Hall Ticket No Question Paper Code: BST005
INSTITUTE OF AERONAUTICAL ENGINEERING
(Autonomous)
M.Tech II Semester End Examinations (Supplementary) January, 2019
Regulation: IARE-R16
FINITE ELEMENT METHOD

Time: 3 Hours Max Marks: 70
Answer ONE Question from each Unit
All Questions Carry Equal Marks
All parts of the question must be answered in one place only
UNIT I
1. Explain the steps involved in finite element method and von mises stress.
Obtain strain displacement relationship for an axi-symmetric element.
2. Explain the term Axi-Symmetric problems and give constitutive law for such problems.
Explain the terms 'Plane stress' and 'Plane strain' problems. Give constitutive laws for these
cases.
UNIT II
3. Derive the general equation for determining the stiffness of an element with usual notations in
the form.
s s s dV
Obtain an expression for strain displacement matrix for a rectangular element shown in Figure
1. Assuming plane stress condition with displacement matrix as 0.051, 0.076, 0.0152, 0.081,
determine the stresses at the centre of the rectangle shown.
Figure 1
4. Derive shape functions and their derivatives for two noded line element
Derive expressions for natural coordinates in a CST element. Show that they are nothing but
area coordinates.
UNIT III
5. Explain the isoparametric elements and their advantages.
Page 1 of 2
Using Lagrange polynomial find shape functions for Two noded bar element. Sketch the shape
function.
6. Derive Jacobian matrix four noded isoparametric element
Obtain strain displacement relation matrix for two dimensional triangular element.
UNIT IV
7. What are the assumptions in thin plate theory? Write the relation between forces and stresses
action on a thin plate.
Evaluate J,B and sigma matrix, assume plane stress condition for 4 noded rectangular element.

8. Describe briefly about Mindlin's theory of plates? List out the assumptions
Write the steps involved in obtaining Jacobian matrix and strain displacement relation matrix
for 4 noded shell element.
UNIT V
9. Explain iterative procedure and modified iterative procedure for the analysis of material nonlinearity
problems.
What are the basic methods for non linear analysis and explain?
10. Explain incremental procedure to handle geometric non-linear problems.
Explain about non linear applications to special structures.