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1. Code: 12D88105
M.Tech I Semester Supplementary Examinations September/October 2015
FEA IN THERMAL ENGINEERING
(Thermal Engineering)
(For students admitted in 2011, 2012, 2013 & 2014 only)
Time: 3 hours Max. Marks: 60
Answer any FIVE questions
All questions carry equal marks
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1 (a) List the advantages and disadvantages of FEM over other traditional variational methods.
(b) Derive the finite element equation using the potential energy approach.
2 (a) Derive shape functions for 1D two noded bar element. Hence explain the conditions that the
shape function has to satisfy.
(b) Write a note on the polynomials involved in linear, quadratic & cubic 1D element.
3 A square plate of 400 cm x 400 cm is subjected to a uniformly distributed load of 5.88 kN/m2
.
The elastic constants used are E = 2 x 103
kN/cm2
and Poison’s ratio is 0.15. If the boundary is
simply supported, then calculate the stresses developed in it.
4 (a) Write the basic equations for 3D problem in stress analysis.
(b) Derive inverse of the Jacobian transformation matrix for 3D tetrahedral elements.
5 (a) Derive the strain displacement matrix for an axi-symmetric triangular element.
(b) Discuss how an axi-symmetric problem may be modeled using triangular elements.
6 (a) Distinguish between consistent mass matrix and lumped mass matrix.
(b) Consider the Eigen value problem where
Compute the Eigen values & Eigen vectors.
7 Formulate the finite element equations for triangular torsion element shown below.
8 Write a short notes on:
(a) Preprocessing.
(b) Elements connecting.
(c) FEA application packages.
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j (12, 8)
i (5, 2)
k (2, 5)