##### FINITE ELEMENT METHOD AM 72501

Course Objectives:
To understand the basic steps of finite element methods, its applications and advantages. To develop the finite element model for discrete structural and non structural problems and continuum problems specially heat transfer, plane elasticity. To develop computer program and use commercial software for 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. 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

3. Continuum Problems(8 hours)
1. Variational method: virtual work, first variation of functional, variational formulation, Euler equation from functional, Ritz method
2. Weighted formulation: Galerkin, Petrov Galerkin, Least square, and point collocation method
3. Weak formulation

4. Interpolation Functions(6 hours)
1. Piecewise defined functions
2. One dimensional element
4. Two dimensional element
1. Triangular element
2. Rectangular element

5. Application in heat transfer and fluid mechanics(10 hours)
1. One dimensional conduction by finite Galerkin method.
2. One dimensional conduction with convection: finite element formulation by Galerkin and variational approach
3. Heat transfer in two dimensions: finite element formulation, internal heat generation, boundary conditions, symmetry, line and point source
4. One dimensional finite element formulation for fluid flow, fluid flow through hydraulic network
5. Two dimensional finite element formulation for fluid flow

6. Applications in Solid Mechanics(6 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:

1. Development of Computer programs for discrete structural problems (Bar, Truss, Beam and Frame).
2. Development of Computer program for discrete non-structural problems (Heat Transfer, Fluid Flow).
3. Development of Computer program for one dimensional continuum problems.
4. Development of Computer program for two dimensional continuum problems with one dependent variable.
5. Development of Computer program for two dimensional continuum problems with two dependent variables.
6. Development FEM model using parametric mapping.
7. 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.
2. D. V. Hutton, “Fundamentals of Finite Element Analysis”, Tata McGraw Hill Publishing Company Limited.
3. J. N. Reddy, “An Introduction to the Finite Element Method”, Tata McGraw Hill Publishing Company Limited.
4. A. Gilat, “MATLAB: An Introduction with Applications”, Wiley India.

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:

 Chapter Marks* 1 & 4 16 2 16 3 16 5 16 6 & 7 16 Total 80

*There might be minor deviation in marks distribution.