STUPIDSID
1 (a)
Explain applications of FEA in various fields.
5 M
1 (b)
State different types of Boundary conditions.
5 M
1 (c)
Explain with sketches: type of elements.
5 M
1 (d)
Explain Shape function graphically for one dimensional Linear and quadratic element.
5 M
1 (e)
Explain Gauss Elimination Method using an example.
5 M
2 (a)
Solve following differential equation \[ \dfrac {d^2y}{dx^2}+3x \dfrac {dy}{dx}- 6y=0; \ \ 0\le x\le 1 \] Bcs: y(0)=0 and y'(1)=0.1: Find y(0.2): using variational method and compare with exact solution.
12 M
2 (b)
Evaluate following integral \( \int^1_{-1}(3^x - x) dx \) Using (a) Newton Cotes Method using 3 sampling points.
(b) Three points Gauss Quadrature
(b) Three points Gauss Quadrature
| r | W1 | W2 | W3 | W4 |
| 1 | 1 | |||
| 2 | 1/2 | 1/2 | ||
| 3 | 1/6 | 4/6 | 1/6 | |
| 4 | 1/8 | 3/8 | 3/8 | 1/8 |
| r | ε1 | W1 |
| 1 | 0.00 | 2.00 |
| 2 | 0.5773 | 1.00 |
| 3 | 0.00 | 0.8889 |
| 0.7746 | 0.5556 |
8 M
3 (a)
Find the natural frequency of axial vibrations of a bar of uniform cross section of 20 mm2 and length 1m. Take, E=2×105 N/mm2 and ρ=8000 kg/m3. Consider two linear elements.
10 M
3 (b)
Using Direct Stiffness method, determine the nodal displacements of stepped bar shown in figure. Take G=100 GPa.
10 M
4 (a)
Explain Lumped and consistent mass matrix.
6 M
4 (b)
Analysis the plane truss for nodal displacement, element stresses and strains. Take, P1=5 KN, P2=2 KN, E=180 GPa. A=6 cm2 for all elements.
14 M
5 (a)
Solve following differential equation \( \dfrac {d^2y}{dx^2}-10x^2 = 5 \ \ 0\le x \le 1 \)
BCs: y(0)=y(1)=0. Using Rayleigh-Ritz method, mapped over entire domain using one parameter method.
BCs: y(0)=y(1)=0. Using Rayleigh-Ritz method, mapped over entire domain using one parameter method.
12 M
5 (b)
Find the shape function for two dimensional eight noded element.
8 M
6 (a)
Coordinates of nodes of a quadrilateral element are as shown in the figure below. Temperature distribution at each node is computed as T1=100°C, T2=60°C, T3=50° C and T4=90°C. Compute temperature at point P{2.5, 2.5}
10 M
6 (b)
What are the h and p version of finite element method?
7 M
6 (c)
Convergence requirement.
3 M
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