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Finite Element Analysis - Dec 2015
Mechanical Engineering (Semester 6)
TOTAL MARKS: 80
TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.
(2) Attempt any three from the remaining questions.
(3) Assume data if required.
(4) Figures to the right indicate full marks.
1 (a) Explain applications of FEA in various fields.(5 marks)
1 (b) State different types of Boundary conditions.(5 marks)
1 (c) Explain with sketches: type of elements.(5 marks)
1 (d) Explain Shape function graphically for one dimensional Linear and quadratic element.(5 marks)
1 (e) Explain Gauss Elimination Method using an example.(5 marks)
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 marks)
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
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 |
BCs: y(0)=y(1)=0. Using Rayleigh-Ritz method, mapped over entire domain using one parameter method.(12 marks) 5 (b) Find the shape function for two dimensional eight noded element.(8 marks) 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 marks) 6 (b) What are the h and p version of finite element method?(7 marks) 6 (c) Convergence requirement.(3 marks)