Finite Element Method
Course Objectives:
 Understand the basic steps of finite element methods, its applications and advantages.
 Develop the finite element model for discrete structural and non structural problems.
 Develop the finite element model for continuum problems: heat transfer, plane elasticity.
 Develop computer program for above mentioned problems.
 Use commercial software to simulate above mentioned problems.
 Overview[2 hours]
 Introduction
 Brief history
 Mathematical modeling of the physical system
 FEM Analysis Process
 FEM Steps
 Applications of the Finite Element Method
 Advantages of the Finite Element Method
 Mathematical Background[2 hours]
 Vector analysis
 Matrix theory
 Differential Equations
 Direct Stiffness Method: Discrete Finite Elements[8 hours]
 Spring/Bar Element
 Truss Element
 Beam Element
 Frame Element
 Analogous problems in one dimension
 Continuum Problems[8 hours]
 Ritz Method
 Method of Weighted residuals
 Strong and Weak formulation
 Interpolation Functions[10 hours]
 Piecewise defined functions
 One dimensional element
 Two dimensional element
 Triangular element
 Rectangular element
 Variation approach
 Applications in Solid Mechanics[10 hours]
 Plane stress
 Plane strain
 3 dimensional element
 Axisymmetric stress analysis
 Thermal stress analysis
 Higher order Elements[5 hours]
 Lagrange elements
 Serendipity elements
 Parametric Mapping
Practical (Programming/Projects)
Development of Computer programs for discrete structural problems (Bar, Truss, Beam and Frame).
 Development of Computer program for discrete nonstructural problems (Heat Transfer, Fluid Flow).
 Development of Computer program for one dimensional continuum problems.
 Development of Computer program for two dimensional continuum problems with one dependent variable.
 Development of Computer program for two dimensional continuum problems with two dependent variables.
 Development FEM model using parametric mapping.
 Use of commercial software for heat transfer and stress analysis.
References:
 D. L. Logan: A First Course in the Finite Element Method, Thomson India Edition, 2007.
 D. V. Hutton: Fundamentals of Finite Element Analysis, Tata McGraw Hill Publishing Company Limited, 2007.
 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:
Chapters 
Hours 
Marks Distributions* 
1 & 2 
4 
8 
3 
8 
14 
4 
8 
14 
5 
10 
18 
6 
10 
18 
7 
5 
8 
Total 
45 
80 
*Note: There may be minor deviation in marks distribution.
