Solve any one question from Q.1(a,b) &Q.2(a,b)

1(a)
Explain importance of Boundary conditions and further explain:

i) Essential Boundary Conditions.

ii) Natural Boundary Conditions.

i) Essential Boundary Conditions.

ii) Natural Boundary Conditions.

6 M

1(b)
Why quality of meshing is important in FEA and how it is ensured and how the convergence of element in FEA formulation is achieved?

4 M

2(a)
Explain the principle of Galerkin's Weighted Residual Method.

6 M

2(b)
Write a step by step procedure for Weak Formulation in elemental formulations.

4 M

Solve any one question from Q.3 & Q.4(a,b)

3
Determine the nodal displacements and element stresses by finite element formulation for the following figure.

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10 M

4(a)
For the truss shown in figure acted by a forced P. The dispplacements of node 2 is found to be Ux = 0.01 mm and Uy = -0.2mm, Determine Force P.

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6 M

Solve any one question from Q.5(a,b,c) & Q.6(a,b)

4(b)
Explain method of Penalty for solution of equation [K] {X} = {F} where, [K] is a stiffness matrix, {X} is displacement vector and {F} is load vector.

4 M

5(a)
What is meant by ISO, SUPER and SUB parametric element and for structural analysis which is mostly preferred?

6 M

5(b)
Determine the Cartesian coordinate of the point P(ζ=0.5, η=0.5) shown in Fig.

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6 M

5(c)
State and explain the three basic laws on which isoparametric concept is developed.

6 M

6(a)
Write short notes on:

i) Uniqueness of mapping of isoparanmetric elements.

ii) Jacobian matrix.

i) Uniqueness of mapping of isoparanmetric elements.

ii) Jacobian matrix.

8 M

6(b)
For the element shown in Fid. Assemable 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 governing eqution 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 = 0.75 W/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

^{2}K°. Determine the steady state temperature 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 = 0.5 W/m C°) at the rate of 2000W/m

^{3}. The plate is 10 cm 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 Ein Heat Transfer Problem.

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 natural frequencies of longitudinal vibrations of the same stepped shaft of areas A = 12000mm

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

10 M

10(a)
Explain difference between consistent and lumped mass matrix technique for modal analysis of structure.

6 M

10(b)
Find the 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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