ALPHA COLLEGE OF ENGINEERING(A Christian Minority Institution

Approved by AICTE & affiliated to Anna University & ISO Certified)Thirumazhisai, Chennai-600 124.

MODEL EXAMINATION Reg.No:

Sub. Code ME 6603 Sub. Name Finite Element AnalysisDepartment Mechanical Year/Sem III / VI

Date of Exam Session FNTime 3 hours Maximum 100 marks

PART -A (10x2=20 Marks)

Answer all Questions

1. What is meant by node or joint? List the types of nodes.2. What is Galerkin method of approximation?3. List the characteristics of shape functions.4. What is meant by longitudinal& transverse vibration?5. Sketch a 4 node quadrilateral element along with nodal degree of freedom.6. Write down the nodal displacement equations for a 2D triangular element7. Write short notes on axisymmetric problems?8. Write down the shape functions for an axisymmetric triangular element.9. Write the Gauss points and weights for 2 point formula of numerical integration.10. What is the function of processor?

PART -B (5x16= 80 Marks)

11(a) The following differential equation is available for a physical phenomenon (d2y/dx2)+50=0, 0≤x≤10 Trail function is y = a1x (10-x) with B.C’s are y (0) =0, y (10) = 0 Find the value of the parameter ‘a1

’ by the following methods

(i) Point collocation (ii) Sub domain collocation (iii) Least squares and (iv) Galerkin. [ OR ] (b) (i) Find the solution of the initial-value problem (d2y/dx2) + (dy/dx) - 2y = 0 With B.C’s are y (0) =2, y’ (0) =5. (ii) Explain the general procedure of FEA .

12 (a) The stepped bar shown in fig. 1 is subjected to an increase in temperature, ΔT = 80° C. Determine the nodal displacements, element stresses in each element and reactions. Take P1 = 10 KN and P2 = 15 KN

[OR]

(b) A wall of 0.6m thickness having thermal conductivity of 1.2 W/m-k the wall is to be insulated with a material thickness of 0.06 m having an average thermal conductivity of 0.3 W/m-k. The inner surface temperature is 1000 ºC and outside of the insulation is exposed to atmospheric air at 30 ºC with heat transfer coefficient of 35 W/m² k. Calculate the nodal temperature using FEA.

13(a) Derive the stiffness matrix for the equilateral triangular element with plane stress conditions shown in fig 14 (a).Prove that the resulting stiffness matrix is singular. Assume v = 0.3

[OR]

(b) (i) Obtain the shape functions of eight noded rectangular element. (ii) Derive the stiffness matrix of 2D heat transfer element.

14 (a) Derive the following elasticity equations (i) Strain-Displacement relationship equations

(ii) Equlibrium Equations [OR] (b)(i) The (r, z) co-ordinates of nodes i, j and k of an axisymmetric triangular element are given

by (3,4), (6,5) and (5, 8) cm respectively, determine the element stresses. Let E = 210Gpa

and v = 0.25. The displacement are u1 = 0.05 mm; w1 = 0.03 mm, u2 = 0.02 mm;

w2 = 0.02 mm, u3 = 0 ; w3 = 0 (10 Marks)

(ii) Write short notes on plate and shell element (6 Marks)

15 (a) A 4 noded rectangular elements whose coordinates are given by (0, 0), (2, 0), (2, 1) and

(0, 1). Determine the following (i) Jacobian matrix (ii) Strain-displacement matrix and

(iii) Element stresses. Take E = 2x105 N/mm2, v = 0.25,

u = (0, 0, 0.003, 0.004, 0.006,0.004, 0,0)T and ε =ή=0.Assume plane stress condition.

[OR]

(b) (i) Evaluate the Cartesian coordinates of point P which has the local coordinates of

ε =0.6, ή=0.8 for the isoparametric quadrilateral element which has the coordinates

(3, 4), (8, 5), (9, 9) and (5, 7) (10 Marks) (ii) Explain in detail about FEA analysis software. (6 Marks)