Finite Element Method

Course Objectives:

1. Understand the basic steps of finite element methods, its applications and advantages.
2. Develop the finite element model for discrete structural and non structural problems.
3. Develop the finite element model for continuum problems: heat transfer, plane elasticity.
4. Develop computer program for above mentioned problems.
5. Use commercial software to simulate above mentioned problems.

1. Overview[2 hours]
1. Introduction
2. Brief history
3. Mathematical modeling of the physical system
4. FEM Analysis Process
5. FEM Steps
6. Applications of the Finite Element Method
7. Advantages of the Finite Element Method


2. Mathematical Background[2 hours]
1. Vector analysis
2. Matrix theory
3. Differential Equations


3. Direct Stiffness Method:  Discrete Finite Elements[8 hours]
1. Spring/Bar Element
2. Truss Element
3. Beam Element
4. Frame Element
5. Analogous problems in one dimension


4. Continuum Problems[8 hours]
1. Ritz Method
2. Method of Weighted residuals
3. Strong and Weak formulation


5. Interpolation Functions[10 hours]
1. Piecewise defined functions
2. One dimensional element
3. Two dimensional element
1. Triangular element
2. Rectangular element
4. Variation approach


6. Applications in Solid Mechanics[10 hours]
1. Plane stress
2. Plane strain
3. 3 dimensional element
4. Axisymmetric stress analysis
5. Thermal stress analysis


7. Higher order Elements[5 hours]
1. Lagrange elements
2. Serendipity elements
3. Parametric Mapping

Practical (Programming/Projects)
Development of Computer programs for discrete structural problems (Bar, Truss, Beam and Frame).

1. Development of Computer program for discrete non-structural problems (Heat Transfer, Fluid Flow).
2. Development of Computer program for one dimensional continuum problems.
3. Development of Computer program for two dimensional continuum problems with one dependent variable.
4. Development of Computer program for two dimensional continuum problems with two dependent variables.
5. Development FEM model using parametric mapping.
6. Use of commercial software for heat transfer and stress analysis.

References:

1. D. L. Logan: A First Course in the Finite Element Method, Thomson India Edition, 2007.
2. D. V. Hutton: Fundamentals of Finite Element Analysis, Tata McGraw Hill Publishing Company Limited, 2007.
3. J. N. Reddy: An Introduction to the Finite Element Method, Tata McGraw Hill Publishing Company Limited, 2006.

Evaluation Scheme:
There will be questions covering all the chapters in the syllabus. The evaluation scheme for the questions will be indicated in the table below: