Kobelev, V: Design and Analysis of Composite Structures for (Automotive Series)

385 Pages·2019·10.325 MB·English

by  Vladimir Kobelev

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DesignandAnalysisofCompositeStructuresforAutomotiveApplications
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Design and Analysis of Composite Structures for
Automotive Applications
ChassisandDrivetrain
VladimirKobelev
DepartmentofNaturalSciences,UniversityofSiegen,Germany
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Thiseditionfirstpublished2019
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LibraryofCongressCataloging-in-PublicationData
Names:Kobelev,Vladimir,1959-author.
Title:Designandanalysisofcompositestructuresforautomotive
applications:chassisanddrivetrain/VladimirKobelev,Departmentof
NaturalSciences,UniversityofSiegen,Germany.
Description:Firstedition.|Hoboken,NJ:Wiley,2019.|Series:Automotive
series|Includesbibliographicalreferencesandindex.|
Identifiers:LCCN2019005286(print)|LCCN2019011866(ebook)|ISBN
9781119513841(AdobePDF)|ISBN9781119513865(ePub)|ISBN9781119513858
(hardback)
Subjects:LCSH:Automobiles–Chassis.|Automobiles–Powertrains.|
Automobiles–Designandconstruction.
Classification:LCCTL255(ebook)|LCCTL255.K6352019(print)|DDC
629.2/4–dc23
LCrecordavailableathttps://lccn.loc.gov/2019005286
CoverDesign:Wiley
CoverImages:©VladimirKobelev,Background:©solarseven/ShuWerstock
Setin10/12ptWarnockProbySPiGlobal,Chennai,India
PrintedandboundbyCPIGroup(UK)Ltd,Croydon,CR04YY
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v
Contents
Foreword xiii
SeriesPreface xv
ListofSymbolsandAbbreviations xvii
Introduction xxiii
AbouttheCompanionWebsite xxxv
1 ElasticAnisotropicBehaviorofCompositeMaterials 1
1.1 AnisotropicElasticityofCompositeMaterials 1
1.1.1 FourthRankTensorNotationofHooke’sLaw 1
1.1.2 Voigt’sMatrixNotationofHooke’sLaw 2
(cid:2) 1.1.3 Kelvin’sMatrixNotationofHooke’sLaw 5 (cid:2)
1.2 UnidirectionalFiberBundle 7
1.2.1 ComponentsofaUnidirectionalFiberBundle 7
1.2.2 ElasticPropertiesofaUnidirectionalFiberBundle 7
1.2.3 EffectiveElasticConstantsofUnidirectionalComposites 8
1.3 RotationalTransformationsofMaterialLaws,StressandStrain 10
1.3.1 RotationofFourthRankElasticityTensors 11
1.3.2 RotationofElasticityMatricesinVoigt’sNotation 11
1.3.3 RotationofElasticityMatricesinKelvin’sNotation 13
1.4 ElasticityMatricesforLaminatedPlates 14
1.4.1 Voigt’sMatrixNotationforAnisotropicPlates 14
1.4.2 RotationofMatricesinVoigt’sNotation 15
1.4.3 Kelvin’sMatrixNotationforAnisotropicPlates 15
1.4.4 RotationofMatricesinKelvin’sNotation 16
1.5 CouplingEffectsofAnisotropicLaminates 17
1.5.1 OrthotropicLaminateWithoutCoupling 17
1.5.2 AnisotropicLaminateWithoutCoupling 17
1.5.3 AnisotropicLaminateWithCoupling 17
1.5.4 CouplingEffectsinLaminatedThin-WalledSections 18
1.6 Conclusions 18
References 19
2 PhenomenologicalFailureCriteriaofComposites 21
2.1 PhenomenologicalFailureCriteria 21
2.1.1 CriteriaforStaticFailureBehavior 21
2.1.2 StressFailureCriteriaforIsotropicHomogenousMaterials 21
2.1.3 PhenomenologicalFailureCriteriaforComposites 22
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2.1.4 PhenomenologicalCriteriaWithoutStressCoupling 23
2.1.4.1 CriterionofMaximumAveragedStresses 23
2.1.4.2 CriterionofMaximumAveragedStrains 24
2.1.5 PhenomenologicalCriteriawithStressCoupling 24
2.1.5.1 Mises–HillAnisotropicFailureCriterion 24
2.1.5.2 Pressure-SensitiveMises–HillAnisotropicFailureCriterion 26
2.1.5.3 Tensor-PolynomialFailureCriterion 27
2.1.5.4 Tsai–WuCriterion 30
2.1.5.5 AssessmentofCoefficientsinTensor-PolynomialCriteria 30
2.2 DifferentiatingCriteria 33
2.2.1 FiberandIntermediateBreakCriteria 33
2.2.2 HashinStrengthCriterion 33
2.2.3 DelaminationCriteria 35
2.3 PhysicallyBasedFailureCriteria 35
2.3.1 PuckCriterion 35
2.3.2 CuntzeCriterion 36
2.4 RotationalTransformationofAnisotropicFailureCriteria 37
2.5 Conclusions 40
References 40
3 MicromechanicalFailureCriteriaofComposites 45
3.1 PulloutofFibersfromtheElastic-PlasticMatrix 45
(cid:2) 3.1.1 AxialTensionofFiberandMatrix 45 (cid:2)
3.1.2 ShearStressesinMatrixCylinders 51
3.1.3 CoupledElongationofFibersandMatrix 53
3.1.4 FailuresinMatrixandFibers 54
3.1.4.1 EquationsforMeanAxialDisplacementsofFibersandMatrix 54
3.1.4.2 SolutionsofEquationsforMeanAxialDisplacementsofFibersand
Matrix 56
3.1.5 RuptureofMatrixandPulloutofFibersfromCrackEdgesinaMatrix 57
3.1.5.1 ElasticElongation(CaseI) 57
3.1.5.2 PlasticSlidingontheFiberSurface(CaseII) 58
3.1.5.3 FiberBreakage(CaseIII) 58
3.1.6 RuptureofFibers,MatrixJointsandCrackEdges 59
3.2 CrackBridginginElastic-PlasticUnidirectionalComposites 60
3.2.1 CrackBridginginUnidirectionalFiber-ReinforcedComposites 60
3.2.2 MatrixCrackGrowth 61
3.2.3 FiberCrackGrowth 62
3.2.4 Penny-ShapedCrack 65
3.2.4.1 CrackinaTransversal-IsotropicMedium 65
3.2.4.2 MechanismsoftheFractureProcess 66
3.2.4.3 CrackBridginginanOrthotropicBodyWithDiskCrack 66
3.2.4.4 SolutiontoanAxiallySymmetricCrackProblem 68
3.2.5 PlaneCrackProblem 72
3.2.5.1 EquationsofthePlaneCrackProblem 72
3.2.5.2 SolutiontothePlaneCrackProblem 74
3.3 DebondingofFibersinUnidirectionalComposites 75
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3.3.1 AxialDeformationofUnidirectionalFiberComposites 75
3.3.2 StressesinUnidirectionalCompositeinCasesofIdealDebondingor
Adhesion 79
3.3.2.1 EquationsofanAxiallyLoadedUnidirectionalCompoundMedium(A) 79
3.3.2.2 TotalDebonding(B) 82
3.3.2.3 IdealAdhesion(C) 83
3.3.3 StressesinaUnidirectionalCompositeinaCaseofPartialDebonding 84
3.3.3.1 PartialRadialLoadontheFiberSurface 84
3.3.3.2 PartialRadialLoadontheMatrixCavitySurface 84
3.3.3.3 PartialDebondingWithCentralAdhesionRegion(D) 85
3.3.3.4 PartialDebondingWithCentralDebondingRegion(E) 88
3.3.3.5 Semi-InfiniteDebondingWithCentralDebondingRegion(F) 89
3.3.4 ContactProblemforaFiniteAdhesionRegion 89
3.3.5 DebondingofaSemi-InfiniteAdhesionRegion 93
3.3.6 DebondingofFibersfromaMatrixUnderCyclicDeformation 95
3.4 Conclusions 98
References 98
4 OptimizationPrinciplesforStructuralElementsMadeof
Composites 105
4.1 StiffnessOptimizationofAnisotropicStructuralElements 105
4.1.1 OptimizationProblem 105
(cid:2) 4.1.2 OptimalityConditions 106 (cid:2)
4.1.3 OptimalSolutionsinAnti-PlaneElasticity 109
4.1.4 OptimalSolutionsinPlaneElasticity 109
4.2 OptimizationofStrengthandLoadingCapacityofAnisotropic
Elements 110
4.2.1 OptimizationProblem 110
4.2.2 OptimalityConditions 113
4.2.3 OptimalSolutionsinAnti-PlaneElasticity 114
4.2.4 OptimalSolutionsinPlaneElasticity 114
4.3 OptimizationofAccumulatedElasticEnergyinFlexibleAnisotropic
Elements 116
4.3.1 OptimizationProblem 116
4.3.2 OptimalityConditions 117
4.3.3 OptimalSolutionsinAnti-PlaneElasticity 118
4.3.4 OptimalSolutionsinPlaneElasticity 119
4.4 OptimalAnisotropyinaTwistedRod 119
4.5 OptimalAnisotropyofBendingConsole 122
4.6 OptimizationofPlatesinBending 123
4.7 Conclusions 125
References 125
5 OptimizationofCompositeDriveshaft 129
5.1 TorsionofAnisotropicShaftsWithSolidCross-Sections 129
5.2 Thin-WalledAnisotropicDriveshaftwithClosedProfile 132
5.2.1 GeometryofCross-Section 132
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5.2.2 MainKinematicHypothesis 133
5.3 DeformationofaCompositeThin-WalledRod 135
5.3.1 EquationsofDeformationofaAnisotropicThin-WalledRod 135
5.3.2 BoundaryConditions 138
5.3.2.1 IdealFixing 138
5.3.2.2 IdeallyFreeEnd 138
5.3.2.3 BoundaryConditionsoftheIntermediateType 140
5.3.3 GoverningEquationsinSpecialCasesofSymmetry 140
5.3.3.1 OrthotropicMaterial 140
5.3.3.2 ConstantElasticPropertiesAlongtheArcofaCross-Section 140
5.3.4 SymmetryofSection 140
5.4 BucklingofCompositeDriveshaftsUnderaTwistMoment 141
5.4.1 Greenhill’sBucklingofDriveshafts 141
5.4.2 OptimalShapeoftheSolidCross-SectionforDriveshaft 143
5.4.3 HollowCircularandTriangularCross-Sections 144
5.5 PatentsforCompositeDriveshafts 146
5.6 Conclusions 150
References 150
6 DynamicsofaVehiclewithRigidStructuralElementsofChassis 155
6.1 ClassificationofWheelSuspensions 155
6.1.1 CommonDesignsofSuspensions 155
(cid:2) 6.1.2 TypesofTwist-BeamAxles 156 (cid:2)
6.1.3 KinematicsofWheelSuspensions 157
6.2 FundamentalModelsinVehicleDynamics 159
6.2.1 BasicVariablesofVehicleDynamics 159
6.2.2 CoordinateSystemsofVehicleandLocalCoordinateSystems 161
6.2.2.1 Earth-FixedCoordinateSystem 161
6.2.2.2 Vehicle-FixedCoordinateSystem 162
6.2.2.3 HorizontalCoordinateSystem 162
6.2.2.4 WheelCoordinateSystem 162
6.2.3 AngleDefinitions 162
6.2.4 ComponentsofForceandMomentsinCarDynamics 163
6.2.5 DegreesofFreedomofaVehicle 163
6.3 ForcesBetweenTiresandRoad 167
6.3.1 TireSlip 167
6.3.2 SideSlipCurveandLateralForceProperties 168
6.4 DynamicEquationsofaSingle-TrackModel 170
6.4.1 HypothesesofaSingle-TrackModel 170
6.4.2 MomentsandForcesinaSingle-TrackModel 171
6.4.3 BalanceofForcesandMomentsinaSingle-TrackModel 173
6.4.4 SteadyCornering 174
6.4.4.1 NecessarySteerAngleforSteadyCornering 174
6.4.4.2 YawGainFactorandSteerAngleGradient 175
6.4.4.3 ClassificationofSelf-SteeringBehavior 176
6.4.5 Non-SteadyCornering 179
6.4.5.1 EquationsofNon-StationaryCornering 179
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6.4.5.2 OscillatoryBehaviorofVehicleDuringNon-SteadyCornering 180
6.4.6 Anti-RollBarsMadeofCompositeMaterials 181
6.5 Conclusions 182
References 182
7 DynamicsofaVehicleWithFlexible,AnisotropicStructuralElements
ofChassis 183
7.1 EffectsofBodyandChassisElasticityonVehicleDynamics 183
7.1.1 InfluenceofBodyStiffnessonVehicleDynamics 183
7.1.2 LateralDynamicsofVehiclesWithStiffRearAxles 184
7.1.3 InducedEffectsonWheelOrientationandPositioningofVehicleswith
FlexibleRearAxle 185
7.2 Self-SteeringBehaviorofaVehicleWithCouplingofBendingand
Torsion 188
7.2.1 CountersteeringforVehicleswithTwist-BeamAxles 188
7.2.1.1 CountersteeringMechanisms 188
7.2.1.2 CountersteeringbyAnisotropicCouplingofBendingandTorsion 190
7.2.2 Bending-TwistCouplingofaCountersteeringTwist-BeamAxle 192
7.2.3 RollAngleofVehicle 193
7.2.3.1 RelationshipBetweenRollAngleandCentrifugalForce 193
7.2.3.2 LateralReactionForcesonWheels 193
(cid:2) 7.2.3.3 SteerAnglesonFrontWheels 194 (cid:2)
7.2.3.4 SteerAnglesonRearWheels 194
7.3 SteadyCorneringofaFlexibleVehicle 196
7.3.1 StationaryCorneringofaCarWithaFlexibleChassis 196
7.3.2 NecessarySteerAnglesforCouplingandFlexibilityofChassis 196
7.3.2.1 LimitCase:LateralAccelerationVanishes 196
7.3.2.2 AbsolutelyRigidFrontandRearWheelSuspensions 197
7.3.2.3 BendingandTorsionofaTwistMemberCompletelyDecoupled 197
7.3.2.4 GeneralCaseofCouplingBetweenBendingandTorsionofaTwist
Member 198
7.3.2.5 NeutralSteeringCausedbyCouplingBetweenBendingandTorsionofa
TwistMember 198
7.4 EstimationofCouplingConstantforaTwistMember 199
7.4.1 CouplingBetweenVehicleRollAngleandTwistofCross-Member 199
7.4.2 StiffnessParametersofaTwist-BeamAxle 200
7.4.2.1 RollSpringRate 200
7.4.2.2 LateralStiffness 201
7.4.2.3 CamberStiffness 203
7.5 DesignoftheCountersteeringTwist-BeamAxle 203
7.5.1 RequirementsforaCountersteeringTwist-BeamAxle 203
7.5.2 SelectionandCalculationoftheCross-SectionfortheCross-Member 205
7.5.3 ElementsofaCountersteeringTwist-BeamAxle 208
7.6 PatentsonTwist-BeamAxles 211
7.7 Conclusions 214
References 214
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