Table Of Content

The Finite Element Method: A Practical Course “fm” — 2002/12/14 — page i — #1 ToZuona,Yun,Kun,Run,andmyfamily forthetimetheygavetome Tomyfellowstudents fortheircompanyinstudyingthissubject G.R.Liu Tomywife,Lingzhi,andmyfamily fortheirsupport Tomymentor,Dr.Liu forhisguidance S.S.Quek “fm” — 2002/12/14 — page ii — #2 The Finite Element Method: A Practical Course G. R. Liu S. S. Quek DepartmentofMechanicalEngineering, NationalUniversityofSingapore OXFORD AMSTERDAM BOSTON LONDON NEWYORK PARIS SANDIEGO SANFRANCISCO SINGAPORE SYDNEY TOKYO “fm” — 2002/12/14 — page iii — #3 Butterworth-Heinemann AnimprintofElsevierScience LinacreHouse,JordanHill,OxfordOX28DP 200WheelerRoad,BurlingtonMA01803 Firstpublished2003 Copyright©2003,ElsevierScienceLtd.Allrightsreserved Nopartofthispublicationmaybe reproducedinanymaterialform(including photocopyingorstoringinanymediumbyelectronic meansandwhetherornottransientlyorincidentally tosomeotheruseofthispublication)withoutthe writtenpermissionofthecopyrightholderexcept inaccordancewiththeprovisionsoftheCopyright, DesignsandPatentsAct1988orunderthetermsofa licenceissuedbytheCopyrightLicensingAgencyLtd, 90TottenhamCourtRoad,London,EnglandW1T4LP. Applicationsforthecopyrightholder’swrittenpermission toreproduceanypartofthispublicationshouldbe addressedtothepublishers BritishLibraryCataloguinginPublicationData AcataloguerecordforthisbookisavailablefromtheBritishLibrary LibraryofCongressCataloguinginPublicationData AcataloguerecordforthisbookisavailablefromtheLibraryofCongress ISBN0750658665 ForinformationonallButterworth-Heinemannpublicationsvisitourwebsiteatwww.bh.com “fm” — 2002/12/14 — page iv — #4 CONTENTS BiographicalInformation ix Preface xi 1 ComputationalModelling 1 1.1 Introduction 1 1.2 PhysicalProblemsinEngineering 3 1.3 ComputationalModellingusingtheFEM 4 1.4 Simulation 7 1.5 Visualization 9 2 IntroductiontoMechanicsforSolidsandStructures 12 2.1 Introduction 12 2.2 EquationsforThree-DimensionalSolids 13 2.3 EquationsforTwo-DimensionalSolids 19 2.4 EquationsforTrussMembers 22 2.5 EquationsforBeams 24 2.6 EquationsforPlates 28 2.7 Remarks 34 3 FundamentalsforFiniteElementMethod 35 3.1 Introduction 35 3.2 StrongandWeakForms 36 3.3 Hamilton’sPrinciple 37 3.4 FEMProcedure 38 3.5 StaticAnalysis 58 3.6 AnalysisofFreeVibration(EigenvalueAnalysis) 58 3.7 TransientResponse 60 3.8 Remarks 64 3.9 ReviewQuestions 65 v “fm” — 2002/12/14 — page v — #5 vi CONTENTS 4 FEMforTrusses 67 4.1 Introduction 67 4.2 FEMEquations 67 4.3 WorkedExamples 76 4.4 HighOrderOne-DimensionalElements 87 4.5 ReviewQuestions 88 5 FEMforBeams 90 5.1 Introduction 90 5.2 FEMEquations 90 5.3 Remarks 95 5.4 WorkedExamples 95 5.5 Casestudy:ResonantFrequenciesofMicroResonantTransducer 98 5.6 ReviewQuestions 107 6 FEMforFrames 108 6.1 Introduction 108 6.2 FEMEquationsforPlanarFrames 109 6.3 FEMEquationsforSpaceFrames 114 6.4 Remarks 120 6.5 CaseStudy:FiniteElementAnalysisofaBicycleFrame 121 6.6 ReviewQuestions 127 7 FEMforTwo-DimensionalSolids 129 7.1 Introduction 129 7.2 LinearTriangularElements 131 7.3 LinearRectangularElements 141 7.4 LinearQuadrilateralElements 148 7.5 HigherOrderElements 153 7.6 ElementswithCurvedEdges 160 7.7 CommentsonGaussIntegration 161 7.8 CaseStudy:SideDriveMicro-Motor 162 7.9 ReviewQuestions 171 8 FEMforPlatesandShells 173 8.1 Introduction 173 8.2 PlateElements 173 8.3 ShellElements 180 8.4 Remarks 184 8.5 CaseStudy:NaturalFrequenciesofMicro-Motor 185 8.6 CaseStudy:TransientAnalysisofaMicro-Motor 192 8.7 ReviewQuestions 198 “fm” — 2002/12/14 — page vi — #6 CONTENTS vii 9 FEMfor3DSolids 199 9.1 Introduction 199 9.2 TetrahedronElement 200 9.3 HexahedronElement 209 9.4 HigherOrderElements 216 9.5 ElementswithCurvedSurfaces 222 9.6 CaseStudy:StressandStrainAnalysisofaQuantumDot Heterostructure 223 9.7 ReviewQuestions 232 10 SpecialPurposeElements 233 10.1 Introduction 233 10.2 CrackTipElements 234 10.3 MethodsforInfiniteDomains 236 10.4 FiniteStripElements 242 10.5 StripElementMethod(SEM) 245 11 ModellingTechniques 246 11.1 Introduction 246 11.2 CPUTimeEstimation 247 11.3 GeometryModelling 248 11.4 Meshing 250 11.5 MeshCompatibility 254 11.6 UseofSymmetry 256 11.7 ModellingofOffsets 265 11.8 ModellingofSupports 270 11.9 ModellingofJoints 271 11.10 OtherApplicationsofMPCEquations 274 11.11 ImplementationofMPCEquations 278 11.12 ReviewQuestions 280 12 FEMforHeatTransferProblems 282 12.1 FieldProblems 282 12.2 WeightedResidualApproachforFEM 288 12.3 1DHeatTransferProblem 289 12.4 2DHeatTransferProblem 303 12.5 Summary 316 12.6 CaseStudy:TemperatureDistributionofHeatedRoadSurface 318 12.7 ReviewQuestions 321 “fm” — 2002/12/14 — page vii — #7 viii CONTENTS 13 UsingABAQUS© 324 13.1 Introduction 324 13.2 BasicBuildingBlock:KeywordsandDataLines 325 13.3 UsingSets 326 13.4 ABAQUSInputSyntaxRules 327 13.5 DefiningaFiniteElementModelinABAQUS 329 13.6 GeneralProcedures 339 References 342 Index 345 “fm” — 2002/12/14 — page viii — #8 BIOGRAPHICAL INFORMATION DR.G.R.LIU Dr. Liu received his PhD from Tohoku University, Japan in 1991. He was a Postdoctoral Fellow at Northwestern University, U.S.A. He is currently the Director of the Centre for AdvancedComputationsinEngineeringScience(ACES),National University of Singapore. He is also an Associate Professor at the Department of Mechanical Engineering, National University of Singapore. He authored more than 200 technical publications including two books and 160 international journal papers. He is therecipientoftheOutstandingUniversityResearchersAwards (1998), and the Defence Technology Prize (National award, 1999).HewontheSilverAwardatCrayQuest2000(Nationwide competition in 2000). His research interests include Computational Mechanics, Mesh- freeMethods, Nano-scaleComputation, VibrationandWavePropagationinComposites, MechanicsofCompositesandSmartMaterials,InverseProblemsandNumericalAnalysis. MR.S.S.QUEK Mr. Quek received his B. Eng. (Hon.) in mechanical engineer- ingfromtheNationalUniversityofSingaporein1999.Hedidan industrial attachment in the then aeronautics laboratory of DSO National Laboratories, Singapore, gaining much experience in using the finite element method in areas of structural dynam- ics. He also did research in the areas of wave propagation and infinite domains using the finite element method. In the course of his research, Mr Quek had gained tremendous experience in theapplicationsofthefiniteelementmethod, especiallyinusing commercially available software like Abaqus. Currently, he is doing research in the field of numerical simulation of quantum ix “fm” — 2002/12/14 — page ix — #9