Table Of Content

EXTENDED FINITE ELEMENT METHOD WILEY SERIES IN COMPUTATIONAL MECHANICS SeriesAdvisors: RenédeBorst PerumalNithiarasu TayfunE.Tezduyar GenkiYagawa TarekZohdi ExtendedFiniteElementMethod: Khoei December2014 TheoryandApplications ComputationalFluid-StructureInteraction: Bazilevs,TakizawaandTezduyar January2013 MethodsandApplications IntroductiontoFiniteStrainTheoryfor HashiguchiandYamakawa November2012 ContinuumElasto-Plasticity NonlinearFiniteElementAnalysisofSolids DeBorst,Crisfield,Remmers August2012 andStructures,SecondEdition andVerhoosel AnIntroductiontoMathematicalModeling: Oden November2011 ACourseinMechanics ComputationalMechanicsofDiscontinua Munjiza,Knight,andRougier November2011 IntroductiontoFiniteElementAnalysis: SzabóandBabuška March2011 Formulation,Verification,andValidation EXTENDED FINITE ELEMENT METHOD THEORY AND APPLICATIONS Amir R. Khoei Sharif University of Technology, Iran Thiseditionfirstpublished2015 ©2015JohnWiley&Sons,Ltd. 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Extendedfiniteelementmethod:theoryandapplications/AmirR.Khoei. pages cm Includesbibliographicalreferencesandindex. ISBN978-1-118-45768-9(cloth) 1. Finiteelementmethod. 2. Numericalanalysis. I. Title. II. Title:Finiteelementmethod. TA347.F5K5452015 620.1'1260151825–dc23 2014029615 Setin9/11ptTimesbySPiPublisherServices,Pondicherry,India 1 2015 To Azadeh and Arsalan Contents SeriesPreface xv Preface xvii 1 Introduction 1 1.1 Introduction 1 1.2 AnEnrichedFiniteElementMethod 3 1.3 AReviewonX-FEM:DevelopmentandApplications 5 1.3.1 CouplingX-FEMwiththeLevel-SetMethod 6 1.3.2 LinearElasticFractureMechanics(LEFM) 7 1.3.3 CohesiveFractureMechanics 11 1.3.4 CompositeMaterialsandMaterialInhomogeneities 14 1.3.5 Plasticity,Damage,andFatigueProblems 16 1.3.6 ShearBandLocalization 19 1.3.7 Fluid–StructureInteraction 19 1.3.8 FluidFlowinFracturedPorousMedia 20 1.3.9 FluidFlowandFluidMechanicsProblems 22 1.3.10 PhaseTransitionandSolidification 23 1.3.11 ThermalandThermo-MechanicalProblems 24 1.3.12 PlatesandShells 24 1.3.13 ContactProblems 26 1.3.14 TopologyOptimization 28 1.3.15 PiezoelectricandMagneto-ElectroelasticProblems 28 1.3.16 Multi-ScaleModeling 29 2 ExtendedFiniteElementFormulation 31 2.1 Introduction 31 2.2 ThePartitionofUnityFiniteElementMethod 33 2.3 TheEnrichmentofApproximationSpace 35 2.3.1 IntrinsicEnrichment 35 2.3.2 ExtrinsicEnrichment 36 2.4 TheBasisofX-FEMApproximation 37 2.4.1 TheSignedDistanceFunction 39 2.4.2 TheHeavisideFunction 43 2.5 BlendingElements 46 2.6 GoverningEquationofaBodywithDiscontinuity 49 2.6.1 TheDivergenceTheoremforDiscontinuousProblems 50 2.6.2 TheWeakformofGoverningEquation 51 viii Contents 2.7 TheX-FEMDiscretizationofGoverningEquation 53 2.7.1 NumericalImplementationofX-FEMFormulation 55 2.7.2 NumericalIntegrationAlgorithm 57 2.8 ApplicationofX-FEMinWeakandStrongDiscontinuities 60 2.8.1 ModelinganElasticBarwithaStrongDiscontinuity 61 2.8.2 ModelinganElasticBarwithaWeakDiscontinuity 63 2.8.3 ModelinganElasticPlatewithaCrackInterfaceatitsCenter 66 2.8.4 ModelinganElasticPlatewithaMaterialInterfaceatitsCenter 68 2.9 HigherOrderX-FEM 70 2.10 ImplementationofX-FEMwithHigherOrderElements 73 2.10.1 HigherOrderX-FEMModelingofaPlatewithaMaterialInterface 73 2.10.2 HigherOrderX-FEMModelingofaPlatewithaCurvedCrackInterface 75 3 EnrichmentElements 77 3.1 Introduction 77 3.2 TrackingMovingBoundaries 78 3.3 LevelSetMethod 81 3.3.1 NumericalImplementationofLSM 82 3.3.2 CouplingtheLSMwithX-FEM 83 3.4 FastMarchingMethod 85 3.4.1 CouplingtheFMMwithX-FEM 87 3.5 X-FEMEnrichmentFunctions 88 3.5.1 Bimaterials,Voids,andInclusions 88 3.5.2 StrongDiscontinuitiesandCrackInterfaces 91 3.5.3 BrittleCracks 93 3.5.4 CohesiveCracks 97 3.5.5 PlasticFractureMechanics 99 3.5.6 MultipleCracks 101 3.5.7 FractureinBimaterialProblems 102 3.5.8 PolycrystallineMicrostructure 106 3.5.9 Dislocations 111 3.5.10 ShearBandLocalization 113 4 BlendingElements 119 4.1 Introduction 119 4.2 ConvergenceAnalysisintheX-FEM 120 4.3 Ill-ConditioningintheX-FEMMethod 124 4.3.1 One-DimensionalProblemwithMaterialInterface 126 4.4 BlendingStrategiesinX-FEM 128 4.5 EnhancedStrainMethod 130 4.5.1 AnEnhancedStrainBlendingElementfortheRampEnrichmentFunction 132 4.5.2 AnEnhancedStrainBlendingElementforAsymptotic EnrichmentFunctions 134 4.6 TheHierarchicalMethod 135 4.6.1 AHierarchicalBlendingElementforDiscontinuousGradientEnrichment 135 4.6.2 AHierarchicalBlendingElementforCrackTipAsymptoticEnrichments 137 4.7 TheCutoffFunctionMethod 138 4.7.1 TheWeightedFunctionBlendingMethod 140 4.7.2 AVariantoftheCutoffFunctionMethod 142 4.8 ADGX-FEMMethod 143