r05322105 Finite Element and Modelling Methods

Set No. 1

Code No: R05322105 R05322105

III B.Tec B.Tech h II Semest Semester er Supplim Supplimen entar tary y Examin Examinati ations ons,, Aug/S Aug/Sep ep 2008 2008 FINITE ELEMENT AND MODELLING METHODS (Aeronautical Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆ ⋆ ⋆ ⋆ ⋆

1. Explai Explain n what what are the the deve developm lopmen ents ts and and specific specificatio ation n of struc structura turall models. models.

[16]

2. Explain about (a) Frame of Reference Reference (b) Non-Dimensi Non-Dimensional onal parameter (c) Nature Nature of coordinates coordinates (d) Field sp ecific systems.

[4+4+4+4]

3. (a) What are are vario various us concepts concepts to specif specify y a node at discont discontin inuti uties? es? (b) (b) Wha Whatt is the the effec effectt of elem elemen entt aspec aspectt rati ratioo in disc discon onti tin nuiti uities es??

[12+ [12+4] 4]

4. (a) What What are the basic basic diffe differen rence ce betw between lumped lumped mass mass matri matrix x and consis consisten tentt matrix. (b) Give Give lumped lumped mass matrices matrices for a beam element element in space and for a triangul triangular ar plane stress element. [8+8] 5. (a) What is refinem refinemen entt strategy strategy of finite elemen elementt analysis analysis techni technique ques? s? Explain Explain them with the examples. (b) What is the better refinement refinement technique technique for solving the heat transfer transfer problems? problems? Explain. [8+8] 6. (a) Discuss Discuss the importance of finite finite element element modeling in solving solving the the field problems. problems. (b) How How to store store the the large large scale scale matri matrices ces?? Expla Explain in differ differen entt methods methods..

[8+8 [8+8]]

7. (a) Derive Derive the the Jacobian Jacobian matrix matrix for for 2-D axi symmet symmetric ric problem problems. s. (b) Explain Explain the method to simplify simplify the given domain using symmetric symmetric boundary conditions with suitable examples. [8+8] 8. (a) What are differe different nt uses uses and applicati applications ons ANSYS ANSYS pack package? Explai Explain n with the simple examples. (b) What is the better pack package to be used used for solving solving nonlinea nonlinearr static static analysis? analysis? Explain. [8+8] ⋆ ⋆ ⋆ ⋆ ⋆

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Set No. 2

Code No: R05322105 R05322105


1. Expl Explai ain n wit with h exa examp mple les. s. What What is is Macn Macnoo and and Micro Micro mech mechani anical cal model models. s.

[8+8 [8+8]]

2. Explain about (a) Generalized Generalized displacement displacement parameters parameters (b) Generalized Generalized Geometrical Geometrical parameters (c) Generalized Generalized Force Force and other parameters (d) Global co ordinates.

[5+3+3+5]


[12+ [12+4] 4]

4. Using Rayleigh-Ritz Rayleigh-Ritz method, determine the expressions for displacement and stresses in a fixed bar sujected to an axial force ‘P’ as shown in figure 4. E=Young‘s Modulus A=Cross sectional area. [16]

Figure 4 5. Derive the strain displacement relation matrix for 4 noded quadrilateral element by treating it as iso parametric element. [16] 6. Differentiate between Gaussian quadrature one point formula and two point formula along with the errors involved in them. Give the examples. [16] 7. (a) Derive Derive the the Jacobian Jacobian matrix matrix for for 2-D axi symmet symmetric ric problem problems. s. (b) Explain Explain the method to simplify simplify the given domain using symmetric symmetric boundary conditions with suitable examples. [8+8] 1 of 2

Set No. 2

Code No: R05322105 R05322105

8. (a) Why Why computati computational onal fluid fluid dynamics dynamics softwa software re is bette b etterr suited for solving solving fluid fluid flow problems than finite element software? Explain. (b) Descri Describe be the method of automat automatic ic mesh generation generation techniq technique ue with with a simple simple example. [8+8] ⋆ ⋆ ⋆ ⋆ ⋆

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Set No. 3

Code No: R05322105 R05322105

III B.Tec B.Tech h II Semest Semester er Supplim Supplimen entar tary y Examin Examinati ations ons,, Aug/S Aug/Sep ep 2008 2008 FINITE ELEMENT AND MODELLING METHODS (Aeronautical Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆

1. (a) How How is a struc structu ture re discre discreti tized zed?? What What are the criter criteria ia to select select large large nu nummber of elements of smaller size and smaller number of elements of large sized elements? (b) Explain Explain the approaches associated associated with the FEM in structural problems?[ problems?[8+8] 8+8] 2. (a) Deri Derive ve the stand standard ard closed closed form form integ integrat ratio ion n for for 1-D 1-D elem elemen entt in natural natural coordinate system. system. (b) Integrate Integrate the following over over the entire entire length ‘L’ of an 1-D element. i. ∫ L21 dx ii. ∫ L31 L2 dx iii. ∫ L21 dx.

[8+8]

3. (a) A tapered tapered bar of 100 100 mm diamete diameterr at the larger larger end end and 50 mm at the the smalle smallerr end is clamped at larger end and it is hanging. hanging. The bar is subjected to a pull of 100 KN at the free end. Length of the bar is 200 mm. Find the displacements in the bar for 3 elements using FEM technique? (b) What are the various various forces that can b e considered in FEM approach?[10+6] approach?[10+6] 4. Using Rayleigh-Ritz Rayleigh-Ritz method, determine the expressions for displacement and stresses in a fixed bar sujected to an axial force ‘P’ as shown in figure 4. E=Young‘s Modulus A=Cross sectional area. [16]

Figure 4 5. (a) Explain Explain the phenomenon phenomenon of iso-parame iso-parametric tric represen representation tation and and explain explain the the advantages and limitations of this method. 1 of 2

Set No. 3

Code No: R05322105 R05322105

(b) Differentiat Differentiatee among sub parametric parametric and super parametric representation. representation.[8+8] [8+8] 6. Differentiate between Gaussian quadrature one point formula and two point formula along with the errors involved in them. Give the examples. [16] 7. (a) Explain Explain the symmetric symmetric boundary boundary condition condition and and derive derive the strain strain displacem displacement ent relations for symmetric problems. (b) Discuss the applications of axi-symmetric problems.

[8+8]

8. (a) Explai Explain n different different methods methods of mesh generatio generation n techniqu techniques es used in decarteli decartelizazation. (b) Descri Describe be the ANSY ANSYS S pack package and and its its uses uses in finit finitee elemen elementt analys analysis. is. ⋆⋆⋆⋆⋆

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[8+8] [8+8]

Set No. 4

Code No: R05322105 R05322105


1. Expl Explai ain n wit with h exa examp mple les. s. What What is is Macn Macnoo and and Micro Micro mech mechani anical cal model models. s.

[8+8 [8+8]]

2. Illustrate the following systems with suitable examples. (a) Global Co-ordinate Co-ordinate system system (b) Local Co-ordinate Co-ordinate system system (c) Natural Co-ordinat Co-ordinatee system (d) Generalized Co-ordinate system.

[4+4+4+4]


[12+ [12+4] 4]

4. Using Rayleigh-Ritz Rayleigh-Ritz method, determine the expressions for displacement and stresses in a fixed bar sujected to an axial force ‘P’ as shown in figure 4. E=Young‘s Modulus A=Cross sectional area. [16]

Figure 4 5. (a) Explain Explain the phenomenon phenomenon of iso-parame iso-parametric tric represen representation tation and and explain explain the the advantages and limitations of this method. (b) Differentiat Differentiatee among sub parametric parametric and super parametric representation. representation.[8+8] [8+8] 6. (a) Explain Explain the twotwo-point point Gaussia Gaussian n quadrature quadrature method method for the numerical numerical integraintegration with suitable example. (b) What are the approximations and errors associated in two point Gaussian quadrature formula? Explain. [8+8] 1 of 2

Set No. 4

Code No: R05322105 R05322105

7. (a) Explai Explain n the methodology methodology to estimate estimate the potentia potentiall energy for axi-sy axi-symme mmetric tric problems with suitable example. (b) Derive Derive the strain displacement displacement relation relation matrix for 2-D axi-symmetric axi-symmetric conditions. [8+8] 8. (a) Discu Discuss ss the import importanc ancee of FLOTRA FLOTRAN N modul modulee in ANSYS ANSYS pack package used for solving the problems using finite element analysis. (b) How to estimate estimate the errors in adaptive adaptive meshing meshing technique? technique? Explain Explain them with suitable diagram. [8+8] ⋆ ⋆ ⋆ ⋆ ⋆

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r05322105 Finite Element and Modelling Methods

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