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= 2000mm

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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.

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.

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/m

^{20}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/m

^{3}. 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/m^{2}C. 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

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 mm

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^{2}and 2A 2500 mm^{2}and of equal lengths (L=1m), when it is constrained at one end, as shown below.!mage

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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