November 11, 2004 16:12 Reddy Reddy66855FMAN INTRODUCTIONTO THEFINITE ELEMENT METHODNovember 11, 2004 16:12 Reddy Reddy66855FMMcGraw-Hill Series in Mechanical EngineeringAlciatore and Histand: Introduction to Mechatronics and Measurement SystemsAnderson: Computational Fluid Dynamics: The Basics with ApplicationsAnderson: Fundamentals of AerodynamicsAnderson: Introduction to FlightAnderson: Modern Compressible FlowBarber: Intermediate Mechanics of MaterialsBeer/Johnston: Vector Mechanics for EngineersBeer/Johnston/DeWolf: Mechanics of MaterialsBudynas: Advanced Strength and Applied Stress AnalysisCengel and Boles: Thermodynamics: An Engineering ApproachCengel and Turner: Fundamentals of Thermal-Fluid SciencesCengel: Heat Transfer: A Practical ApproachCengel: Introduction to Thermodynamics & Heat TransferCrespo da Silva: Intermediate DynamicsDieter: Engineering Design: A Materials & Processing ApproachDieter: Mechanical MetallurgyDoebelin: Measurement Systems: Application & DesignDunn: Measurement & Data Analysis for Engineering & ScienceEDS, Inc.: I-DEAS Student GuideHamrock/Schmid/Jacobson: Fundamentals of Machine ElementsHeywood: Internal Combustion Engine FundamentalsHolman: Experimental Methods for EngineersHolman: Heat TransferHutton: Fundamentals of Finite Element AnalysisKays/Crawford/Weigand: Convective Heat and Mass TransferMeirovitch: Fundamentals of VibrationsNorton: Design of MachineryPalm: System DynamicsReddy: An Introduction to the Finite Element MethodSchaffer et al.: The Science and Design of Engineering MaterialsSchey: Introduction to Manufacturing ProcessesShames: Mechanics of FluidsShigley/Mischke/Budynas: Mechanical Engineering DesignSmith: Foundations of Materials Science and EngineeringSuryanarayana and Arici: Design and Simulation of Thermal SystemsTurns: An Introduction to Combustion: Concepts and ApplicationsUgural: Mechanical Design: An Integrated ApproachUllman: The Mechanical Design ProcessWhite: Fluid MechanicsWhite: Viscous Fluid FlowZeid: Mastering CAD/CAMNovember 11, 2004 16:12 Reddy Reddy66855FMAn Introduction to theFinite Element MethodThird EditionJ. N. REDDYDepartment of Mechanical EngineeringTexas A&M UniversityCollege Station, Texas, USA 77843Boston Burr Ridge, IL Dubuque, IA Madison, WI New York San Francisco St. LouisBangkok Bogot Caracas Kuala Lumpur Lisbon London Madrid Mexico CityMilan Montreal New Delhi Santiago Seoul Singapore Sydney Taipei TorontoNovember 11, 2004 16:12 Reddy Reddy66855FMAN INTRODUCTION TO THE FINITE ELEMENT METHOD, THIRD EDITIONPublished by McGraw-Hill, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of the Americas,New York, NY 10020. Copyright c 2006, 1993, 1984 by The McGraw-Hill Companies, Inc. All rights reserved.No part of this publication may be reproduced or distributed in any form or by any means, or stored in a databaseor retrieval system, without the prior written consent of The McGraw-Hill Companies, Inc., including, but notlimited to, in any network or other electronic storage or transmission, or broadcast for distance learning.Some ancillaries, including electronic and print components, may not be available to customersoutside the United States.This book is printed on acid-free paper.1234567890QPF/QPF 0987654ISBN 0-07-246685-5Senior Sponsoring Editor: Suzanne JeansDevelopmental Editor: Amanda J. GreenSenior Marketing Manager: Mary K. KittellProject Manager: Peggy S. LucasSenior Production Supervisor: Kara KudronowiczMedia Technology Producer: Eric A. WeberSenior Coordinator of Freelance Design: Michelle D. WhitakerCover Designer: Rebidas Design & AssociatesLead Photo Research Coordinator: Carrie K. BurgerSupplement Producer: Brenda A. ErnzenCompositor: International Typesetting and CompositionTypeface: 10 Computer Modern (cmr 10)Printer: Quebecor World Fairfield, PA(USE) Cover Images: Pinched Cylinder image is generated by the data included in the paper “Least-squaresfinite element formulation for shear-deformable shells,” by J. P. Pontaza and J. N. Reddy,Computer Methods in Applied Mechanics and Engineering, 2004.Connecting Rod image courtesy of MSC.SoftwareCorporation. www.mscsoftware.comLibrary of Congress Cataloging-in-Publication DataReddy, J. N. (Junuthula Narasimha), 1945An introduction to the finite element method / J. N. Reddy.3rd ed.p. cm.(McGraw-Hill series in mechanical engineering)Includes bibliographical references and index.ISBN 0-07-246685-51. Finite element method. I. Title. II. Series.TA347.F5R4 2006620prime.001prime51825dc22 2004058177www.mhhe.comNovember 11, 2004 16:12 Reddy Reddy66855FMABOUT THE AUTHORJ. N. Reddy is a Distinguished Professor and the inaugural holder of the Oscar S. WyattEndowed Chair in the Department of Mechanical Engineering at Texas A&M University,College Station, Texas. Prior to his current position, he worked as a postdoctoral fellow atthe University of Texas at Austin, as a rese