Hall Ticket No Question Paper Code: BST005
INSTITUTE OF AERONAUTICAL ENGINEERING
(Autonomous)
M.Tech II Semester End Examinations (Regular/ Supplementary) July, 2018
Regulation: IARE-R16
FINITE ELEMENT METHOD
(Structural Engineering)
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. Applying Rayleigh Ritz method, develop the force displacement relation and evaluate the nodal
displacements, support reactions and stresses in each element.
Figure 1
Classify the different types of elements with sketches and outline the application of these elements.

2. Analyze the tapering bar shown by using principle of minimum PE and determine the internal
forces in all the elements. Use three elements. E 200GPa Compare the solution with exact
results and comment. Both ends are fixed.
Figure 2
write the basic stress strain relations of a linear elastic materials in the finite element method.

UNIT II
3. Develop the shape functions for a two node beam element in cartesian coordinates and derive the
consistent load vector for a two node beam element shown below.
Page 1 of 2
Figure 3
Determine the shape functions for a Constant Strain Triangular element intermes of natural
coordinate systems. Take 3 nodes.
4. Discuss mesh refinement with higher order elements with suitable examples.
Illustrate with an example how numbering of nodes has to be carried out to minimize band width.

5. Develop the shape functions for a triangular element with six nodes with isoparametric formulation.

Applying Lagrangian's polynomials develop the shape functions for an 8 -noded brick element.

UNIT III
6. Develop an expression for strain displacement matrix and outline the procedure for developing
element stiffness matrix in plane stress linear rectangular element with isoparametric formulation.

Develop the strain displacement matrix for constant train triangle element with three nodes.

UNIT IV
7. Discuss the formulation of plate bending elements based on Kirchhoff's plate theory.
Discuss and write the basic relations in the thin plate theory with neat sketch.
8. Discuss the formulation of plate bending elements based on Mindlin'splate theory.
Explain the displacementmodels for plate analysis interms of continuity element.
UNIT V
9. Explain modified Newton Raphson method in nonlinear analysis.
Discuss convergence requirements in nonlinear analysis.
10. Explain how plasticity is considered in uniaxial stress with respect to nonlinear analysis.
What are the different non linear problems in finite element analysis ans explain.