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

3 (b) Using Direct Stiffness method, determine the nodal displacements of stepped bar shown in figure. Take G=100 GPa. (10 marks)

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 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)