewport, select the die. c. Click mouse button 2 in the viewport or click Done in the prompt area to confirm the selection. d. You will be prompted to choose a side of the edge. Choose the side facing the blank by selecting the corresponding color, Magenta or Yellow, in the prompt area. e. In the prompt area, select Surface as the second surface type. In the viewport, select the blank. f. Click mouse button 2 in the viewport or click Done in the prompt area to confirm the selection. g. Again, you will be prompted to choose a side of the edge. Choose the side facing the die. The interaction editor appears. h. In the Edit Interaction dialog box, view and accept the default setting. Click OK to create the interaction and exit the interaction editor. Note that Abaqus/CAE automatically assigns the previously-created interaction property to this interaction. 3. Using a similar procedure, define an additional surface-to-surface contact interaction named blank_punch between the blank and punch. Question W8–4: What effect will an increase in friction have on the solution?



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W8.6

Defining material properties In this section you will add the material definition of the blank. The blank material is steel with Young’s modulus E =210E9 Pa, Poisson’s ratio v =0.3, and density  =7800 kg/m3. Figure W8–3 shows the nominal stress-strain curve for the blank as tabulated in Table W8–1. The data are provided in a text file named w_solver_can_props.txt.

Figure W8–3. Nominal stress vs. nominal strain Question W8–5: When entering plasticity data into the material model, what

are the stress and strain measures that Abaqus uses? Table W8–1. Nominal stress vs. nominal strain Nominal stress (Pa) 90.96  106 130.71  106 169.75  106 207.08  106 240.99  106 268.89  106 287.59  106 290.57  106


334

Nominal strain 4.334  104 2.216  103 7.331  103 1.888  10-2 4.153  102 8.218  102 1.509  101 3.456 101


W8.7

Note that a dummy material named Steel has been created and assigned to the part BLANK. You will need to add the material properties. Rather than convert the stress-strain data and define the material properties manually, you will use the material calibration capability to define the material properties. 1. In the Model Tree, double-click Calibrations. 2. Name the calibration steel and click OK. 3. Expand the Calibrations container and then expand the steel item. 4. Double-click Data Sets. a. In the Create Data Set dialog box, name the data set nominal and click Import Data Set. b. In the Read Data From Text File dialog box, click named w_solver_can_props.txt.

and choose the file

c. In the Properties region of this dialog box, specify that strain values will be read from field 2 and stress values from field 1. d. Select Nominal as the data set form. e. Click OK to close the Read Data From Text File dialog box. f. Click OK to close the Create Data Set dialog box. Since the data is provided in nominal stress-strain format, it must be converted to true stress-strain format. 5. Click mouse button 3 on nominal and select Process from the menu that appears. a. In the Data Set Processing dialog box, select Convert and click Continue. b. In the Change Data Set Form dialog box, select True Form and name the new data set true. Click OK. 6. Double-click Behaviors. a. Choose Elastic Plastic Isotropic as the type, and click Continue. b. In the Edit Behavior dialog box, choose true as the data set for ElasticPlastic Data. c. Click next to Yield point. In the viewport zoom in to select the yield point, as indicated in Figure W8–4.



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W8.8

Alternative: Enter 0.00043, 91E+06 in the text field to define the yield

point precisely.

Figure W8–4 Yield point. d. Drag the Plastic points slider between Min and Max to generate plastic data points. The plastic data points appear as shown in Figure W8–5.

Figure W8–5 Plastic data points. e. Enter a Poisson's ratio of 0.3. f. In the Edit Behavior dialog box, choose Steel from the Material dropdown list, as shown in Figure W8–6.


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W8.9

Figure W8–6 Material behavior editor. g. Click OK to add the properties to the material named steel. 7. In the Model Tree, expand the Materials container and examine the contents of the material model. You will note that both elastic and plastic properties have been defined (Young’s modulus should be approximately 2.1E11 Pa). If you wish to change the number of plastic points or need to modify the yield point, simply return to the Edit Behavior dialog box, make the necessary changes, select the name of the material to which the properties will be applied, and click OK. The contents of the material model are updated automatically. 8. To complete the material properties, define the density. From the menu bar of the material editor, select General→Density and enter a value of 7800 for Mass Density.



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W8.10

9. To reduce high-frequency noise in the solution (caused primarily by the oscillations of the blank’s free end) add stiffness proportional damping to the material definition of the blank. It is best to use the smallest amount of damping possible to obtain the desired solution since increasing the stiffness damping decreases the stable time increment and, thus, increases the computer time. To avoid a dramatic drop in the stable time increment, the stiffness proportional damping factor R should be less than, or of the same order of magnitude as, the initial stable time increment without damping. We choose a damping factor of R=1107. From the material editor’s menu bar, select Mechanical→ Damping and enter a value of 1.e-7 in the Beta field. 10. Click OK to save the data and exit the material editor. Question W8–6: What effects would a higher damping coefficient have?


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W8.11

Defining displacement boundary conditions To form the can bottom, we will displace the punch by moving its rigid body reference point 0.015 m in the negative 2-direction. The punch displacement will be applied in the form of a displacement boundary condition. Because Abaqus/Explicit does not permit displacement discontinuities, prescribed displacements must refer to an amplitude definition. Figure W8–7 shows the desired displacement behavior for the punch. Note that this curve is smooth in its first and second derivatives. Question W8–7: What is the slope of the curve at the beginning and end, and

why is this important? 1. In the Model Tree, double-click Amplitudes to define an amplitude curve corresponding to Figure W8–7. a. In the Create Amplitude dialog box, name the amplitude FORM1, choose the Smooth step type, and click Continue. b. In the Edit Amplitude dialog box, enter the data pair 0, 0 for the first row and 0.033, 1 for the second row. c. Click OK to exit the amplitude editor. 2. In the Model Tree, double-click BCs to create a Displacement/Rotation boundary condition named PunchMove in Step-1 to move the punch reference point in the 2-direction by –0.015 m. a. In the Edit Boundary Condition dialog box, toggle on U1, U2, and UR3. b. Enter a value of -0.015 for U2 and 0 for U1 and UR3. c. Choose the amplitude curve FORM1. The amplitude values will be multiplied by the displacement you define in the boundary condition. Question W8–8: How would the results change if a linear amplitude definition

was used instead?



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W8.12

Figure W8–7. Displacement curve of punch Speeding up the analysis In general, quasi-static processes cannot be modeled in their natural time scale in Abaqus/Explicit since a large number of time increments would be required (recall that time increments in Abaqus/Explicit are generally very small). Thus, it is sometimes necessary to increase the speed of the simulation artificially to reduce the computational cost. One method to reduce the cost of the analysis is to use mass scaling. While various forms of mass scaling are available in Abaqus/Explicit, we will concentrate on fixed mass scaling in this workshop and will implement it using the fixed mass scaling option available in the step editor. The reason for choosing fixed mass scaling is that it provides a simple means to modify the mass properties of a quasi-static model at the beginning of the analysis. It is also computationally less expensive than variable mass scaling, because the mass is scaled only once at the beginning of the step. 1. In the Model Tree, expand the Steps container and double-click Step-1 to edit this step definition to include mass scaling. 2. In the Edit Step dialog box, click the Mass scaling tab. 3. In the Mass scaling tabbed page, choose Use scaling definitions below and click Create. 4. In the Edit mass scaling dialog box that appears, accept all defaults and enter 10 in the Scale by factor field. 5. Click OK to save the data and exit the mass scaling editor. 6. Click OK to save the changes and exit the step editor.


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W8.13

Question W8–9: How do you determine if an analysis that includes mass

scaling produces acceptable results? Question W8–10: How does mass scaling affect the solution time?

Running job and postprocessing results 1. Create a job named draw_bot for the model Stamp. 2. Save your model database file, submit the job for analysis, and monitor its progress. 3. When the analysis is complete, open the output database file draw_bot.odb in the Visualization module. 4. Display the curves of internal and kinetic energy (i.e., ALLIE and ALLKE) in the same plot by selecting them from the Results Tree (underneath the History Output container). Use the XY Curve Options tool

in the toolbox to display the curve symbols. You should see a plot similar to Figure W8–8. Note this figure has been customized for clarity. Tip: Use [Ctrl]+Click for multiple selections.

Figure W8–8. Internal and kinetic energy 5. Certain elements have hourglass modes that affect their behavior. Hourglass modes are modes of deformation that do not cause any strains at the integration points. An indication of whether hourglassing has an effect on the solution is the artificial energy, variable ALLAE. Plot the artificial energy and the internal energy, variable ALLIE, on the same plot. The artificial energy should always be much less than the internal energy (say less than 0.5%).



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W8.14

Question W8–11: What elements are used to model the blank, and does this

element type have an hourglass deformation mode? 6. Display the deformed shape of the blank only. In the Results Tree, expand the Instances container underneath the output database draw_bot.odb. Click mouse button 3 on the instance BLANK-1 and select Replace from the menu that appears. 7. Expand the displayed area to 180o by selecting View→ODB Display Options from the main menu bar. In the Sweep/Extrude tabbed page in the ODB Display Options dialog box, toggle on Sweep elements and accept the default settings. You should see a shape similar to that in Figure W8–9.

Figure W8–9. 180 expanded deformed shape 8. Contour the Mises stress distribution of the 180o model using the Plot Contours on Deformed Shape tool in the toolbox. To select other variables for contouring, use the Field Output toolbar.

9. Plot the punch displacement history (U2 for the node set PUNCHRP) shown in Figure W8–7 by double-clicking Spatial displacement: U2 PI: PUNCH1-1 NODE xyz in NSET PUNCHRP under the History Output container in the Results Tree.

Note: A scripts that creates the complete stamping model are available for your convenience. Run this script if you encounter difficulties following the instructions or if you wish to check your work. The script named ws_solver_can_bottom_answer.py is available using the Abaqus fetch utility.


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W8.15

Answers Question W8–1: What analysis procedure is used in this model? Answer:

The analysis procedure is a natural frequency extraction.

Question W8–2: In Abaqus a distinction is made between linear perturbation

Answer:

analysis steps and general analysis steps. What type of procedure is the analysis procedure in this model? Frequency extraction is a linear perturbation procedure.

Question W8–3: In an analysis with more than one step in the same model,

Answer:

what influence does the result of a linear perturbation step have on the base state of the model for the following analysis step? None. Only general analysis steps change the base state of the model.

Question W8–4: What effect will an increase in friction have on the solution? Answer:

An increased friction coefficient will increase the critical shear stress crit at which sliding of the blank begins. Thus, the material will be stretched more, causing further thinning of the material and increasing the stresses.

Question W8–5: When entering plasticity data into the material model, what Answer:

are the stress and strain measures that Abaqus uses? Abaqus uses true (Cauchy) stress and log strain.

Question W8–6: What effects would a higher damping coefficient have? Answer:


A higher damping coefficient would reduce the stable time increment. In general, damping should be chosen such that high frequency oscillations are smoothed or eliminated with minimal effect on the stable time increment. Figure WA8–1 shows a plot of the kinetic energy with and without damping. Note the high frequency oscillations in the analysis without damping.


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Figure WA8–1. Kinetic energy with and without damping

Question W8–7: What is the slope of the curve at the beginning and end, and Answer:

why is this important? The slope of the amplitude curve at the beginning and end of the step is zero. This is important because it prevents discontinuities in the punch displacement, which lead to oscillations in an Abaqus/Explicit analysis.

Question W8–8: How would the results change if a linear amplitude definition Answer:

were used instead? With a linear amplitude definition the displacement of the punch will be applied suddenly at the beginning of the step and stopped suddenly at the end of the step, causing oscillations in the solution. A linear amplitude definition results in large spikes in the kinetic energy, especially at the beginning of the step. As a result, the kinetic energy may be large compared to the internal energy and the early solution may not be quasi-static. The preferred approach is to move the punch as smoothly as possible. Figure WA8–2 compares the kinetic energy history when a linear amplitude definition is used and when the smooth step amplitude definition is used.


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W8.17

Figure WA8–2. Kinetic energy plot with and without SMOOTH STEP

Question W8–9: How do you determine if an analysis that includes mass Answer:

scaling produces acceptable results? The kinetic energy should be a small fraction of the internal energy. As the kinetic energy increases, inertia effects have to be considered and the solution is no longer quasi-static. Figure WA8–3 shows the internal and kinetic energy for mass scaling factors of 10 (used in our simulation), 100, and 900, which correspond to a solution speedup of 10 , 10, and 30, respectively.



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Figure WA8–3. Energies with different mass scaling

Question W8–10: How does mass scaling affect the solution time? Answer:

The stable time increment is calculated according to  Le tstable  min  c  d

 ,  

where Le is a characteristic element length and cd is the dilatational wave speed. An increase in density decreases cd, which in turn increases tstable.

Question W8–11: What elements are used to model the blank, and does this Answer:


346

element type have an hourglass deformation mode? The analysis uses SAX1 elements. These elements have no hourglass modes. Consequently, hourglassing is not of concern in the analysis.


Notes

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Notes

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Workshop 9 Import Analysis Interactive Version Note: This workshop provides instructions in terms of the Abaqus GUI interface. If you wish to use the Abaqus Keywords interface instead, please see the “Keywords” version of these instructions. Please complete either the Keywords or Interactive version of this workshop.

Goals 

Transfer results between Abaqus/Explicit and Abaqus/Standard.

Introduction In this workshop you will use the import capability is used to transfer the results between Abaqus/Explicit and Abaqus/Standard to examine the effects of springback in the analysis of the deep drawing of a can bottom. The deformed shape of the can after the forming stage is shown in Figure W9–1.

Figure W9–1. Final deformed shape



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W9.2

Preliminaries 1. Enter the working directory for this workshop: ../abaqus_solvers/interactive/forming

2. Open the model database file created in the previous workshop (canBottom.cae):

Springback analysis In the manufacturing process the part is removed after the forming has been completed and the material is free to springback into an unconstrained state. To understand the final shape after this physical effect, we perform a springback analysis in Abaqus/Standard. 1. Copy the model named stamp to a model named springback. Make all subsequent model changes to the springback model. 2. Since only the blank needs to be imported, delete the following features from the springback model: a. Part instances DIE1-1 and PUNCH1-1. b. All assembly-level sets and surfaces associated with the die and punch. c. All contact interactions and properties. d. Boundary conditions FixDie and PunchMove. e. History output request for PunchRP. 3. Replace the dynamic, explicit step with a general, static step. Set the time period to 1 and the initial increment to 0.1, and include the effects of geometric nonlinearity. Rename the step springback. 4. Define an initial state. a. In the Model Tree, double-click Predefined Fields. b. In the Create Predefined Field dialog box, select Initial as the step, Other as the category, and Initial state as the type. c. Click Continue. d. Select the blank as the instance to assign the initial state. e. In the Edit Predefined Field dialog box that appears, enter the job name draw_bot, accept all other default settings, and click OK. This definition will allow the state of the model—stresses, strains, etc.—to be imported. By not updating the reference configuration, the springback displacements will be referred to the original undeformed configuration.


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W9.3

5. Note that the XSYMM boundary condition BlankSymm specified on the set BSYM constrains rigid body motions in the U1 and UR3 directions of the blank. Thus, you need an additional boundary condition to prevent rigid body motion along U2. In what follows you will fix the node at its final position at the end of the forming stage. a. In the Model Tree, double-click BCs to apply a Displacement/Rotation boundary condition to the set BSYM in Step-1. b. In the Edit Boundary Condition dialog box, choose the Fixed at Current Position method and fix U2. 6. Create a job named springback for the model springback. 7. Save your model database file, submit the job for analysis, and monitor its progress. Question W9–1: Why is it advantageous to use Abaqus/Standard for the

springback analysis?

Postprocessing 1. When the analysis is complete, open the output database file springback.odb in the Visualization module. 2. Contour the Mises stress distribution of the 180o model. 3. Plot the final deformed shape for the model springback. 4. Plot the springback and formed shapes together. (First toggle off the Sweep elements option.) By not updating the reference configuration, the formed shape is stored in frame 0 of the output database. You must use overlay plots to superimpose the images: a. From the main menu bar, select View→Overlay Plot. b. Use the Frame Selector or the arrows in the context bar to select frame 0. c. In the Overlay Plot Layer Manager, click Create. Name the layer formed. d. Use the Frame Selector

to select the last frame.

e. Use the Common Plot Options tool to change the fill color of the elements to blue. f. In the Overlay Plot Layer Manager, click Create. Name the layer springback. In the Overlay Plot Layer Manager, click Plot Overlay. Zoom in to examine the shape differences more closely.



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W9.4

If you had updated the reference configuration, the formed shape is treated as the undeformed shape of the import analysis model (recall that when the reference configuration is updated, the end state of the previous analysis becomes the reference configuration of the import analysis; the reference configuration is considered the undeformed shape): a. In the toolbox, click the Allow Multiple Plot States tool . b. In the toolbox, click both the Plot Undeformed Shape and Plot Deformed Shape tools

.

c. Use the Common Plot Options tool to increase the deformation scale factor so that the differences between the formed and springback shapes are clearly visible.

Note: A scripts that creates the complete stamping model are available for your convenience. Run this script if you encounter difficulties following the instructions or if you wish to check your work. The script named ws_solver_can_bottom_answer.py is available using the Abaqus fetch utility.


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W9.5

Answers Question W9–1: Why is it advantageous to choose Abaqus/Standard for the Answer:


springback analysis? A true static procedure is the preferred approach for modeling springback. The imported model will not be in static equilibrium at the beginning of the step. Thus, Abaqus/Standard applies a set of artificial internal stresses to the imported model state and then gradually removes these stresses. This leads to the springback deformation. In Abaqus/Explicit the removal of the contact between the blank and the tools represents a sudden load removal, which leads to low frequency vibrations of the blank. While these vibrations will eventually dissipate, this approach leads to lengthy computation times.


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Notes

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Notes

356

Workshop 1 Basic Input and Output Keywords Version Note: This workshop provides instructions in terms of the Abaqus Keywords interface. If you wish to use the Abaqus GUI interface instead, please see the “Interactive” version of these instructions. Please complete either the Keywords or Interactive version of this workshop.

Goals     

Learn to use Abaqus utilities and documentation. Understand the basic structure of an input file, and be able to make simple modifications to it. Learn how to perform a datacheck analysis and how to submit an analysis job using the Abaqus driver. Gain familiarity with Abaqus/Viewer. Explore the structure and contents of the data (.dat) and log (.log) files.

Abaqus utilities and documentation Abaqus provides various utilities for obtaining information on usage, system configuration, example problems, and environment settings for the analysis package. 1. At the prompt, enter the command abaqus information=system

to obtain information on the system. Note that abaqus is a generic command that may have been renamed on your system. For example, if more than one version is installed on the system, the command might include the version number, as in abq6121. In the remainder of this workshop as well as all subsequent workshops, use the appropriate command for your system. Question W1–1: What is the processor on your machine? Question W1–2: What is the operating system (OS) level?



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W1.2

2. Open the online documentation with the command abaqus doc

Open the Abaqus Analysis User’s Manual, and search for the string DSLOAD to find information on the DSLOAD option. You can find information related to the data line syntax in the Abaqus Keywords Reference Manual (use the hyperlink for the DSLOAD option, or open the Keywords Manual directly). The online documentation graphical user interface is shown in Figure W1–1.

Figure W1–1. Online documentation 3. Open the online Abaqus Example Problems Manual. Search for plate buckling to find example problems that discuss plate buckling. Question W1–3: What are the four example problems that fit the search

criteria? 4. Go to Example Problem 1.1.14 in the online Abaqus Example Problems Manual. In the left panel of the window, display the subtopics of the problem and click Input files. In the right panel of the window, the list of input files associated with this problem appears. You can select any input filename from the list; a separate window will open containing that file.


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W1.3

5. All example problem input files are included in the Abaqus release and can be obtained using the abaqus fetch utility. In your terminal window, enter abaqus fetch job=damagefailcomplate_cps4

at the command line prompt. 6. Use the online documentation to determine the input syntax for some options. A keyword line starts with an asterisk ( followed directly by the keyword option. Parameters and their associated values appear on the keyword line, separated by commas. Many options require data lines, which follow directly after their associated keyword line and contain the data specified in the Abaqus Keywords Reference Manual for each option. Data items are separated by commas. Refer to the discussions of keyword line and data line syntax in Lecture 1, as necessary. Question W1–4: In the space provided, write the input you would use to define a node set called TOP_NODES that contains previously defined nodes 21, 22, 23, and node set TOP_LEFT.

Hint: Use the information on the NSET option in the Abaqus Keywords Reference Manual to determine the necessary parameter and data line. *NSET,



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W1.4

Question W1–5: In the space provided, write the input you would use to define a velocity boundary condition on a node set named NALL

using the direct format. The velocity is 7.0 m/s in the 2-direction. Will this option appear in the model data or the history data portion of the input file? Hint: Use the information on the BOUNDARY option in the Abaqus Keywords Reference Manual, including the reference to the ―Boundary Conditions‖ Section of the Abaqus Analysis User’s Manual, to determine the appropriate syntax.

Question W1–6: (Optional) In the space provided, write the input you would

use to define the BEAM SECTION option for beam elements in element set ELBEAMS referring to a material named STEEL. The beam has a rectangular cross-section with a height of 0.5 m and a width of 0.2 m. Hint: This option requires one data line for the beam section geometric data. Follow the hyperlink to the beam cross-section library and the rectangular section to determine the appropriate data line input. *BEAM SECTION,


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W1.5

Analyzing a connecting lug

Figure W1–2. Sketch of the connecting lug In this workshop you will model the connecting lug shown in Figure W1–2. The lug is welded to a massive structure at one end, so we assume that this end is fixed. The other end contains a hole through which a bolt is placed when the lug is in service. You have to calculate the deflection of the lug when a load of 30kN is applied to the bolt in the 2 direction. To model this problem, you will use three-dimensional continuum elements and perform a linear analysis with elastic materials. You will model the load transmitted to the lug through the bolt as a uniform pressure load applied to the bottom half of the hole, as shown in Figure W1–2. In this workshop SI units (N, m, and s) will be used. Creating the input file 1. Change to the ../abaqus_solvers/keywords/lug directory. 2. View the contents of w_lug.inp. The model and history data are incomplete, and no mesh or loading is defined. Question W1–7: What is the first option in the model data? What is the last

option in the model data? Question W1–8: What is the first option in the history data? Question W1–9: How many steps are there in this analysis?



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W1.6

3. View the files w_lug_nodes.inp and w_lug_elem.inp. Boundary conditions and loads will be defined using the node and element sets defined in these files. Question W1–10: What type of elements are used to model the lug?

4. Edit the input file to set the INPUT parameter on the INCLUDE options to read the appropriate node and element data files. 5. Complete the MATERIAL option block by defining an elastic material with elastic modulus E = 200 GPa and Poisson’s ratio  = 0.3. The complete material block should appear as follows: *MATERIAL, NAME=STEEL *ELASTIC 200E9, 0.3 Question W1–11: Do you need to define a density to complete the material

definition? Material density is necessary for what types of analyses? The boundary conditions and the loads cannot be defined without knowledge of the node and element sets and surfaces. Figure W1–3 shows the various sets and surfaces.

Node set LHEND

Element set BUILTIN

Surface PRESS Node set HOLEBOT

Figure W1–3. Useful sets and surfaces


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W1.7

6. Boundary conditions are applied using the BOUNDARY option. Use the online documentation to obtain a description of the option. The left end of the lug is fixed. Thus, constrain degrees of freedom 1 through 6 of all nodes in node set LHEND by entering *BOUNDARY LHEND, 1, 6 Question W1–12: How else could you define a completely constrained boundary

condition? 7. Distributed loads are applied to surfaces using the *DSLOAD option. In this problem, the load should be applied to the surface named PRESS (which covers the bottom region of the hole). The option to specify the distributed (pressure) load on this surface is *DSLOAD PRESS, P, 50.E6

The magnitude of the applied uniform pressure is 50 MPa. We determined the load magnitude by dividing the total load by the projected horizontal area of the 30kN hole, where  50MPa . 2  0.015m  0.02m 8. Add printed output requests to the step using the NODE PRINT and EL PRINT options. Abaqus includes a large amount of printed output by default. Requesting printed output of specific variables allows you to limit the volume of output to the data (.dat) file. Request printed data output of nodal displacements for node set HOLEBOT and reaction forces for node set LHEND (including the total force). In addition, request output for stresses in element set BUILTIN. You can do this by entering *NODE PRINT, NSET=HOLEBOT U2 *NODE PRINT, NSET=LHEND, TOTAL=YES, SUMMARY=NO RF *EL PRINT, ELSET=BUILTIN S, MISES

Default output requests for the output database are made automatically, and they will be sufficient for this workshop. Submitting a datacheck analysis 1. Submit the job for a datacheck analysis by entering the command abaqus datacheck job=w_lug interactive



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W1.8

at the prompt. The interactive parameter will cause all log file output to print to the screen. 2. View the data file (w_lug.dat) in a text editor. Question W1–13: What version of Abaqus are you using?

3. Search for the strings ―WARNING‖ and ―ERROR‖ to find any warning and error messages. These messages will indicate whether anything unusual was encountered during the datacheck analysis (keep in mind that your editor may be case-sensitive for searching). Question W1–14: What warning messages did you get? Do they require changes

to the input file, or can you ignore them? 4. Search for the string ―P R O B L E M‖ to see the summary of the problem size. Include spaces between the letters of the search string. Question W1–15: How many elements are there in the model? How many variables are there? Running a complete analysis 1. Submit w_lug.inp as an Abaqus job in interactive mode by typing abaqus job=w_lug interactive

at the prompt. If the driver asks if you want to overwrite old job files, type ―y.‖ This means that output files with the same job name that exist from a previous analysis will be overwritten. 2. Now resubmit the job in background mode by typing abaqus job=w_lug

at the prompt. The log file output will be saved in w_lug.log instead of printing to the screen. You can open w_lug.log in a text editor and view its contents. 3. You can also let the Abaqus driver prompt you for the necessary job information by typing abaqus

at the prompt. Specify w_lug at the prompt for the job identifier, enter [RETURN] at the prompt for user subroutines (since there are none for this job), and type ―y‖ to overwrite the files from the last run with the same name. Doing so will submit the analysis job in background mode. 4. List all files with w_lug as the root of the file name (using a ―long‖ format on Unix systems):


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W1.9

dir w_lug.*

(NT)

ls -l w_lug.*

(Unix)

Note the files that were created by Abaqus. We will take a closer look at the printed output file (w_lug.dat) later in this workshop. Results visualization in Abaqus/Viewer 1. To run Abaqus/Viewer and load the output database for the lug analysis, type abaqus viewer odb=w_lug

at the prompt. Note: The file name extension (.odb) is not needed. If an output database is not specified on the command line, you can select File→Open from the main menu bar in Abaqus/Viewer to access the Open Database dialog box, as shown in Figure W1–4. Select the file w_lug.odb from the output database list.

Figure W1–4. Open Database dialog box



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W1.10

2. When Abaqus/Viewer opens the output database, the undeformed model shape will be displayed. To change the plot mode, you can use either the Plot menu or the toolbox icons displayed on the left side of the viewport (see Figure W1–5). You can identify the function of each tool in the toolbox by positioning your cursor above the icon for that tool. A label for the icon will pop up describing its function. 3. To plot the deformed shape, click the Plot Deformed Shape tool toolbox or select Plot→Deformed Shape from the main menu bar.

in the

4. Open the Common Plot Options dialog box by clicking in the toolbox. Turn on the node and element numbers, and make the nodes visible. 5. Use the display option tools to switch to hidden line, filled, or wireframe display. View manipulation tools

Display option tools

Results Tree

Toolbox

Figure W1–5. Abaqus/Viewer main window


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W1.11

6. Note the displacement magnification factor shown in the bottom of the title. By default, Abaqus/Viewer automatically scales the displacement according to the maximum model dimensions for a small-displacement analysis. Displacements are scaled so that the deformed shape will be clear. For a large-displacement analysis the scale factor is 1.0 by default. Set the displacement magnification factor to 1.0 so that you can see the actual displacement, and redraw the displaced shape plot. Hint: You will have to use the Common Plot Options dialog box.

7. Create a contour plot of the Mises stress by clicking the Plot Contours on Deformed Shape tool

in the toolbox. 8. Frequently users want to remove all annotations that are written on the plots, especially when they are creating hard-copy images or animations. From the main menu bar, select Viewport→Viewport Annotation Options to suppress the annotations used in the plots. The annotations are divided into three categories: legend, title block, and state block. Each category can be controlled separately. The title block contains information about which Abaqus version was used and when the analysis was performed. The state block contains the step title (which is the text provided on the data line of the STEP option), the increment and step time of the data being displayed, and information on the variable and magnification factor used to calculate the shape of the model. 9. From the main menu bar, select File→Exit to exit from Abaqus/Viewer. Viewing the printed output file Open the printed output file w_lug.dat in the text editor of your choice. 1. Look at the input echo near the top of the file. Below this you will find the section titled ―OPTIONS BEING PROCESSED.‖ This is the first place any warning or error messages will appear. 2. A summary of model data follows. Here you can check that Abaqus has correctly interpreted your model definition. Question W1–16: Which elements are in element set HOLEIN?

3. Next you will find the summary of history data for each step. Search for the strings ―B O U N D A R Y‖ and ―D I S T R I B U T E D‖ to verify that the boundary conditions and distributed loads have been interpreted correctly. Include spaces between the letters of the search string. To start a search through the entire file, go to the top of the file (some editors will wrap to the top of the file upon reaching the end).



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4. The next section in the data file is the results section. The tables are printed according to the various output requests. Search for the strings ―N O D E‖ and ―E L E M E N T‖ to find the tables that contain the output requested. The maximum deflection and peak stress are reported at the ends of the respective tables. Question W1–17: What are the maximum direct stresses in the 1- and 2-

directions (i.e.,  11 and  22 )?

(Hint: The maximum direct stresses will occur in element set BUILTIN.) Question W1–18: What is the deflection of node 20001 in node set HOLEBOT in

the 2-direction? 5. Search for the string ―TOTAL‖ to find the sum of the reaction forces in the 2direction. Question W1–19: What is the net reaction force in the 2-direction at the nodes in node set LHEND? Is this equal to the applied load? Question W1–20: Why is the sum of the reaction forces at the nodes in node set LHEND in the horizontal direction (1-direction) zero?

Modifying the model and understanding changes in the results 1. Open the input file w_lug.inp in the text editor. 2. Reduce the distributed pressure load to 25 MPa. 3. Save the modified file to a new file named w_lugmod.inp. 4. Submit the new input file as an Abaqus job. 5. Look at the output database file in Abaqus/Viewer. Question W1–21: What is the deflection of node 20001 in node set HOLEBOT? Do the results reflect the reduction in loading?

Note: A complete input file is available for your convenience. You may consult this file if you encounter difficulties following the instructions outlined here or if you wish to check your work. The input file is named w_lug_complete.inp



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W1.13

Answers Question W1–1: What is the processor on your machine? Answer:


Question W1–2: What is the operating system (OS) level? Answer:


Question W1–3: What are the four example problems that fit the search Answer:

criteria? Problem 1.1.14, ―Damage and failure of a laminated composite plate‖ Problem 1.2.2, ―Laminated composite shells: buckling of a cylindrical panel with a circular hole‖ Problem 1.2.5, ―Unstable static problem: reinforced plate under compressive loads‖ Problem 9.1.8, ―Deformation of a sandwich plate under CONWEP blast loading‖

Question W1–4: In the space provided, write the input you would use to define a node set called TOP_NODES that contains previously defined nodes 21, 22, 23, and node set TOP_LEFT. Answer: *NSET, NSET=TOP_NODES 21, 22, 23, TOP_LEFT Question W1–5: In the space provided, write the input you would use to define a velocity boundary condition on a node set named NALL

Answer:

using the direct format. The velocity is 7.0 m/s in the 2-direction. Will this option appear in the model data or the history data portion of the input file? This option will appear in the history data section of the input file because it is a nonzero boundary condition. *BOUNDARY, TYPE=VELOCITY NALL, 2, 2, 7.0



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Question W1–6: (Optional) In the space provided, write the input you would

use to define the BEAM SECTION option for beam elements in element set ELBEAMS referring to a material named STEEL. The beam has a rectangular cross-section with a height of 0.5 m and a width of 0.2 m. Answer:

*BEAM SECTION, SECTION=RECT, ELSET=ELBEAMS, MATERIAL=STEEL 0.2, 0.5

Question W1–7: What is the first option in the model data? What is the last

option in the model data? Answer:

The beginning of the model data is the HEADING option. The last option in the model data is the MATERIAL option in the material option block that defines the material properties of the model.

Question W1–8: What is the first option in the history data? Answer:

The history data begin with the STEP option.

Question W1–9: How many steps are there in this analysis? Answer:

There is only one step in this analysis.

Question W1–10: What type of elements is used to model the lug? Answer:

C3D20R elements—i.e., 20-node brick elements (threedimensional hexahedral continuum elements) with reduced integration—are used to model the lug.

Question W1–11: Do you need to define a density to complete the material

Answer:


370

definition? Material density is necessary for what types of analyses? No. The density is necessary for analysis procedures that consider inertia effects. In a static analysis inertia effects are not considered.


W1.15

Question W1–12: How else could you define a completely constrained boundary Answer:

condition? ―Type‖ boundary condition labels (such as ENCASTRE) can be also used to define fixed boundary conditions in the model data: *BOUNDARY LHEND, ENCASTRE

Question W1–13: What version of Abaqus are you using? Answer:

The version number appears at the top of the printed output (.dat) file.

Question W1–14: What warning messages did you get? Do they require changes Answer:

to the input file, or can you ignore them? If you followed the instructions correctly to this point, there should be warning messages in the data (.dat) file indicating that the rotational degrees of freedom—4, 5, and 6—are not active in this model and cannot be restrained. Abaqus ignores boundary conditions on degrees of freedom that cannot be restrained; therefore, you can safely ignore these warning messages.

Question W1–15: How many elements are there in the model? How many Answer:

variables are there? The model has 112 elements. The total number of variables, including degrees of freedom plus any Lagrange multiplier variables, is 2376.

Question W1–16: Which elements are in element set HOLEIN? Answer:

Elements 1 and 16.

Question W1–17: What are the maximum direct stresses in the 1- and 2Answer:


directions (i.e., 11 and 22)? The maximum direct stress in the 1-direction (S11) is 3.4766E+08 Pa; the maximum direct stress in the 2-direction (S22) is 8.7629E+07 Pa.


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Question W1–18: What is the deflection of node 20001 in node set HOLEBOT in

the 2-direction? Answer:

The deflection is 3.1342 E04 m.

Question W1–19: What is the net reaction force in the 2-direction at the nodes in node set LHEND? Is this equal to the applied load? Answer:

The reaction forces in the node set LHEND sum to 30 kN, which is equal to the applied load.

Question W1–20: Why is the sum of the reaction forces at the nodes in node set LHEND in the horizontal direction (1-direction) zero? Answer:

At the section represented by node set LHEND, the reaction forces in the horizontal direction simply couple to resist the moment induced by the applied vertical load. Since there is no external load in the horizontal direction, the reaction forces add up to zero in the horizontal direction.

Question W1–21: What is the deflection of node 20001 in node set HOLEBOT? Answer:


372

Do the results reflect the reduction in loading? The deflection of the nodes in node set HOLEBOT is now reduced to 1.5671E04 m. The deflections, reaction forces, and stresses decrease in proportion to the reduction in loading since this is a linear analysis; in this case by a factor of 2.


Notes

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Notes

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Workshop 2 Linear Static Analysis of a Cantilever Beam: Multiple Load Cases Keywords Version Note: This workshop provides instructions in terms of the Abaqus Keywords interface. If you wish to use the Abaqus GUI interface instead, please see the “Interactive” version of these instructions. Please complete either the Keywords or Interactive version of this workshop.

Introduction In this workshop you will become familiar with using load cases in a linear static analysis. You will model a cantilever beam. The left end of the beam is encastred while a series of loads are applied to the free end. Six load cases are considered: unit forces in the global X-, Y-, and Z-directions as well as unit moments about the global X-, Y-, and Zdirections. The model is shown in Figure W2–1. You will solve the problem using a single perturbation step with six load cases and (optionally) using six perturbation steps with a single load case in each step.

Figure W2–1. Cantilever beam model



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W2.2

As indicated in Figure W2–1, we wish to apply forces and moments to the right end of the beam. However, the beam is modeled with solid C3D8I elements, which possess only displacement degrees of freedom. Thus, only forces may be directly applied to the nodes of the model. Rather than applying force couples to the model, we will apply concentrated moments to the end of the beam. To this end, all loads will be transmitted to the beam through a rigid body constraint. This approach is adopted to take advantage of the fact that the rigid body reference node possesses six degrees of freedom in threedimensions: 3 translations and 3 rotations and thus allows direct application of concentrated moments. Rigid bodies and constraints will be discussed further in Lecture 5.

Defining loads and load cases in the input file 1. Change to the ../abaqus_solvers/keywords/load_cases directory. 2. Open the file w_beam_loadcase.inp in a text editor. The file includes all the model data required for this problem: node, element, and set definitions; material and section properties; and fixed boundary conditions. The history data (i.e., step definition) is incomplete. 3. Complete the step definition by defining the loads and load cases. The loads will be applied in the form of concentrated forces and moments via the *CLOAD option to the rigid body reference node. This node is contained in node set refPt. For example, for the force acting along the axial direction of the beam (i.e., the Xdirection), the following load case may be defined: *Load Case, name=Force-X *Cload refPt, 1, 1.0 *End Load Case


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4. The complete step definition should resemble the following: *Step, name=BeamLoadCases, perturbation *Static ** *Load Case, name=Force-X *Cload refPt, 1, 1.0 *End Load Case ** *Load Case, name=Force-Y *Cload refPt, 2, 1.0 *End Load Case ** *Load Case, name=Force-Z *Cload refPt, 3, 1.0 *End Load Case ** *Load Case, name=Moment-X *Cload refPt, 4, 1.0 *End Load Case ** *Load Case, name=Moment-Y *Cload refPt, 5, 1.0 *End Load Case ** *Load Case, name=Moment-Z *Cload refPt, 6, 1.0 *End Load Case ** *End Step

Note that the fixed-end boundary conditions have been defined as part of the model data, and as such, are active in each load case. 5. Save the input file. 6. Submit the job for analysis by entering the following command at your system prompt: abaqus job=w_beam_loadcase

7. Monitor the status of the job by looking at the log (.log) or status (.sta) files.



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Viewing the analysis results 1. When the job has completed successfully, start a session of Abaqus/Viewer by entering the following command at your system prompt: abaqus viewer odb=w_beam_loadcase Abaqus/Viewer opens the output database file w_beam_loadcase.odb created

by the job and displays the undeformed model shape. Examine the results of the analysis. Note that load case output is stored in separate frames in the output database file. Use the Frame Selector (click in the context bar) to choose which load case is displayed (alternatively, open the Step/Frame dialog box by selecting Result→Step/Frame). Figure W2–2, for example, shows contour plots of the Mises stress for each of the load cases.

Force-X

Force-Y

Force-Z

Moment-X

Moment-Y

Moment-Z

Figure W2–2. Mises stress contours


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W2.5

Combining results from the load cases and envelope plots You will now linearly combine the results of each load case to plot the stress and deformation in the beam under a given load combination. Recall that each load case is based on a unit load; the results of each load case will be scaled relative to those obtained for LC-Force-Y when combining the data. 1. From the main menu bar, select Tools→Create Field Output→From Frames. 2. In the dialog box that appears, accept Sum values over all frames as the operation. 3. In the Frames tabbed page, click . In the Add Frames dialog box that appears, choose Step-1 as the step from which to obtain the data. Click Select All and then click OK to close the dialog box. 4. Remove the initial frame; for the remaining frames, enter the scale factors shown in Figure W2–3.

Figure W2–3 Scale factors for linear combination of load cases. 5. Switch to the Fields tabbed page to examine the data that will be combined. Accept the default selection (all available field data) and click OK to close the dialog box. 6. From the main menu bar, select Result→Step/Frame.



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7. In the Step/Frame dialog box, select Session Step as the active step for output and click OK. 8. Plot the Mises stress as shown in Figure W2–4. Note that this figure has been customized to overlay the undeformed model shape on the contour plot and a deformation scale factor of 5e4 has been used.

Figure W2–4 Mises stress due to combined loading. 9. Now create an envelope plot of the maximum stress in the beam: a. From the main menu bar, select Tools→Create Field Output→From Frames. b. In the dialog box that appears, select Find the maximum value over all frames as the operation. c. In the Frames tabbed page, click . In the Add Frames dialog box that appears, choose Step-1 as the step from which to obtain the data. Select all but the initial frame then click OK to close the dialog box. d. Switch to the Fields tabbed page. Unselect all output and then select only S and U. e. Click OK to close the dialog box. f. From the main menu bar, select Result→Step/Frame. g. In the Step/Frame dialog box, select Session Step as the active step for output and The maxmum value over all selected frames as the frame, as shown in Figure W2–5.


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W2.7

Figure W2–5 Frame selection for envelope plot. h. In the Field Output dialog box (Result→Field Output), select S_max as the primary variable and U_max as the deformed variable. i. Plot the Mises stress as shown in Figure W2–6. Note that this figure has been customized to overlay the undeformed model shape on the contour plot and a deformation scale factor of 5e4 has been used.

Figure W2–6 Envelope plot of maximum Mises stress.

Using Multiple Perturbation Steps (Optional) Now perform the same analysis using multiple perturbation steps rather than multiple load cases. 1. Open the file w_beam_multstep.inp in a text editor. As before, the file includes all the model data required for this problem: node, element, and set definitions; material and section properties; and fixed boundary conditions. The history data (i.e., step definition) is incomplete. 2. Complete the history data by defining the steps. As before, the loads will be applied in the form of concentrated forces and moments via the *CLOAD option to the rigid body reference node. This node is contained in node set refPt. For



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example, for the force acting along the axial direction of the beam (i.e., the Xdirection), the following step may be defined: *Step, name=Force-X, perturbation *Static *Cload refPt, 1, 1. *End Step

3. The complete set of step definitions should resemble the following: *Step, name=Force-X, perturbation *Static *Cload refPt, 1, 1.0 *End Step ** *Step, name=Force-Y, perturbation *Static *Cload refPt, 2, 1.0 *End Step ** *Step, name=Force-Z, perturbation *Static *Cload refPt, 3, 1.0 *End Step ** *Step, name=Moment-X, perturbation *Static *Cload refPt, 4, 1.0 *End Step ** *Step, name=Moment-Y, perturbation *Static *Cload refPt, 5, 1.0 *End Step ** *Step, name=Moment-Z, perturbation *Static *Cload refPt, 6, 1.0 *End Step


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W2.9

Note that the fixed-end boundary conditions have been defined as part of the model data, and as such, are active in each step. 4. Save the input file. 5. Submit the job for analysis by entering the following command at your system prompt: abaqus job=w_beam_multstep

6. Monitor the status of the job by looking at the log (.log) or status (.sta) files. 7. When the job has completed successfully, open the output database w_beam_multstep.odb created by the job in Abaqus/Viewer and compare the results obtained using both modeling approaches. You will find that the results are identical.

Comparing solution times Next, open the message (.msg) file for each job in the job monitor. Scroll to the bottom of the file and compare the solution times. You will notice that the multiple step analysis required 2.5 times as much CPU time as the multiple load case analysis. For a small model such as this one, the overall analysis time is small so speeding up the analysis by a factor of three may not appear significant. However, it is clear that for large jobs, the speedup offered by multiple load cases will play a significant role in reducing the time required to obtain a solution for a given problem.



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Multiple load case analysis: ANALYSIS SUMMARY: TOTAL OF 1 0 1 1 : :



= = = =

0.10000 0.10000 0.20000 1

Multiple perturbation step analysis: ANALYSIS SUMMARY: TOTAL OF 6 0 6 6 : :



= = = =

0.4000 0.1000 0.5000 1

Note: Complete input files are available for your convenience. You may consult these files if you encounter difficulties following the instructions outlined here or if you wish to check your work. The input files are named w_beam_loadcase_complete.inp w_beam_multstep_complete.inp

and are available using the Abaqus fetch utility.


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Workshop 3 Nonlinear Statics Keywords Version Note: This workshop provides instructions in terms of the Abaqus Keywords interface. If you wish to use the Abaqus GUI interface instead, please see the “Interactive” version of these instructions. Please complete either the Keywords or Interactive version of this workshop.

Goals    

Define alternate nodal and material directions. Include nonlinear geometric effects by adding the NLGEOM parameter. Include nonlinear material effects by defining plastic material behavior. Become familiar with the output for an incremental analysis.

Introduction In this workshop you will model the plate shown in Figure W3–1. It is skewed at 30 to the global 1-axis, built-in at one end, and constrained to move on rails parallel to the plate axis at the other end. You will determine the midspan deflection when the plate carries a uniform pressure. You will modify the input file that models this problem to include alternate nodal and material directions as well as nonlinear effects. You will first add the necessary data to complete the linear analysis model. You will later perform the simulation considering both geometrically and material nonlinear effects. In a subsequent workshop a restart analysis will be performed to study the unloading of the plate.



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W3.2

Alternate nodal and material directions 1. Change to the ../abaqus_solvers/keywords/skew directory, and open the file w_skew_plate_linear.inp in an editor. You will need to specify local nodal and material directions by following the steps given below. 2. The right end of the plate is constrained to move parallel to an axis that is skewed relative to the global axes. Thus, the nodes at this end of the plate must be transformed into a local coordinate system that is aligned with the plate. The following TRANSFORM option block defines a local coordinate system, x , y , z  , by specifying points a and b, as shown in Figure W3–2 (see the Abaqus Analysis User’s Manual for a detailed explanation of the data line). *TRANSFORM, NSET=ENDB, TYPE=R 0.1, 0.0577, 0.0, -0.0577, 0.1, 0.0

x, y, z of point a

x, y, z of point b


Figure W3–1. Sketch of the skewed plate


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W3.3

Figure W3–2. Rectangular Cartesian transformation 3. The default material directions in this model are aligned with the global axes. In this default system the direct stress in the material 1-direction,  11 , will contain contributions from both the axial stress (produced by the bending of the plate) and the stress transverse to the axis of the plate. The results will be easier to interpret if the material directions are aligned with the axis of the plate and the transverse direction. These local material directions can be defined with the following ORIENTATION option. The first data line defines a local coordinate system by specifying points a and b, as shown in Figure W3–2. The second data line defines an additional rotation of 0.0 about the 3-axis (see the Abaqus Keywords Reference Manual for detailed explanations of the data lines). *ORIENTATION, NAME=SKEW, SYSTEM=RECTANGULAR 0.1, 0.0577, 0.0, -0.0577, 0.1, 0.0 3, 0.0

This option acts independently of the TRANSFORM option. 4. Run the analysis. To submit this job, you must enter abaqus job=w_skew_plate_linear

at the prompt. 5. When the analysis is complete, open the data (.dat) file and find the value of the vertical displacement (degree of freedom 3) at the midspan (node 357). Enter this value in the “Linear” column of Table W3–1.



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Geometric Nonlinearity 1. Copy the input file to a new file called w_skew_plate_nonlin.inp, and make the following changes to account for geometric nonlinearity: 2. Set NLGEOM = YES on the STEP option. This parameter indicates that geometric nonlinearity will be accounted for during the step. 3. Set the initial time increment to 0.1 and the total time to 1.0 on the data line following the STATIC option. “Time” in a static analysis is just a convenient way to measure the progress of an incremental solution unless rate-dependent behavior is involved. The beginning of the step definition should look something like this: *STEP, NLGEOM=YES *STATIC 0.1, 1.0

Run the new analysis, and enter the vertical displacement (degree of freedom 3) of node 357 in the “NLGEOM” column of Table W3–1. Table W3–1. Midspan displacements Load (kPa)

Linear (m)

NLGEOM (m)

20 60

4. Triple the load in both the linear and nonlinear analysis input files, rerun each of these analyses, and enter the vertical displacement of node 357 from each analysis in Table W3–1. The pressure loading is applied normal to the shell surface with the DLOAD option. Question W3–1: How does tripling the load affect the midspan displacement in

the linear analyses? Question W3–2: How do the results of the nonlinear analyses compare to each other and to those from the linear analyses?


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W3.5

Plasticity You will now include another source of nonlinearity: plasticity. The material data are shown in Figure W3–3 (in terms of true stress vs. total log strain). Abaqus, however, requires the plastic material data be defined in terms of true stress and plastic log strain. Thus, you will need to determine the plastic strains corresponding to each data point (see the hint below). 1. In the material block of the input file w_skew_plate_nonlin.inp add the PLASTIC option and enter the data lines corresponding to points A and B on the stress-strain curve shown in Figure W3–3. The Young’s modulus for this material is 30E9 Pa. Hint: The total stain tot at any point on the curve is equal to the sum of the elastic

strain el and plastic strain pl. The elastic strain at any point on the curve can be evaluated from Young’s modulus and the true stress:el= / E. Use the following relationship to determine the plastic strains:

 pl   tot   el   tot   E . Add the PLASTIC option underneath *MATERIAL to complete the material block. The complete material option block is given below: *MATERIAL, NAME=MAT1 *ELASTIC 3.0E10,0.3 *PLASTIC 2.E7, 0.0 3.E7, 0.019 Question W3–3: Why is the second entry on the first data line of the

PLASTIC option equal to 0.0? 2. Change the pressure to 10 kPa.



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W3.6

Figure W3–3. Stress versus strain curve 3. Make the following additional changes: a. Modify the RESTART option to write restart output every 10th

increment. Set the FREQUENCY parameter equal to 10. b. You will use Abaqus/Viewer to postprocess the results. To create a more readable printed output (.dat) file, set the output frequency to this file to every 100 increments. Specifying a frequency larger than or equal to the maximum number of increments ensures that output to the data file is written only at the end of the last increment of the step. c. It is useful to be able to check the progress of an analysis by monitoring the value of one degree of freedom. To do so, add the MONITOR option to the history section of the input file. Set the value of the NODE parameter to 357, and set the value of the DOF parameter to 3. 4. Run the analysis. While the job is running, you can check on the progress of the analysis by looking at the status (.sta) file. The “DOF MONITOR” column should show the value of the midspan displacement.


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W3.7

Postprocessing an Incremental Analysis in Abaqus/Viewer 1. Start Abaqus/Viewer by entering the following command at the prompt: abaqus viewer

Open the appropriate output database by selecting File→Open from the main menu bar. Select the file w_skew_plate_nonlin.odb, and click OK. 2. By default, the last increment of the last step is selected. Use the Frame Selector in the context bar to select other steps or increments; alternatively, use the Step/Frame dialog box (Result→Step/Frame).

3. Use the view manipulation tools to position the model as you wish. Turn perspective on or off by clicking the Turn Perspective On tool Perspective Off tool

or the Turn

in the toolbar.

4. Plot the deformed shape by clicking the Plot Deformed Shape tool

.

A sample deformed shape plot is shown in Figure W3–4. Your plot may look different if you have positioned your model differently

Figure W3–4. Final deformed shape 5. Create a contour plot of variable S11 by following this procedure: a. b. c. d. e.

Click the Plot Contours tool in the toolbox. Select Result→Field Output. In the Field Output dialog box, select S11 as the stress component. Click Section Points to select a section point. In the Section Points dialog box that appears, select Top and bottom as the active locations and click OK. Your contour plot should look similar to Figure W3–5. Abaqus plots the contours of the Mises stress on both the top and bottom faces of each shell element. To see this more clearly, rotate the model in the viewport.



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Figure W3–5. Contour plot of S11: SPOS, top image; SNEG, bottom image Question W3–4: Where do the peak displacements and stresses occur in the

model? 6. Click the Animate: Time History tool to animate the results. You can stop the animation and move between frames and steps by using the arrow buttons in the context bar. 7. Render the shell thickness (View→ODB Display Options; toggle on Render shell thickness). The plot appears as shown in Figure W3–6. Note that for the purpose of visualization, a linear interpolation is used between the contours on the top and bottom surfaces of the shell.


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W3.9

Figure W3–6 Contour plot with shell thickness visible. 8. Use the following procedure to create a history plot of displacement U3 for node 357: a. In the Results Tree, expand the History Output container underneath the output database named w_skew_plate_nonlin.odb. b. Click History Output and press F2; filter the container according to *U3*. c. Double-click the data object for node 357. Your plot should look similar to Figure W3–7. Note this figure has been customized.

Figure W3–7. History of displacement at the midspan



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W3.10

Note: Complete input files are available for your convenience. You may consult these files if you encounter difficulties following the instructions outlined here or if you wish to check your work. The input files are named w_skew_plate_linear_complete.inp w_skew_plate_nonlin_complete.inp



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W3.11

Answers

Question W3–1: How does tripling the load affect the midspan displacement in Answer:

the linear analyses? The midspan displacement is tripled in the linear analysis.

Question W3–2: How do the results of the nonlinear analyses compare to each Answer:

other and to those from the linear analyses? The midspan displacement is not tripled in the nonlinear analysis when the load is tripled; at the higher load, the value of the displacement predicted by the nonlinear analysis is less than the value predicted by the linear analysis.

Question W3–3: Why is the second entry on the first data line of the

PLASTIC option equal to 0.0? Answer:

The first data line of the PLASTIC option defines the initial yield point. The plastic strain at this point is zero.

Question W3–4: Where do the peak displacements and stresses occur in the Answer:


model? The peak value of U3 occurs at the midspan. The supports of the plate are likely to be heavily stressed; this is confirmed by contour plots of S11.


397

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399

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400

Workshop 4 Unloading Analysis of a Skew Plate Keywords Version Note: This workshop provides instructions in terms of the Abaqus Keywords interface. If you wish to use the Abaqus GUI interface instead, please see the “Interactive” version of these instructions. Please complete either the Keywords or Interactive version of this workshop.

Introduction You will now continue the analysis of the plate shown in Figure W4–1. Recall our analysis includes geometric and material nonlinearity. We previously determined the plate exceeded the material yield strength and therefore has some plastic deformation. Since we requested restart output, we can resume the analysis to determine the residual stress state. In this workshop we will remove the load in order to recover the elastic deformation; the plastic deformation will remain.


Figure W4–1 Sketch of the skew plate.



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W4.2

Creating a restart analysis model Change to the ../abaqus_solvers/keywords/skew directory. Create a new input file named w_skew_plate_restart.inp. In this new input file, do the following: 1. Add the HEADING option at the top of the file. 2. Add the RESTART option immediately after the HEADING option: *RESTART, READ, STEP=1

This option specifies that the analysis will be continued from the end of the first step of the previous job. The name of the previous job will be specified at the time of job submission. 3. Define a step named UNLOAD within which to deactivate the applied pressure load: *STEP, NAME=UNLOAD, NLGEOM=YES *STATIC 0.1, 1. *DLOAD, OP=NEW *END STEP

The OP=NEW parameter on the *DLOAD option removes the applied load in the current step. The load will be ramped off according to the automatic time incrementation in effect. 4. Use the following command to submit this job: abaqus job=w_skew_plate_restart oldjob=w_skew_plate_nonlin

5. Monitor the solution progress. 6. Correct any modeling errors, and investigate the source of any warning messages.


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Postprocessing In the Visualization module, contour the U3 displacement component in the plate: 1. Click the Plot Contours tool in the toolbox. 2. From the list of variable types on the left side of the Field Output toolbar, select Primary (if it is not already selected). 3. From the list of available output variables in the center of the toolbar, select output variable U (spatial displacement at nodes). 4. From the list of available components and invariants on the right side of the Field Output toolbar, select U3. 5. Compare to the results at the end of the Apply Pressure step. Note that in this output database file, the results for frame 0 correspond to the results at the end of the Apply Pressure step (use the Frame Selector to switch to a different frame). The difference between the final state of the model and its initial state is due to the elastic springback that has occurred. The deformation that remains is permanent and unrecoverable.

Note: A complete input file is available for your convenience. You may consult this file if you encounter difficulties following the instructions outlined here or if you wish to check your work. The input file is named w_skew_plate_restart_complete.inp




403

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406

Workshop 5 CLD Analysis of a Seal using Abaqus/Standard Keywords Version Note: This workshop provides instructions in terms of the Abaqus Keywords interface. If you wish to use the Abaqus GUI interface instead, please see the “Interactive” version of these instructions. Please complete either the Keywords or Interactive version of this workshop.

Goals    

Evaluate a hyperelastic material. Define contact interactions using contact pairs and general contact. Perform a large displacement analysis with Abaqus/Standard. Use Abaqus/Viewer to create a compression load-deflection curve.

Introduction In this workshop, a compression analysis of a rubber seal is performed to determine the seal’s performance. The goal is to determine the seal’s compression load-deflection (CLD) curve, deformation and stresses. The analysis will be performed using Abaqus/Standard. Two analyses are performed: one using contact pairs and the other using general contact. As shown in Figure W5–1, the top outer surface of the seal is covered with a polymer layer, and the seal is compressed between two rigid surfaces (the upper one is displaced along the negative 2-direction; the lower one is fixed). During compression, the cover contacts the top rigid surface; the outer surface of the seal is in contact with the cover and the bottom rigid surface; in addition the inner surface of the seal may come into contact with itself.



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W5.2

U2

Cover

Rigid Surfaces Seal fixed

Figure W5–1. Seal model

Seal analysis 1. Change to the ../abaqus_solvers/keywords/seal directory. 2. Open the input file w_seal.inp, which already contains the nodes, elements, and material model data for the analysis. You will first use Abaqus/CAE functionality to evaluate the stability of the hyperelastic material model and then edit the input file to include the contact, step and boundary condition definitions.

Material Evaluation It is important to determine whether the material model of the seal will be stable during the analysis. Before completing the input file, evaluate the material definition that is used for the seal. 1. Use your text editor to review the supplied workshop model contained in the file w_seal.inp. 2. The material named SANTOPRENE is used for the seal. Locate the *MATERIAL, NAME=SANTOPRENE option. It is a hyperelastic material with a first order polynomial strain energy potential. The coefficients are already specified for the analysis. 3. Evaluate the material definition. Abaqus/CAE provides a convenient Evaluate option that allows you to view the behavior predicted by a hyperelastic material by performing standard tests to choose a suitable material formulation. You will use this option to view the behavior predicted by the material SANTOPRENE. a. Start a session of AQUS/CAE using the following command at the

command prompt: abaqus cae

In the Start Session dialog box, underneath Create Model Database, click With Standard/Explicit Model.


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W5.3

b. In the Model Tree, double-click the Materials container to create a material definition as specified in the input file. In the Edit Material dialog box, name the material Santoprene; from the menu bar, select Mechanical→Elasticity→Hyperelastic; in the Hyperelastic field, select the Polynomial strain energy potential and the Coefficients input source,

accept a strain energy potential order of 1, and enter the values of the coefficients (defined in the input file) as shown in Figure W5–2. Click OK to save the material definition and exit the material editor.

Figure W5–2. Material editor c. From the main menu bar in the Property module, select Material→Evaluate→Santoprene. d. The Evaluate Material dialog box appears. Notice that you can choose either the Coefficients or Test data source for evaluating the material.

Typically the test data are used to define a material model; you can use the Evaluate option to view the predicted behavior and adjust the material definition as necessary. In this workshop you will only evaluate the stability of the material model for the given coefficients.



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W5.4

e. In the Evaluate Material dialog box, accept all defaults and click OK.

Abaqus/CAE creates and submits a job to perform the standard tests using the material Santoprene; at the same time, Abaqus/CAE switches to the Visualization module and displays the evaluation results when the job is complete. Figure W5–3 shows the Material Parameters and Stability Limit Information dialog box; Figure W5–4 shows three stress vs. strain plots from uniaxial, biaxial, and planar tests. Question W5–1: What do the plots indicate about the stability of the material?

Based on these results, you can have confidence that your material will remain stable.

Figure W5–3. Material parameters and stability limit information


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W5.5

Figure W5–4. Material evaluation results for uniaxial, biaxial, and planar tests After evaluating the material, you can exit Abaqus/CAE and will now complete the model definition.



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W5.6

Part 1: Analysis using contact pairs Contact interactions 1. Open the input file w_seal.inp in a text editor. 2. Define contact pairs as listed in Table W5–1. The surfaces which will be used in the contact pair definitions are shown in Figure W5–5. The required option is: *CONTACT PAIR, INTERACTION=frictionless, TYPE=SURFACE TO SURFACE

sealOuter, bottom sealOuter, cover cover, top

Note that the interaction property named frictionless has already been defined in the input file. Locate the *SURFACE INTERACTION, NAME=frictionless option to review its definition. Table W5–1. Contact pairs Slave Surface

Master Surface

sealOuter

bottom

sealOuter

cover

cover

top

cover top sealInner

bottom sealOuter

Figure W5–5. Contact surfaces 3. Define a self-contact definition for the inner surface of the seal: *CONTACT PAIR, INTERACTION=frictionless, TYPE=SURFACE TO SURFACE

sealInner, Question W5–2: In the interaction between the seal and the cover, why do we choose SealOuter as the slave surface?


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W5.7

Step definition 1. Define a general static step considering geometric nonlinearity. Set the initial time increment size to 0.5% of the total time period. Invoke the unsymmetric solver (the unsymmetric solver is generally recommended for the surface-to-surface contact discretization method). The following option defines the procedure: *STEP, NLGEOM=YES, UNSYMM=YES *STATIC 0.005, 1.

2. Use the following solution control parameter to improve the efficiency of the analysis: *CONTROLS, ANALYSIS=DISCONTINUOUS

Boundary conditions and history output requests 1. Asymmetric lateral sliding of the model is prevented by constraining the seal and the cover along their vertical symmetry axes in the X-direction. The bottom rigid surface is fixed, and a displacement of –6 units is applied to the top rigid surface along the Y-direction to compress the seal between the two surfaces. The node sets on which the boundary conditions will be defined are shown in Figure W5–6. The following option completes these boundary conditions: *BOUNDARY fix1, 1, 1 botRP, ENCASTRE topRP, 1, 1 topRP, 2, 2, -6. topRP, 6, 6

topRP

fix1

botRP

Figure W5–6. Node sets



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W5.8

2. The preselected default field output does not include the nominal strain NE; to visualize the nominal strain in Abaqus/Viewer, you will write additional field output to the output database file. Locate the *OUTPUT, FIELD, VARIABLE=PRESELECT option and add the following sub-option: *ELEMENT OUTPUT NE,

3. Add a history output request to write the history of RF2 and U2 for the set topRP to the output database file. The required option is: *OUTPUT, HISTORY *NODE OUTPUT, NSET=topRP RF2, U2

4. Save all the changes and close the input file.


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W5.9

Running the job and visualizing the results: Run the analysis using the following command: abaqus job=w_seal

When the job is complete, use the following procedure to visualize the results using Abaqus/Viewer: 1. Start Abaqus/Viewer and open the file w_seal.odb: abaqus viewer odb=w_seal.odb

2. Plot the undeformed and the deformed model shapes. To distinguish between the different parts, color code the model based on section assignments. Tip: From the toolbar, select Sections from the color-coding pull down menu, as shown in Figure W5–7 (or use the Color Code Dialog tool color for each section).

to customize the

Figure W5–7. Color-coding pull down menu 3. Use the Animate: Time History tool to animate the deformation history. 4. Display only the seal. In the Results Tree, expand the Instances container underneath the output database file named seal.odb. Click mouse button 3 on the instance SEAL-1 and select Replace from the menu that appears. Abaqus/CAE now displays only the elements associated with the seal. 5. Contour the Mises stress of the seal on the deformed shape. If necessary, use the frame selector in the context bar to select the last increment. The contour plot is shown in Figure W5–8.



415

W5.10

Figure W5–8. Mises contour plot 6. Contour the minimum and maximum principal nominal strains. Elastic strains can be very high for hyperelastic materials. Because of this, the linear elastic material model is not used because it is not appropriate for elastic strains greater than approximately 5%. 7. Display the reaction force history at the reference node of the top rigid surface: In the Results Tree, expand the History Output container underneath the output database file named w_seal.odb and double-click Reaction force: RF2 PI: TOP-1 Node 3 in NSET TOPRP to display the reaction force history at the reference node of the top rigid surface. 8. You will now create the CLD curve. a. In the History Output container, click mouse button 3 on Reaction force: RF2 PI: TOP-1 Node 3 in NSET TOPRP and select Save As from the menu that appears. Save the data as Force. b. Click mouse button 3 on Spatial displacement: U2 PI: TOP-1 Node 3 in NSET TOPRP and select Save As from the menu that appears. Save the data as Disp. c. In the Results Tree, double-click XYData. In the Create XY Data dialog box, select Operate on XY data as the source and click Continue.

The Operate on XY Data dialog box appears. d. From the Operators listed in the Operate on XY Data dialog box, select combine(X, X) and then abs(A). Note that the abs(A) operator is used to obtain the absolute values. In the XY Data field, double-click the curve Disp. The current expression reads combine(abs("Disp")). Move the cursor before the far-right bracket, enter a comma, and then select the operator abs(A). In the XY Data field, double-click the curve Force. The final expression reads combine(abs("Disp"), abs("Force") ). Click Plot Expression to plot this expression. Save this plot as CLD.


416


W5.11

9. Customize the plot as follows: a. From the main menu bar, select Options→XY Options→Plot.  In the Plot Options dialog box, fill the plot background in white. b. Double-click anywhere on the chart to open the Chart Options dialog box. 

In the Grid Display tabbed page, toggle on the major X- and Ygrid lines. Set the line color to blue and the line style to dashed.



Change the fill color using the following RGB values: red: 175; green: 250; blue: 185.



In the Grid Area tabbed page, select Square as the size and drag the slider to 80. From the list of auto-alignments, choose the one that places the chart in the center of the viewport c. Double-click the legend to open the Chart Legend Options dialog box. 

In the Contents tabbed page, click font size to 10.






Toggle on Fill to flood the legend with a white background.

to increase the legend text

 In the viewport, drag the legend over the chart. d. Double-click either axis to open the Axis Options dialog box. 

In the X Axis region of the dialog box, select the displacement axis.



In the Scale tabbed page, place 4 major tick marks on the X-axis at (use the By count method).



In the Title tabbed page, change the X-axis title to Displacement (inch).



In the Y Axis region of the dialog box, select the force axis.



In the Scale tabbed page, specify that the Y-axis should extend from 0 (the Y-axis minimum) to 250 (the Y-axis maximum).



Increase the number of Y-axis minor tick marks per increment to 4.



In the Title tabbed page, change the Y-axis title to Force (lbf).



In the Axes tabbed page, change the font size for both axes to 10.

e. Expand the list of plot option icons in the toolbox:



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W5.12

f. Examine the remaining options. Add the following plot title: CLD Diagram. Double-click the plot title to open the Plot Title Options dialog box. 

In the Title tabbed page, click bold.






In the viewport, drag the plot title above the chart.

to change the legend text style to

g. Click in the toolbox to open the Curve Options dialog box. Change the legend text to Top Surface Ref Point and toggle on Show symbol. Set the color for both the line and symbols to red. Use large filled circles for the symbols. Reposition the legend as necessary. The final plot appears as shown in Figure W5–9.

Figure W5–9. Compression load deflection diagram Question W5–3: What does the inverted peak near 4 inches of deflection

represent?


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W5.13

Part 2: Analysis using general contact 1. Copy the input file named w_seal.inp to one named w_seal_gc.inp. Edit this input file as described below. 2. Locate the contact pairs defined earlier and delete them. 3. Create a general contact interaction using the default all-inclusive element-based surface and apply the frictionless contact property globally. The following options define the interaction: *CONTACT *CONTACT INCLUSIONS, ALL EXTERIOR *CONTACT PROPERTY ASSIGNMENT , , FRICTIONLESS

4. Save all the changes and close the input file. 5. Run the analysis using the following command: abaqus job=w_seal_gc

6. When the job is complete, use the following procedure to visualize the results using Abaqus/Viewer. 7. Compare the results with those obtained using contact pairs. A comparison of the stress state in the seal is shown in Figure W5–10 while a comparison of the forcedisplacement curve is shown in Figure W5–11. The agreement between the two approaches is excellent. The general contact approach, however, provides a much simpler user interface since the entire contact domain is defined automatically and properties are assigned globally.



419

W5.14

Figure W5–10. Comparison of the stress state in the seal (general contact, top; contact pairs, bottom)

Figure W5–11. Comparison of force-displacement curves


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W5.15

Note: Complete input files are available for your convenience. You may consult these files if you encounter difficulties following the instructions outlined here or if you wish to check your work. The input files are named w_seal_cp_complete.inp w_seal_gc_complete.inp




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W5.16

Answers Question W5–1: What do the plots indicate about the stability of the material? Answer:

The plots never have a negative slope, indicating that the material is stable throughout the entire strain range.

Question W5–2: In the interaction between the seal and the cover, why do we choose SealOuter as the slave surface? Answer:

SealOuter has a more refined mesh and should therefore be

specified as the slave surface.

Question W5–3: What does the inverted peak near 4 inches of deflection Answer:


422

represent? This peak represents the inward bucking that occurs at the bottom corners of the seal during compression. If you look at the deformed shape at the time corresponding to approximately 3.7 inches of displacement, you will observe this phenomenon.


Notes

423

Notes

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Workshop 6 Dynamics Keywords Version Note: This workshop provides instructions in terms of the Abaqus Keywords interface. If you wish to use the Abaqus GUI interface instead, please see the “Interactive” version of these instructions. Please complete either the Keywords or Interactive version of this workshop.

Goals   

Become familiar with the Abaqus/CAE procedures for frequency extraction and implicit dynamic analyses. Become more familiar with the status (.sta) and message (.msg) files. Learn how to plot eigenmodes and create history plots using Abaqus/Viewer.

Introduction In this workshop the dynamic response of the cantilever beam shown in Figure W6–1 is investigated. A frequency extraction is performed to determine the 10 lowest vibration modes of the beam. The effects of mesh refinement, element interpolation order, and element dimension will be considered. The problem is also solved by performing a direct integration dynamic analysis to simulate the vibration of the beam upon removal of the tip load. The frequency of the vibration predicted by the transient analysis will be compared with the natural frequency results.

Figure W6–1. Problem description



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W6.2

Part 1: Frequency extraction analysis Change to the ../abaqus_solvers/keywords/dynamics directory, and copy w_beam.inp to a new file named w_beam_freq.inp. Currently 5 B21 elements are used to discretize the beam. You will edit this model further as described below. Input specification 1. Make the following changes to w_beam_freq.inp. Refer to the online documentation as necessary. a. Include a density of 2.3E6 in the material definition. Add the following option block below the MATERIAL option: *DENSITY 2.3E-6,

b. Comment out the STATIC step currently in the model, including the loading: ***STEP **SMALL DISPLACEMENT ANALYSIS ***STATIC ***CLOAD **TIP, 2, -1200. ***END STEP

c. Add a new step using the FREQUENCY procedure, and select the Lanczos eigensolver. Request 10 modes. The finished option block should look like the following: *STEP FREQUENCY EXTRACTION *FREQUENCY, EIGENSOLVER=LANCZOS 10, *END STEP

d. Retain the built-in boundary condition at the left end of the beam. 2. Submit the frequency extraction analysis as an Abaqus job. 3. After the analysis has completed, check the printed output file and make any necessary corrections to the input.


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W6.3

Examining the eigenmodes and eigenvalues 1. Open the printed output file in the text editor of your choice. 2. Search for the second occurrence of “E I G E N” to find the beginning of the analysis results. The first table gives the eigenvalue output. Find the frequency (cycles/time) for the lowest mode. 3. Visualize results: a. Start Abaqus/Viewer, and open the output database associated with this analysis. b. Plot the first eigenmode (plot the deformed model shape and use the or the Step/Frame dialog box to choose the frame corresponding to Mode 1). c. Using the arrow keys in the context bar, select different mode shapes. d. The results for modes 1 and 4 are shown in Figure W6–2. These correspond to the first and fourth transverse modes of the structure. Frame Selector

Figure W6–2. First and fourth transverse modes (coarse mesh; 2D linear beam elements) Question W6–1: Are there modes of the physical system that cannot be

captured by your model because of limitations in element type or mesh? (Remember that the elements are planar and the mesh is somewhat coarse.) Question W6–2: Do any of the mode shapes for your model look nonphysical?



427

W6.4

Effect of mesh on extracted modes From Figure W6–2 it is apparent that such a coarse mesh of linear-interpolation elements is unable to adequately represent the mode shapes associated with the higher modes. In fact the current mesh is unable to represent anything beyond the fifth mode. To obtain accurate results for all extracted modes, a sufficiently refined mesh is required. Thus, you will increase the mesh refinement. Also, you will switch to quadratic interpolation elements since these provide superior accuracy for frequency extraction analysis. 1. Open the file w_beam_freq.inp. Note the presence of the *PARAMETER option block near the top of the file. The parameters defined in this block are used to control the mesh density. In particular, the parameter nel defines the number of elements along the length of the beam. 2. In the *PARAMETER option block, set nel to 40. The relevant portion of this option block is shown below. *PARAMETER nel = 40

… The model explicitly defines the first beam element and then uses the *ELGEN option to define the rest. 3. Locate the *ELEMENT option block. Change the element type to B22 and modify the connectivity list of the first element so that nodes 1, 2, 3 are used to define the element: *ELEMENT, TYPE=B22, ELSET=BEAMS 1, 1, 2, 3

4. Run the job, and compare the results with those obtained previously. The results for modes 1 and 4 are shown in Figure W6–3.


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W6.5

Figure W6–3. First and fourth transverse modes (fine mesh; 2D quadratic beam elements)

The results indicate that the refined mesh is able to represent all extracted modes. The natural frequency of the first mode predicted by the fine-mesh model is within 2% of that predicted by the coarse mesh model. The difference in results for the fourth mode is more significant: there is an 8% difference in the predicted natural frequency for this mode. Note that all modes with the exception of modes 6 and 10 are transverse modes. Modes 6 and 10 are longitudinal modes. To see the longitudinal modes more clearly, superimpose the undeformed model shape on the deformed model shape.



429

W6.6

Torsional and out-of-plane modes The current model, given that it uses two-dimensional beam elements, is unable to capture any torsional or out-of-plane modes. For this a three-dimensional model is required (using either beam, solid, or shell elements). With three-dimensional beam elements, however, it is not possible to visualize the modes. Thus, in what follows, shell elements are used to capture the out-of-plane modes. A predefined model is available in w_beam_freq_s8r_complete.inp. This model uses three-dimensional quadratic shell elements to represent the beam structure. The shell part is 200 units long by 50 units wide. The part mesh consists of 40 S8R elements along the length of the structure and 10 along its width. Homogeneous shell section properties with the same material properties used earlier and a thickness of 5 units are assigned to the part. 1. Run the job, and compare the results with those obtained previously. 2. The results for the first and fourth transverse modes are shown in Figure W6–4. The agreement in terms of both mode shape and natural frequency between the (refined) beam and shell models is excellent (compare with Figure W6–3).

Figure W6–4. First and fourth transverse modes (3D shell model)


430


W6.7

3. The three-dimensional model captures the torsional and out-of-plane modes that are suppressed by the two-dimensional model. The first three of these modes are shown in Figure W6–5.

Figure W6–5. Torsional and out-of-plane modes (3D shell model)



431

W6.8

Part 2: Transient dynamic analysis We now investigate the free vibration of the beam upon removal of the tip load. Input specification 1. Copy w_beam_freq.inp to a new file named w_beam_dynam.inp. Use the following steps to modify the file so that the tip of the model is loaded and then released and allowed to vibrate freely: a. Uncomment the static step. b. Delete the frequency extraction step. c. Add another step to the analysis history using the DYNAMIC procedure. Set the maximum number of time increments to 200 and specify an initial time increment of 0.01 and a time period of 1.0. d. Remove the tip load in the dynamic step by specifying CLOAD, OP=NEW. This option removes all existing concentrated loads. e. Request predefined field output and that the tip displacement be written every increment to the output database (.odb) file as history data. Use the predefined node set named TIP for this purpose. This set contains the node at the loaded end of the beam. Add the following output requests to the input file: *OUTPUT, FIELD, VARIABLE=PRESELECT *OUTPUT, HISTORY, FREQUENCY=1 *NODE OUTPUT, NSET=TIP U,

f. It is useful to be able to monitor the progress of an analysis by noting the value of one degree of freedom. To do so, add the following option to the first analysis step: *MONITOR, NODE=TIP, DOF=2

2. Save the input file and run the Abaqus job. While the job is running, you can check on the progress of the analysis by looking at the status file.


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W6.9

Visualizing results 1. Open the file w_beam_dynam.odb in the Visualization module. 2. Plot the history of the displacement component U2 at the tip node. In the Results Tree, expand the History Output container underneath the output database named dynamic.odb and double-click Spatial displacement: U2 at Node … in NSET TIP. The tip response is shown in Figure W6–7. From this plot, you can estimate the frequency of the first vibration mode. Note that there are nearly 6 cycles in a 1 second time period. This is in agreement with the results obtained earlier using the natural frequency extraction procedure (5.95 Hz).

Figure W6–7. Tip node displacement history Question W6–3: How does this compare with the frequency calculated in the

eigenvalue analysis?

Note: Complete input files are available for your convenience. You may consult these files if you encounter difficulties following the instructions outlined here or if you wish to check your work. The input files are named w_beam_freq_b21_complete.inp w_beam_freq_b22_complete.inp w_beam_dynam_b22_complete.inp




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W6.10

Answers


Answer:

captured by your model because of limitations in element type or mesh? (Remember that the elements are planar and the mesh is somewhat coarse). Because the model is two-dimensional, it cannot capture the modes that occur out of the plane of the model, including torsional modes. The mesh is too coarse to capture modes other than the first five. Use more elements to look at all 10 requested modes.

Question W6–2: Do any of the mode shapes for your model look nonphysical? Answer:

No.

Question W6–3: How does this compare with the frequency calculated in the Answer:


434

eigenvalue analysis? The frequency calculated from the history plot of the tip displacement is approximately 5.9, which agrees very closely with the frequency calculated in the eigenvalue analysis.


Notes

435

Notes

436

Workshop 7 Contact with Abaqus/Explicit Keywords Version Note: This workshop provides instructions in terms of the Abaqus Keywords interface. If you wish to use the Abaqus GUI interface instead, please see the “Interactive” version of these instructions. Please complete either the Keywords or Interactive version of this workshop.

Goals     

Define a rigid body constraint. Define a general contact interaction. Apply boundary and initial conditions. Perform an impact analysis. Use Abaqus/Viewer to view results.

Introduction This workshop involves the simulation of a pipe-on-pipe impact resulting from the rupture of a high-pressure line in a power plant. It is assumed that a sudden release of fluid could cause one segment of the pipe to rotate about its support and strike a neighboring pipe. The goal of the analysis is to determine strain and stress conditions in both pipes and their deformed shapes. The simulation will be performed using Abaqus/Explicit. This workshop is based on “Pipe whip simulation,” Section 1.3.9 of the Abaqus Benchmarks Manual.



437

W7.2

Impacting pipe Fixed pipe

Figure W7–1. Pipe whip model: finite element mesh Both pipes have a mean diameter of 6.5 inches with a 0.432 inch wall thickness and a span of 50 inches between supports. The fixed pipe is assumed to be fully restrained at both ends, while the impacting pipe is allowed to rotate about a fixed pivot located at one of its ends, with the other end free. We exploit the symmetry of the structure and the loading and, thus, model only the geometry on one side of the central symmetry plane, as shown in Figure W7–1. Pivot point

edge

refPt

fixed

zsymm

Figure W7–2. Node sets © Dassault Systèmes, 2012

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W7.3

Impact analysis The model geometry, material properties, and loading history for the impact analysis are already defined and can be found in ../abaqus_solvers/keywords/pipe_whip/w_pipe_whip.inp. You will have to edit the input file to include the material properties, rigid body constraint, contact interaction, initial conditions, boundary conditions, step definition, and output requests. Predefined sets are included to ease your work. These are shown in Figure W7–2. Material and section properties 1. Both pipes are made of steel. A von Mises elastic, perfectly plastic material model is used. Create a material named Steel with the following properties: Modulus of elasticity:

30E6 psi

Poisson's ratio:

0.3

Yield Stress:

45.0E3 psi

Density:

7.324E-4 lb-sec /in

2

4

Question W7–1: Why is density required in the material model definition? Can

you comment on the units of density used in this problem? 2. Assign shell section properties to each pipe. Each pipe is 0.432 inches thick. Use Gauss integration with 3 points through the thickness for each section property. The elements of the impacting pipe are contained in element set pipeimpacting, while the elements of the fixed pipe are in element set pipefixed. Question W7–2: Why are only three integration points used through the

thickness? Rigid body constraint Define a rigid body constraint between the nodes at the pivot end of the impacting pipe (node set edge) and the rigid body reference point (node set refPt). Both the translations and rotations of the pipe nodes are controlled by the rigid body constraint. Question W7–3: In order to drive both the translations and rotations of the pipe edge nodes, what type of node set needs to be used in the rigid body constraint? Contact interaction Define general contact between the two pipes. Assume frictional contact with a coefficient of friction equal to 0.2. Question W7–4: Are the contact constraints part of the model or history data?



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W7.4

Initial conditions The impacting pipe has an initial angular velocity of 75 radians/sec about its supported (pinned) end. Assign a rotating velocity initial condition to all the nodes in the impacting pipe (node set pipe-impacting). The rotation is about the positive Z-direction passing though the rigid body reference point. The coordinates of the reference point are 25.0, 6.932, 25.0. Question W7–5:

How can you use the coordinates of the reference point to define the axis of rotation?

Boundary conditions The edges located on the symmetry plane (node set zsymm) must be given appropriate symmetry boundary conditions. One end of the fixed pipe is fully restrained (node set fixed). The rigid body reference point (node set refPt) is free to rotate about its position. Question W7–6: Are the boundary conditions part of the model or history data

in an Abaqus/Explicit analysis? Step definition and output requests Because of the high-speed nature of the event, the simulation is performed using a single explicit dynamics step. 1. Create an explicit dynamics step with a time period of 0.015 seconds. 2. Write preselected field output to the output database at 12 equally spaced intervals. 3. Request reaction force history output at the constrained end of the impacting pipe. Write the data to the output database at 100 evenly spaced time intervals during the analysis. 4. Request preselected history output at the default number of intervals. Save the input file, and run the impact analysis by entering the following command at the prompt: abaqus job=w_pipe_whip

Visualization 1. Once the analysis completes successfully, open the output database file in Abaqus/Viewer. 2. Plot the undeformed and the deformed model shapes. From the main menu bar, select Tools→Color Code (or click


440

in the toolbar) and assign different


W7.5

colors to the two pipes (you can distinguish between them using section assignments), as shown in Figure W7–3.

Figure W7–3. Deformed model shape 3. Use the Animate: Time History tool to animate the deformation history. 4. Contour the Mises stress and equivalent plastic strain (PEEQ) on the deformed shape, as shown in Figure W7–4. MISES

PEEQ

Figure W7–4. Contour plots 5. Create X–Y plots of the model’s kinetic energy (ALLKE), internal energy (ALLIE), and dissipated energy (ALLPD). The energy plot is shown in Figure W7–5. Note this figure has been customized for clarity. Tip: Expand the History Output container in the Results Tree and select the three curves noted above. Click mouse button 3 and select Plot from the menu that appears.



441

W7.6

Figure W7–5. Energy histories Question W7–7: What do the energy history plots indicate?


442


W7.7

6. Select and plot the pinned node reaction force components RF1, RF2, and RF3. The curves appear in Figure W7–6. Note this figure has been customized for clarity.

Figure W7–6. Reaction force histories

Note: A complete input file is available for your convenience. You may consult this file if you encounter difficulties following the instructions outlined here or if you wish to check your work. The input file is named w_pipe_whip_complete.inp




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W7.8

Answers Question W7–1: Why is density required in the material model definition? Can Answer:

you comment on the units of density used in this problem? All Abaqus/Explicit analyses require a density value because Abaqus/Explicit solves for dynamic equilibrium (i.e., inertia effects are considered). The units for all material parameters must be consistent; in this problem the English system is used with pounds and inches as the units for force and length, respectively. Thus, the consistent unit for density is lb-sec2/in4. The options required to complete the material model definition are: *material, name=steel *density 7.324e-4, *elastic 3e+07, 0.3 *plastic 45000.,0.

Question W7–2: Why are only three integration points used through the Answer:

thickness? Three section points are used to reduce the run time of the job. The options required to complete the section definitions are: *shell section, material=steel, 0.432, 3 *shell section, material=steel, 0.432, 3

elset=pipe-impacting, section integration=gauss elset=pipe-fixed, section integration =gauss


Answer:

edge nodes, what type of node set needs to be used in the rigid body constraint? A tie node set needs to be used. The option required to define the rigid body constraint is: *rigid body, ref node=refPt, tie nset=edge


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W7.9

Question W7–4: Should you add the contact definition to the model data or the Answer:

history data? General contact definitions can be part of either the model data or the history data. The surface interaction properties are model data when used with general contact. The (model data) options required to complete the contact definition are: *contact *contact inclusions, all exterior *contact property assignment , , fric *surface interaction, name=fric *friction 0.2,

Question W7–5: How can you use the coordinates of the reference point to Answer:

define the axis of rotation? The axis passes through the reference point and is parallel to the Z-direction. Thus, define the axis using two points. Each of the “axis” points must have the same X- and Y-coordinates as the reference point; the values of the Z-coordinates of the “axis” points will dictate the sense of positive rotation. For example: *initial conditions, type=rotating velocity pipe-impacting, 75., 0., 0., 0., 25., 6.932, 0., 25., 6.932, 1.,

The second data line defines the axis of rotation.



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W7.10

Question W7–6: Are the boundary conditions part of the model data or the Answer:

history data in an Abaqus/Explicit analysis? As with Abaqus/Standard, fixed boundary conditions can be defined as either model or history data. Named boundary conditions improve the readability of your input file and provide a shortcut to defining commonly encountered support conditions. The options required to define the boundary conditions, step, and output are: *dynamic, explicit , 0.015 ** *boundary zsymm, zsymm fixed, encastre refPt, pinned *output, field, variable=preselect, number intervals=12 *output, history, time interval=0.00015 *node output, nset=refpt rf1, rf2, rf3 *output, history, variable=preselect

Question W7–7: What do the energy history plots indicate? Answer:


446

Near the end of the simulation, the impacting pipe is beginning to rebound, having dissipated the majority of its kinetic energy by inelastic deformation in the crushed zone.


Notes

447

Notes

448

Workshop 8 Quasi-Static Analysis Keywords Version Note: This workshop provides instructions in terms of the Abaqus Keywords interface. If you wish to use the Abaqus GUI interface instead, please see the “Interactive” version of these instructions. Please complete either the Keywords or Interactive version of this workshop.

Goals  

Approximate a quasi-static solution using Abaqus/Explicit. Understand the effects of mass scaling.

Introduction In this workshop you will examine the deep drawing of a can bottom. A one-stage forming process is simulated in Abaqus/Explicit; the springback analysis is performed in Abaqus/Standard. The final deformed shape of the can bottom is shown in Figure W8–1. In a subsequent workshop the import capability is used to transfer the results between Abaqus/Explicit and Abaqus/Standard in order to perform a springback analysis. One of the advantages of using Abaqus/Explicit for metal forming simulations is that, in general, Abaqus/Explicit resolves complicated contact conditions more readily than Abaqus/Standard.



449

W8.2

Figure W8–1. Final deformed shape Change to the ../abaqus_solvers/keywords/forming directory.

Establishing the Abaqus/Explicit analysis time In this section you will determine the first eigenmode of the blank and use it to establish the step time for the subsequent Abaqus/Explicit analysis. 1. Open the file w_draw_freq.inp, and examine its contents to help you answer the following questions: Question W8–1: What analysis procedure is used in this input file? Question W8–2: In Abaqus a distinction is made between linear perturbation

analysis steps and general analysis steps. What type of procedure is the analysis procedure in this input file? Question W8–3: In an analysis with more than one step in the same input file, what influence does the result of a linear perturbation step have on the base state of the model for the following analysis step? 2. Run the job by entering the following command: abaqus job=w_draw_freq

Plot the first eigenmode in Abaqus/Viewer. The fundamental frequency, f, of the blank is 304 Hz, corresponding to a time period of 0.0033 s ( T  1/ f ). This time period provides a lower bound on the step time for the first forming stage. Choosing the step time to be 10 times the time period of the fundamental natural frequency, or 0.033 s, should ensure a quality quasi-static solution. This time period corresponds to a constant punch velocity of 0.45 m/s, which is typical for metal forming.


450


W8.3

Geometry definition In this section you will complete the geometry definition of the can forming model by defining the punch as an analytical rigid surface. Figure W8–2 shows the components of the model—the punch, the die, and the blank—in their initial positions. The blank is modeled using axisymmetric shell elements (SAX1). The shell reference surface lies at the shell midsurface.

(0.032, 0.03025)

(0.0, 0.00025)

Origin (0.0, 0.0)

Figure W8–2. Model geometry 1. Open the file w_draw_bot.inp in an editor, and define punch 1 as an analytical rigid surface (see Figure W8–2 for the relevant dimensions). Use the definition of die 1 in the input file as an example of the input for an analytical rigid surface. The end point for punch 1 lies on the symmetry axis, a distance of half the blank thickness above the shell midsurface. Give the rigid surface the name PUNCH1, and use node 1001 as the rigid body reference node. The RIGID BODY option has been defined already.

Question W8–4: How does the order of the line segments affect the ability of

Abaqus to resolve the contact condition?



451

W8.4

2. Define the surfaces, the contact pairs, and the surface interaction for the complete model using the SURFACE, CONTACT PAIR, and SURFACE INTERACTION options. The blank is defined such that the element normal direction points toward the punch. The friction coefficient between the rigid tools and the blank is 0.1. Question W8–5: What effect will an increase in friction have on the solution? Question W8–6: In Abaqus the input data are classified as either model or

history data. What type of data is the contact pair definition in Abaqus/Explicit? What type of data is the contact pair definition in Abaqus/Standard?

Material definition In this section you will add the entire material definition to the input file. The material is steel with Young’s modulus E =210E9 Pa, Poisson’s ratio v =0.3, and density  =7800 kg/m3. Figure W8–3 shows the nominal plasticity material data for the blank as tabulated in Table W8–1.

Figure W8–3. Nominal stress vs. nominal strain

Question W8–7: When entering plasticity data with the PLASTIC option,

what are the stress and strain measures that Abaqus uses?


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W8.5

Table W8–1 Nominal stress (Pa) 90.96  106 130.71  106 169.75  106 207.08  106 240.99  106 268.89  106 287.59  106 290.57  106

Nominal strain 4.334  104 2.216  103 7.331  103 1.888  10-2 4.153  102 8.218  102 1.509  101 3.456 101

Table W8–2 True stress (Pa) 91  106 131  106 171  106 211  106 251  106 291  106 331  106 391  106

Log plastic strain 0.0 0.159  102 0.649  102 0.177  101 0.395  101 0.776  101 0.139 0.295

Table W8–2 lists the corresponding true stress and logarithmic strain values. These values were obtained using the following relationships:

   nom (1   nom )

  1n(1   nom )

 pl  tot   el   tot   / E These equations are valid for isotropic materials and establish the relationships between the true stress and strain measures (used in Abaqus) and the nominal stress and strain measures. 1. Complete the material definition, and name the material STEEL. Use the ELASTIC option to enter Young’s modulus and Poisson’s ratio and the PLASTIC option to enter the material data in Table W8–2. Tip: Both of these options must be grouped under the *MATERIAL option. 2. To reduce high-frequency noise in the solution (caused primarily by the oscillations of the blank’s free end), add stiffness proportional damping to the material definition of the blank. It is best to use the smallest amount of damping possible to obtain the desired solution since increasing the stiffness damping decreases the stable time increment and, thus, increases the computer time. To avoid a dramatic drop in the stable time increment, the stiffness proportional



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damping factor R should be less than, or of the same order of magnitude as, the initial stable time increment without damping. We choose a damping factor of R = 1107, which is included by using the DAMPING, BETA=1.E7 material option. Question W8–8: What effects would a higher damping coefficient have?

Amplitude definition To form the can bottom, we will displace the punch by moving its rigid body reference node 0.015 m in the negative 2-direction. The punch displacement will be applied in the form of a displacement boundary condition. Because Abaqus/Explicit does not permit displacement discontinuities, prescribed displacements must refer to an amplitude definition. In this section you will add the amplitude definition to the input file. Figure W8–4 shows the desired displacement behavior for the punch. Question W8–9: What is the slope of the curve at the beginning and end, and

why is this important? 1. Define the amplitude curve corresponding to Figure W8–4. The curve shown in Figure W8–4 is smooth in its first and second derivatives and is defined by using the DEFINITION=SMOOTH STEP parameter with the AMPLITUDE option. Define the punch displacement amplitude, and name the amplitude FORM1. Question W8–10: How would the results change if a linear amplitude definition

was used instead? 2. Note that in the input file there is a boundary condition that refers to the amplitude definition (FORM1) just completed.

Speeding up the analysis In general, quasi-static processes cannot be modeled in their natural time scale in Abaqus/Explicit since a large number of time increments would be required. (Recall that time increments in Abaqus/Explicit are generally very small). Thus, it is sometimes necessary to increase the speed of the simulation artificially to reduce the computational cost. One method to reduce the cost of the analysis is to use mass scaling.


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Figure W8–4. Displacement curve of punch While various forms of mass scaling are available in Abaqus/Explicit, we will concentrate on fixed mass scaling in this workshop and will implement it using the FIXED MASS SCALING option. The reason for choosing fixed mass scaling is that it provides a simple means to modify the mass properties of a quasi-static model at the beginning of the analysis. It is also computationally less expensive than variable mass scaling, because the mass is scaled only once at the beginning of the step. 1. Specify a mass scaling factor of 10 by setting the FACTOR parameter on the FIXED MASS SCALING option, and complete the mass scaling definition in the input file. Question W8–11: How do you determine if an analysis that includes mass

scaling produces acceptable results? Question W8–12: How does mass scaling affect the solution time?

Analysis and results evaluation 1. Run the analysis with the input file w_draw_bot.inp. 2. Monitor the progress of the solution in the status file. 3. Open the output database w_draw_bot.odb in Abaqus/Viewer. 4. Display the curves for internal and kinetic energy (variables ALLIE and ALLKE, respectively) in the same plot by selecting them from the Results Tree (underneath the History Output container). To display the curve symbols, use the



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XY Curve Options tool

in the toolbox. You should see a plot similar to Figure W8–5. Note this figure has been customized for clarity.

Figure W8–5. Internal and kinetic energy 5. Certain elements have hourglass modes that affect their behavior. Hourglass modes are modes of deformation that do not cause any strains at the integration points. An indication of whether hourglassing has an effect on the solution is the artificial energy, variable ALLAE. Plot the artificial energy and the internal energy, variable ALLIE, on the same plot. The artificial energy should always be much less than the internal energy (say less than 0.5%). Question W8–13: What elements are used to model the blank, and does this

element type have an hourglass deformation mode? 6. Display only the deformed shape of the blank: a. Expand the Materials container in the Results Tree and click mouse button 3 on STEEL. b. From the menu that appears, select Replace. 7. Expand the displayed area to 180o: a. Select ViewODB Display Options from the main menu. b. In the Sweep/Extrude tabbed page of the ODB Display Options dialog box, toggle on Sweep elements. You should see a shape similar to that in Figure W8–6.


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Figure W8–6. 180 expanded deformed shape c. Contour the Mises stress distribution of the 180o model using the Plot Contours tool in the toolbox; to select other variables for contouring, use the Field Output toolbar.

d. Plot the punch displacement shown in Figure W8–4 by double-clicking the U2 curve for node 1001 in the Results Tree (underneath the History Output container).

Note: A complete input file is available for your convenience. You may consult this file if you encounter difficulties following the instructions outlined here or if you wish to check your work. The input file is named w_draw_bot_complete.inp




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W8.10

Answers Question W8–1: What analysis procedure is used in this input file? Answer:

The analysis procedure is a natural frequency extraction (FREQUENCY). The procedure option must immediately follow the STEP option.

Question W8–2: In Abaqus a distinction is made between linear perturbation

analysis steps and general analysis steps. What type of procedure is the analysis procedure in this input file? Answer:

The FREQUENCY option is a linear perturbation procedure.

Question W8–3: In an analysis with more than one step in the same input file,

Answer:

what influence does the result of a linear perturbation step have on the base state of the model for the following analysis step? None. Only general analysis steps change the base state of the model.

Question W8–4: How does the order of the line segments affect the ability of Answer:

Abaqus to resolve the contact condition? The order of the line segments determines the direction of the outward normal vector of the rigid surface. If the outward normal points in the wrong direction, Abaqus cannot establish the contact between the surfaces and, therefore, cannot find a solution.

Question W8–5: What effect will an increase in friction have on the solution? Answer:


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An increased friction coefficient will increase the critical shear stress crit at which sliding of the blank begins. Thus, the material will be stretched more, causing further thinning of the material and increasing the stresses.


W8.11

Question W8–6: In Abaqus the input data are classified as either model or

Answer:

history data. What type of data is the contact pair definition in Abaqus/Explicit? What type of data is the contact pair definition in Abaqus/Standard? The contact pair definition is history data in Abaqus/Explicit and model data in Abaqus/Standard.

Question W8–7: When entering plasticity data with the PLASTIC option, Answer:

what are the stress and strain measures that Abaqus uses? Abaqus uses true (Cauchy) stress and log strain.

Question W8–8: What effects would a higher damping coefficient have? Answer:

A higher damping coefficient would reduce the stable time increment. In general, damping should be chosen such that high frequency oscillations are smoothed or eliminated with minimal effect on the stable time increment. Figure WA8–1 shows a plot of the kinetic energy with and without damping. Note the high frequency oscillations in the analysis without damping.

Figure WA8–1. Kinetic energy with and without damping



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Question W8–9: What is the slope of the curve at the beginning and end, and Answer:

why is this important? The slope of the amplitude curve at the beginning and end of the step is zero. This is important because it prevents discontinuities in the punch displacement that lead to oscillations in an Abaqus/Explicit analysis.

Question W8–10: How would the results change if a linear amplitude definition Answer:

were used instead? With a linear amplitude definition the displacement of the punch will be applied suddenly at the beginning of the step and stopped suddenly at the end of the step, causing oscillations in the solution. A linear amplitude definition results in large spikes in the kinetic energy, especially at the beginning of the step. As a result, the kinetic energy may be large compared to the internal energy and the early solution may not be quasi-static. The preferred approach is to move the punch as smoothly as possible. Figure WA8–2 compares the kinetic energy history when a linear amplitude definition is used and when the smooth step amplitude definition is used.

Figure WA8–2. Kinetic energy plot with and without SMOOTH STEP


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W8.13

Question W8–11: How do you determine if an analysis that includes mass Answer:

scaling produces acceptable results? The kinetic energy should be a small fraction of the internal energy. As the kinetic energy increases, inertia effects have to be considered and the solution is no longer quasi-static. Figure WA8–1 shows the internal and kinetic energy for mass scaling factors of 10 (used in our simulation), 100, and 900, which correspond to a solution speedup of 10 , 10, and 30, respectively.

Figure WA8–3. Energies with different mass scaling

Question W8–12: How does mass scaling affect the solution time? Answer:

The stable time increment is calculated according to  Le tstable  min  c  d

 ,  

where Le is a characteristic element length and cd is the dilatational wave speed. An increase in density decreases cd, which in turn increases tstable.



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W8.14

Question W8–13: What elements are used to model the blank, and does this Answer:


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element type have an hourglass deformation mode? The analysis uses SAX1 elements. These elements have no hourglass modes. Consequently, hourglassing is not of concern in the analysis.


Notes

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Workshop 9 Import Analysis Keywords Version Note: This workshop provides instructions in terms of the Abaqus Keywords interface. If you wish to use the Abaqus GUI interface instead, please see the “Interactive” version of these instructions. Please complete either the Keywords or Interactive version of this workshop.

Goals 

Transfer results between Abaqus/Explicit and Abaqus/Standard.

Introduction In this workshop you will use the import capability is used to transfer the results between Abaqus/Explicit and Abaqus/Standard to examine the effects of springback in the analysis of the deep drawing of a can bottom. The deformed shape of the can after the forming stage is shown in Figure W9–1.

Figure W9–1. Final deformed shape Before proceeding, change to the ../abaqus_solvers/keywords/forming directory.



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Springback analysis In the manufacturing process the part is removed after the forming has been completed and the material is free to springback into an unconstrained state. To understand the final shape after this physical effect, we perform a springback analysis in Abaqus/Standard. 1. Open the file w_draw_bot_spring.inp in an editor, and import the blank from the end of the w_draw_bot analysis. Use the STATE=YES parameter on the IMPORT option to import the material state of the elements. Question W9–1: To what value should the UPDATE parameter on the

IMPORT option be set if the total Mises stresses are to be plotted at the end of the springback analysis? Question W9–2: Where do you find the information to define the STEP and INTERVAL parameters on the IMPORT option? 2. The boundary conditions are not imported and must be respecified. In addition, it is necessary to fix a single point, such as node set BSYM, in the 2-direction to prevent rigid body motion. It is important to use the FIXED parameter on the *BOUNDARY option so that BSYM is fixed at its final position at the end of the forming stage. Question W9–3: Why is it advantageous to choose Abaqus/Standard for the

springback analysis?

Analysis and postprocessing 1. Run the analysis by entering the following command: abaqus job=w_draw_bot_spring oldjob=w_draw_bot

2. Open the output database w_draw_bot_spring.odb in Abaqus/Viewer. 3. Contour the Mises stress distribution of the 180o model. 4. Plot the final deformed model shape, as shown in Figure W9–1. 5. Plot the springback and formed shapes together. (First toggle off the Sweep elements option.) If you used UPDATE=NO, the formed shape is stored in frame 0 of the output database. You must use overlay plots to superimpose the images in this case: a. Select View→Overlay Plot from the main menu bar. b. Use the Frame Selector or the arrows in the context bar to select frame 0. c. In the Overlay Plot Layer Manager, click Create. Name the layer formed.


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d. Use the Frame Selector frame 1.

or the arrows in the context bar to select

e. Use the Common Plot Options tool to change the fill color of the elements to blue. f. In the Overlay Plot Layer Manager, click Create. Name the layer springback. g. In the Overlay Plot Layer Manager, click Plot Overlay. h. Zoom in to examine the shape differences more closely. If you used UPDATE=YES, the formed shape is treated as the undeformed shape of the import analysis model (recall that when UPDATE=YES, the end state of the previous analysis becomes the reference configuration of the import analysis; the reference configuration is considered the undeformed shape): a. In the toolbox, click the Allow Multiple Plot States tool . b. In the toolbox, click both the Plot Undeformed Shape and Plot Deformed Shape tools

.

c. Use the Common Plot Options tool to increase the deformation scale factor so that the differences between the formed and springback shapes are clearly visible. Note: A complete input file is available for your convenience. You may consult this file if you encounter difficulties following the instructions outlined here or if you wish to check your work. The input file is named w_draw_bot_spring_complete.inp




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Answers Question W9–1: To what value should the UPDATE parameter on the

Answer:

IMPORT option be set if the total Mises stresses are to be plotted at the end of the springback analysis? The UPDATE parameter should be set to NO. When the UPDATE parameter is set to YES, the deformed configuration of the previous analysis is used as the reference configuration for the import analysis. All stresses, strains, displacements, etc. are reported relative to the updated reference configuration and not as total values.

Question W9–2: Where do you find the information to define the STEP and

INTERVAL parameters on the IMPORT option?

Answer:

The status (.sta) file gives an overview of the progression on the analysis. Information about the number of steps and the number of increments completed in each step can be obtained from this file. In this analysis we wish to model the springback of the can after the forming of the can bottom is complete: this is STEP=1, INTERVAL=1.

Question W9–3: Why is it advantageous to choose Abaqus/Standard for the Answer:


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springback analysis? A true static procedure is the preferred approach for modeling springback. The imported model will not be in static equilibrium at the beginning of the step. Thus, Abaqus/Standard applies a set of artificial internal stresses to the imported model state and then gradually removes these stresses. This leads to the springback deformation. In Abaqus/Explicit the removal of the contact between the blank and the tools represents a sudden load removal, which leads to low frequency vibrations of the blank. While these vibrations will eventually dissipate, this approach leads to lengthy computation times.


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Abaqus Analysis Intro-book

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