##### FINITE ELEMENT ANALYSIS

Course Objective
Study of Finite Element makes student capable to solve and analysis structural problems, evaluation of displacement (Strain), Stress and operating phenomena of body under different boundary conditions.

Course Outline

1. Introduction to FEM (6 hours)
1. Need for Sue of FEM – Advantages and Disadvantages of FEM Matrix Algebra
2. Terminologies Relating to Matrices, Methods of Solution of Linear Algebraic Equations.
3. Eigen Values and Eigen Vectors,
4. Simple Numeric
5. Gaussian Quadrature – 1 Pt. 2pt and 3pt Formula.

2. Basic of Theory of Elasticity (6 hours)
1. Definition of Stress And Strain,
2. Stress-Strain Relations;
3. Strain-Displacement
4. Relations in 2D And 3D Cartesian and Polar Coordinates.

3. Continuum Methods (7 hours)
1. Variational Methods Rayleigh-Ritz Methods Applied to Simple Problems on Axially Loaded Members Cantilever.
2. Simply Supported and Fixed Beam with Point Loads and UDL
3. Galerkin Method as Applied to Simple Elasticity Problem.

4. FEM-Basic Definitions (6 hours)
1. Displacement Method, Nodal Degrees of Freedom, Different Coordinate Systems, Shape Functions.
2. Lagrangian Polynomial; Complete Formulation of Bar, Truss, beam, Triangular, Quadrilateral, Tetrahedral, Hexahedral Elements.

5. Boundary Conditions (7 hours)
1. SPC and MPC.
2. Methods of Handling Boundary Conditions Eliminating
3. Method-Penalty Method.
4. Simple Numericals,
5. ISO Parametric Sub Parametric
6. Super Parametric Elements Convergence Criteria –
7. Requirements of Convergence of a Displacement Model.

6. Higher Order Elements (7 hours)
2. Tetrahedral and Hexahedral Elements
3. (Non-Formulation) – Pascal Triangle – Pascal Pyramid.
4. Introduction to Axis Symmetric Problems-Formulation of Axis Symmetric Triangular Element.

7. Dynamic Analysis (6 hours)
1. Formulating-Element Mass Matrics for 1D and 2D Element, Computation of Eigen Value and Vector for Simple One Dimensional Analysis.
2. One Dimensional Steady State Heat Conduction Formulation of 1D Element
3. Simple Numerical Using 1D Element. Structure of a Commercial FE Package.
4. Pre-Processor. Solver Post Processor.

Practical:
Use any kind of software for analysis of different types of material properties i.e. CATIA, ANSYS 12.0, STAD, RESA, MATLAB.

1. Learn and practice to define boundary condition, mesh etc.
2. Analysis under UDL Point load in different boundary condition.
3. Analysis of dynamic parts and equipments.
4. Operation
5. More exercise concerning the analysis of material if available
6. Connect different body part.

Reference Books:

1. Daryl. L. Logon - A First course in Finite Element methods Thomson Learning 3rd edition. 2001.
2. Hutton Fundamentals of Finite Element method – Mc Graw Hill,2004.
3. Robert Cook etal Concepts & applications of FEA – Jonh willey& sons 2002.
4. J.N.Reddy – Finite Element Method – Tat McGraw Hill edition2002.
5. Chandraupatla andBelegundu Introduction to Finite elements in engineering– Pearson edn, 2002.

Evaluation Scheme:
The Questions will cover all the chapters in the syllabus. The evaluation scheme will be as indicated in the table below:

 Unit Chapters Hour Mark Distribution* 1 Introduction to FEM 6 8 2 Basic of Theory of Elasticity 6 12 3 Continuum Methods 7 12 4 Basic Definitions 6 12 5 Boundary Conditions 7 12 6 Higher Order Elements 7 12 7 Dynamic Analysis 6 12 Total 45 80

*There could be minor deviation in mark distribution.