(AUTONOMOUS)
B. Tech VII Semester Supplementary Examinations, May 2018
(Regulations: VCE-R11/R11A)
FINITE ELEMENTS METHODS IN CIVIL ENGINEERING
(Civil Engineering)
Date: 14 May, 2018 AN Time: 3 hours Max Marks: 75
Answer ONE question from each Unit
All Questions Carry Equal Marks
Unit I
1. Explain the basic steps in the formulation of finite element analysis with suitable
examples.
10M
Compare FEM with other methods of solving engineering problems.
5M
2. State and explain the principle of minimum potential energy. 5M
using Raleigh-Ritz method, find the deflection at the free end of a cantilever beam of
length subjected to point load at the free end.
10M
Unit II
3. Find the nodal displacements, stresses in the thickest section and left support reaction for
structure shown in Fig.1.
Fig.1
15M
4. Explain the term shape function. Why polynomial terms are used for shape function in
finite element method.
7M
Using generalized coordinate approach, find shape functions for 2 noded bar/truss
element.
8M
Unit III
5. Derive the shape function for Linear Strain Triangle element. Use natural coordinate
system. Plot the variation of shape functions.
15M
6. Distinguish between local and natural coordinate system. 6M
Determine the N1, N2, N3 for a triangular element shown in Fig.2. The x coordinate of
interior point is 3.85 and y coordinate of interior point is 4.8.
Fig.2
9M
Cont…2
2
Unit IV
7. Explain Iso-parametric, sub-parametric and super-parametric elements. 6M
Derive Jacobian matrix for CST element.
9M
8. Differentiate between Lagrangian and serendipity elements with suitable examples. 7M
Write the shape functions 8 noded iso-parametric quadrilateral element.
8M
Unit V
9.
Evaluate the integral .
6M
Explain briefly static condensation.
7M
10. Explain in detail full integration and under integration methods. 5M
Derive the element stiffness matrix for a four noded axisymmetric element. 10M