کتاب آموزش تحلیل اجزای محدود کامپوزیتها با استفاده از نرم افزار Abaqus

شامل مثالهای حل شده فراوان با استفاده از FEM در نرم افزار اباکوس

در نظر داشته باشید این کتاب با قیمت پایینی که دارد صرفا جهت استفاده دانشجویان گرامی بوده و کپی ان شرعا و عرفا حرام است.

List of Examples xxix
1 Mechanics of Orthotropic Materials 1
1.1 LaminaCoordinateSystem ....................... 1
1.2 Displacements............................... 1
1.3 Strain ................................... 2
1.4 Stress ................................... 3
1.5 ContractedNotation ........................... 4
1.5.1 AlternateContractedNotation ................. 5
1.6 Equilibrium and Virtual Work . . . . ................. 6
1.7 Boundary Conditions . . . ........................ 8
1.7.1 Traction Boundary Conditions ................. 8
1.7.2 Free Surface Boundary Conditions . . . . . . . . ....... 8
1.8 ContinuityConditions .......................... 8
1.8.1 TractionContinuity ....................... 8
1.8.2 DisplacementContinuity..................... 9
1.9 Compatibility . . . . . . . ........................ 9
1.10 CoordinateTransformations....................... 10
1.10.1 StressTransformation ...................... 12
1.10.2 StrainTransformation ...................... 14
1.11 TransformationofConstitutiveEquations ............... 15
1.12 3DConstitutiveEquations........................ 17
1.12.1 AnisotropicMaterial ....................... 18
1.12.2 MonoclinicMaterial ....................... 19
1.12.3 OrthotropicMaterial....................... 20
1.12.4 TransverselyIsotropicMaterial ................. 21
1.12.5 IsotropicMaterial ........................ 23
vii
viii Finite Element Analysis of Composite Materials
1.13 EngineeringConstants .......................... 24
1.13.1 RestrictionsonEngineeringConstants ............. 27
1.14 From3DtoPlaneStressEquations................... 29
1.15 ApparentLaminateProperties ..................... 30
SuggestedProblems .............................. 32
2 Introduction to Finite Element Analysis 35
2.1 BasicFEMProcedure .......................... 35
2.1.1 Discretization........................... 36
2.1.2 ElementEquations........................ 36
2.1.3 ApproximationoveranElement ................ 37
2.1.4 InterpolationFunctions ..................... 38
2.1.5 ElementEquationsforaSpecificProblem ........... 40
2.1.6 AssemblyofElementEquations................. 41
2.1.7 Boundary Conditions . . . ................... 42
2.1.8 SolutionoftheEquations .................... 42
2.1.9 SolutionInsidetheElements .................. 42
2.1.10 DerivedResults.......................... 43
2.2 GeneralFiniteElementProcedure ................... 43
2.3 SolidModeling,Analysis,andVisualization .............. 46
2.3.1 ModelGeometry ......................... 47
2.3.2 MaterialandSectionProperties................. 57
2.3.3 Assembly ............................. 61
2.3.4 SolutionSteps .......................... 63
2.3.5 Loads ............................... 63
2.3.6 Boundary Conditions . . . ................... 65
2.3.7 MeshingandElementType ................... 68
2.3.8 SolutionPhase .......................... 70
2.3.9 Post-processingandVisualization................ 73
SuggestedProblems .............................. 89
3 Elasticity and Strength of Laminates 91
3.1 KinematicofShells............................ 92
3.1.1 First-OrderShearDeformationTheory............. 93
3.1.2 KirchhoffTheory......................... 97
3.1.3 Simply Supported Boundary Conditions ............ 99
3.2 FiniteElementAnalysisofLaminates ................. 100
3.2.1 ElementTypesandNamingConvention ............ 101
3.2.2 Thin(Kirchhoff)ShellElements ................ 104
3.2.3 ThickShellElements....................... 104
3.2.4 General-purpose(FSDT)ShellElements............ 104
3.2.5 ContinuumShellElements.................... 105
3.2.6 SandwichShells.......................... 106
3.2.7 NodesandCurvature ...................... 106
3.2.8 Drilling Rotation . . . . . . ................... 106
Table of Contents ix
3.2.9 A, B, D, H Input Data for Laminate FEA . . . . ....... 107
3.2.10 Equivalent Orthotropic Input for Laminate FEA ....... 113
3.2.11 LSSforMultidirectionalLaminateFEA ............ 119
3.2.12 FEAofPlyDrop-OffLaminates ................ 129
3.2.13 FEAofSandwichShells ..................... 139
3.2.14 ElementCoordinateSystem................... 150
3.2.15 Constraints ............................ 159
3.3 FailureCriteria .............................. 163
3.3.1 2DFailureCriteria........................ 163
3.3.2 3DFailureCriteria........................ 166
3.4 PredefinedFields ............................. 171
SuggestedProblems .............................. 173
4 Buckling 177
4.1 EigenvalueBucklingAnalysis ...................... 177
4.1.1 ImperfectionSensitivity ..................... 183
4.1.2 AsymmetricBifurcation ..................... 183
4.1.3 Post-criticalPath......................... 184
4.2 ContinuationMethods .......................... 187
SuggestedProblems .............................. 192
5 Free Edge Stresses 195
5.1 Poisson’sMismatch............................ 196
5.1.1 InterlaminarForce ........................ 196
5.1.2 InterlaminarMoment ...................... 197
5.2 Coefficient of Mutual Influence . . . . ................. 204
5.2.1 Interlaminar Stress due to Mutual Influence . . . ....... 207
SuggestedProblems .............................. 212
6 Computational Micromechanics 215
6.1 AnalyticalHomogenization ....................... 216
6.1.1 ReussModel ........................... 216
6.1.2 VoigtModel............................ 217
6.1.3 PeriodicMicrostructureModel ................. 217
6.1.4 TransverselyIsotropicAveraging ................ 218
6.2 NumericalHomogenization ....................... 220
6.3 Local-GlobalAnalysis .......................... 238
6.4 LaminatedRVE.............................. 241
SuggestedProblems .............................. 247
7 Viscoelasticity 249
7.1 ViscoelasticModels............................ 251
7.1.1 MaxwellModel .......................... 251
7.1.2 KelvinModel ........................... 252
7.1.3 StandardLinearSolid ...................... 253
x Finite Element Analysis of Composite Materials
7.1.4 Maxwell-KelvinModel...................... 253
7.1.5 PowerLaw ............................ 254
7.1.6 PronySeries ........................... 254
7.1.7 StandardNonlinearSolid .................... 256
7.1.8 NonlinearPowerLaw ...................... 256
7.2 BoltzmannSuperposition ........................ 258
7.2.1 LinearViscoelasticMaterial................... 258
7.2.2 UnagingViscoelasticMaterial.................. 259
7.3 CorrespondencePrinciple ........................ 260
7.4 FrequencyDomain ............................ 261
7.5 SpectrumRepresentation ........................ 262
7.6 MicromechanicsofViscoelasticComposites .............. 262
7.6.1 One-DimensionalCase...................... 262
7.6.2 Three-DimensionalCase..................... 264
7.7 MacromechanicsofViscoelasticComposites .............. 269
7.7.1 BalancedSymmetricLaminates................. 269
7.7.2 GeneralLaminates ........................ 269
7.8 FEAofViscoelasticComposites..................... 269
SuggestedProblems .............................. 280
8 Continuum Damage Mechanics 283
8.1 One-DimensionalDamageMechanics.................. 284
8.1.1 DamageVariable ......................... 284
8.1.2 Damage Threshold and Activation Function . . . . . . . . . . 286
8.1.3 KineticEquation ......................... 287
8.1.4 Statistical Interpretation of the Kinetic Equation . . . . . . . 288
8.1.5 One-Dimensional Random-Strength Model . . . . . . . . . . 289
8.1.6 Fiber-Direction,TensionDamage................ 294
8.1.7 Fiber-Direction,CompressionDamage ............. 300
8.2 MultidimensionalDamageandEffectiveSpaces ............ 304
8.3 ThermodynamicsFormulation...................... 305
8.3.1 FirstLaw ............................. 306
8.3.2 SecondLaw............................ 307
8.4 KineticLawinThree-DimensionalSpace................ 313
8.4.1 Return-MappingAlgorithm ................... 316
8.5 DamageandPlasticity .......................... 322
SuggestedProblems .............................. 324
9 Discrete Damage Mechanics 327
9.1 Overview ................................. 328
9.2 Approximations.............................. 332
9.3 LaminaConstitutiveEquation ..................... 333
9.4 DisplacementField ............................ 334
9.4.1 Boundary Conditions for ΔT=0................ 335
9.4.2 Boundary Conditions for ΔT=0................ 336
Table of Contents xi
9.5 DegradedLaminateStiffnessandCTE................. 337
9.6 DegradedLaminaStiffness........................ 338
9.7 FractureEnergy ............................. 339
9.8 SolutionAlgorithm............................ 340
9.8.1 LaminaIterations ........................ 340
9.8.2 LaminateIterations ....................... 340
SuggestedProblems .............................. 351
10 Delaminations 353
10.1 CohesiveZoneMethod.......................... 356
10.1.1 SingleModeCohesiveModel .................. 358
10.1.2 MixedModeCohesiveModel .................. 361
10.2 VirtualCrackClosureTechnique .................... 371
SuggestedProblems .............................. 375
A Tensor Algebra 377
A.1 PrincipalDirectionsofStressandStrain................ 377
A.2 TensorSymmetry............................. 377
A.3 MatrixRepresentationofaTensor ................... 378
A.4 DoubleContraction............................ 379
A.5 TensorInversion ............................. 379
A.6 TensorDifferentiation .......................... 380
A.6.1 DerivativeofaTensorwithRespecttoItself ......... 380
A.6.2 Derivative of the Inverse of a Tensor with Respect to the Ten-sor ................................ 381
B Second-Order Diagonal Damage Models 383
B.1 EffectiveandDamagedSpaces ..................... 383
B.2 Thermodynamic ForceY ........................ 384
B.3 DamageSurface.............................. 386
B.4 Unrecoverable-StrainSurface ...................... 387
C Software Used 389
C.1 Abaqus................................... 389
C.1.1 AbaqusProgrammableFeatures................. 391
C.2 BMI3 ................................... 393

References 395