The Finite Element Method: A Practical Course

365 Pages·2003·10.39 MB·English

by  S. S. Quek

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
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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
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Butterworth-Heinemann
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Firstpublished2003
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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
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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
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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
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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
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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
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