 MORE IN Finite Element Analysis
SPPU Mechanical Engineering (Semester 8)
Finite Element Analysis
December 2016
Total marks: --
Total time: --
INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary

Solve any one question from Q.1(a,b)& Q.2(a,b)
1(a) Explain step by step procedure for FEA and comments on convergence based on elemental size.
6 M
1(b) Explain concept of Plane Stress with appropriate example
4 M

2(a) Write down the difference between Weighted Residual Method and Weak Formulations.
6 M
2(b) Explain LST (Linear Strain Triangle Element) Element.
4 M

Solve any one question from Q.3 & Q.4(a,b)
3 Determine the forces in the members of the truss shown in Fig. Take E= 200GPa. A= 2000mm2.
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10 M

4(a) Determine the nodal displacement, element stresses and support reactions of the axially loaded bar as shown in Fig. Take E = 200GPa and P =30kN
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6 M
4(b) Write a note on Lagrendge interpolation functions used in FEA formulations.
4 M

Solve any one question from Q.5(a,b,c,d) & Q.6(a,b)
5(a) Write a note on isoparametric formulations and how the geometric as well as field variable variation is taken into account?
6 M
5(b) Determine the Cartesian coordinate of the point P(ζ0.5,η0.6
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4 M
5(c) Wrie short notes on
i) Uniqueness of mapping of isoparametric elements.
ii) Jacobian matrix.
4 M
5(d) State and explain the three basic laws on which isoparametric concept is developed.
4 M

6(a) Wrie short notes on
i) Uniqueness of mapping of isoparametric elements.
ii) Jacobian matrix.
8 M
6(b) For the elements shown in Fig. Asssemble Jacobian matrix and strain displacement matrix for the Gaussian point (0.7, 0.5).
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10 M

Solve any one question from Q.7(a,b) & Q.8(a,b)
7(a) Write down govering equation of steady state heat transfer and also write down elemental stiffness matrix and compare with Bar element.
6 M
7(b) Consider a brick wall of thickness 0.6m, k=0.75W/m °K. The inner surface is at 15°C and the outer surface is exposed to cold air at-15°C. The heat transfer coefficient associated with the outside surface is 40W/m20 K. Determine the steady state temerature distribution within the wall and also the heat flux through the wall. Use two elements and obtain the solution.
10 M

8(a) Heat is generated in a large plate (K=0.5W/m°C) at the rate of 2000W/m3. The plate is 10cm thick. Outside surface of the plate is exposed to ambient air at 30°C with a convective heat transfer coefficient of 40W/m2C. Determine the temperature distribution in the wall.
10 M
8(b) Derive FEA stiffness matrix for Pin Fin Heat Transfer probelm.
6 M

Solve any one question from Q.9(a,b) & Q.10(a,b)
9(a) Write down Consistent Mass and Lumped Mass Matrix for
i) Bar Element
ii) Plane Stress Element
6 M
9(b) Find the nautral frequencies of longitudinal vibrations of the same stepped shaft of areas A = 1200 mm2 and 2A 2500 mm2 and of equal lengths (L=1m), when it is constrained at one end, as shown below.
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10 M

10(a) Explain difference between cosistent and lumped mass matrix technique for modal analysis of structure.
6 M
10(b) Fidn natural frequencies of longitudinal vibrations of the unconstrained stepped shaft of areas A and 2A and of equal lengths (L), as shown below.
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10 M

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