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Finite Element Analysis

G. Lakshmi Narasaiah
Prof. & Head Aeronautical Engineering Dept. MLR Institute of Technology Dundigal, Hyderabad 500 043 Formerly Senior Manager, Corp. R&D, BHEL Vikasnagar, Hyderabad 500 093

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BSP BS Publications
4-4-309, Giriraj Lane, Sultan Bazar, Hyderabad - 500 095 - AP. Phone: 040-23445688

Copyright © 2008, by Author All rights reserved /

Nopart of this book or parts thereof may be reproduced, stored in a retrieval system or transmitted in any language or by any means, electronic, mechanical, phototcopying, recording or otherwise without the prior written permission of the Author.

"This book references ANSYS software, Release (Ed 5.5) is used by the author and should not be considered the definitive source of information regardingthe ANSYS program. Please consult the ANSYS product documentation for the release of ANSYS with which you are working for the most current information ". Published by :

BSPBS Publications
4-4-309, Giriraj Lane, Sultan Bazar, Hyderabad - 500 095 - A. P. Phone: 040-23445688 Fax: 91+40-23445611

e-mail: contactus@bspublications.net

Pr;ntedat
Adithya Art Printers

Hyderabad.

ISBN:978-81-7800-140-1

Contents

Chapter 1

Introduction

1-34

1.1 Design and Analysis of a Component.. ............................................................ 1 1.2 Approximate Method vs. Exact Method ........................................................ 4 1.3 Weighted Residual Methods ........................................................................... 5 1.4 Variational Methodor Rayleigh - Ritz Method ............................................ 12 1.5 Principle of Minimum Potential Energy ........................................................ 22 1.6 Origin ofFEM .............................................................................................. 26 1.7 Principle ofFEM.......................................................................................... 27 1.8, Classification ofFEM ................................................................................... 31 1.9 Types of Analyses ........................................................................................ 32 1.10 Summary ....................................................................................................... 33

Objective Questions.................................................................................................. 33

Chapter 2 Matrix Operations

35-60

2.1 Types of Matrices ........................................................................................ 35 2.2 MatrixAlgebra ....................................................................... ~ ..................... 37

Contents

(xiv)

2.3 Detenninant.................................................................................................. 39 2.4 Inversion of a Matrix .................................................................................... 41 2.5 Methods of Solution of Simultaneous Equations .......................................... 41 2.5.1 2.5.2 2.5.3 By Inversion of the Coefficient Matrix............................................. 42 Direct Methods ................................................................................. 44 Iterative Methods .............................................................................. 53

2.6 Eigen Values and Eigen Vectors ................................................................... 55 2.7 Matrix Inversion Through Characteristic Equation...................................... 59 2.8 Summary ....................................................................................................... 60

Chapter 3 Theory of Elasticity 61-84

3.1 Degrees of Freedom .................................................................................... 61 3.2 Rigid Body Motion ...........................................................................................
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