A two-step perturbation method in nonlinear analysis of beams, plates and shells

369 Pages·2013·5.878 MB·English

by  Hui-Shen Shen

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SHen
Hui-SHen SHen
A Two-Step Perturbation Method
in Nonlinear Analysis of Beams,
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Plates and Shells o
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Hui-SHen SHen, Shanghai Jiao Tong University, Shanghai, China -
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at Perturbation Method in
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The capability to predict the nonlinear response of beams, plates and shells when Ap
subjected to thermal and mechanical loads is of prime interest to structural analysis. n P Nonlinear Analysis of
in fact, many structures are subjected to high load levels that may result in nonlinear ae
load-deflection relationships due to large deformations. One of the important problems lr
deserving special attention is the study of their nonlinear response to large deflection, yt
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postbuckling and nonlinear vibration. i Beams, Plates and Shells
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A two-step perturbation method is firstly proposed by Shen and Zhang (1988) for b
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postbuckling analysis of isotropic plates. This approach gives parametrical analytical
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expressions of the variables in the postbuckling range and has been generalized to other i
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plate postbuckling situations. This approach is then successfully used in solving many
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nonlinear bending, postbuckling, and nonlinear vibration problems of composite laminated
plates and shells, in particular for some difficult tasks, for example, shear deformable plates a
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with four free edges resting on elastic foundations, contact postbuckling of laminated
plates and shells, nonlinear vibration of anisotropic cylindrical shells. This approach may se
be found its more extensive applications in nonlinear analysis of nano-scale structures. ,t
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Z Concentrates on three types of nonlinear analyses: vibration, bending and postbuckling td
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Z Presents not only the theoretical aspect of the techniques, but also engineering sin
applications of the method
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A Two-Step Perturbation Method in Nonlinear Analysis of Beams, Plates and Shells is an

original and unique technique devoted entirely to solve geometrically nonlinear problems S
of beams, plates and shells. it is ideal for academics, researchers and postgraduates in h
mechanical engineering, civil engineering and aeronautical engineering. e
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A TWO-STEP
PERTURBATION
METHOD IN NONLINEAR
ANALYSIS OF BEAMS,
PLATES AND SHELLS
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EDITORIALBOARD
LizBacon UniversityofGreenwich, UK
Kefei Chen Shanghai Jiaotong University, China
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A TWO-STEP
PERTURBATION
METHOD IN NONLINEAR
ANALYSIS OF BEAMS,
PLATES AND SHELLS
Hui-ShenShen
ShanghaiJiaoTongUniversity,Shanghai,China
This edition first published 2013
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LibraryofCongressCataloging-in-PublicationData
Shen,Hui-Shen.
Atwo-stepperturbationmethodinnonlinearanalysisofbeams,plates,andshells/Hui-ShenShen.
pages cm
Includesbibliographicalreferencesandindex.
ISBN978-1-118-64988-6(cloth)
1. Girders–Mathematicalmodels. 2. Shells(Engineering)–Mathematicalmodels. 3. Plates(Engineering)–
Mathematicalmodels. 4. Deformations(Mechanics)–Mathematicalmodels. 5. Perturbation(Mathematics)
I. Title.
TA492.G5S542013
624.1082015157248–dc23
2013014723
Typesetin10/12ptTimesbyThomsonDigital,Noida,India.
Contents
AbouttheAuthor ix
Preface xi
ListofSymbols xiii
1 TraditionalPerturbationMethod 1
1.1 Introduction 1
1.2 Load-typePerturbationMethod 2
1.3 Deflection-typePerturbationMethod 3
1.4 Multi-parameterPerturbationMethod 4
1.5 LimitationsoftheTraditionalPerturbationMethod 5
References 6
2 NonlinearAnalysisofBeams 9
2.1 Introduction 9
2.2 NonlinearMotionEquationsofEuler–BernoulliBeams 10
2.3 PostbucklingAnalysisofEuler–BernoulliBeams 13
2.4 NonlinearBendingAnalysisofEuler–BernoulliBeams 17
2.5 LargeAmplitudeVibrationAnalysisofEuler–BernoulliBeams 21
References 25
3 NonlinearVibrationAnalysisofPlates 27
3.1 Introduction 27
3.2 Reddy’sHigherOrderShearDeformationPlateTheory 29
3.3 GeneralizedK(cid:1)arm(cid:1)an-typeMotionEquations 35
3.4 NonlinearVibrationofFunctionallyGradedFiberReinforcedComposite
Plates 42
3.5 HygrothermalEffectsontheNonlinearVibrationofShearDeformable
LaminatedPlate 63
3.6 NonlinearVibrationofShearDeformableLaminatedPlateswith
PFRCActuators 69
References 74
vi Contents
4 NonlinearBendingAnalysisofPlates 79
4.1 Introduction 79
4.2 NonlinearBendingofRectangularPlateswithFreeEdgesunder
TransverseandIn-planeLoadsandRestingonTwo-parameterElastic
Foundations 80
4.3 NonlinearBendingofRectangularPlateswithFreeEdgesunder
TransverseandThermalLoadingandRestingonTwo-parameter
ElasticFoundations 91
4.4 NonlinearBendingofRectangularPlateswithFreeEdgesRestingon
TensionlessElasticFoundations 94
4.5 NonlinearBendingofShearDeformableLaminatedPlatesunderTransverse
andIn-planeLoads 97
4.6 NonlinearBendingofShearDeformableLaminatedPlatesunderTransverse
andThermalLoading 109
4.7 NonlinearBendingofFunctionallyGradedFiberReinforcedComposite
Plates 116
Appendix4.A 126
Appendix4.B 131
Appendix4.C 132
Appendix4.D 133
Appendix4.E 136
Appendix4.F 137
References 141
5 PostbucklingAnalysisofPlates 145
5.1 Introduction 145
5.2 PostbucklingofThinPlatesRestingonTensionlessElasticFoundation 147
5.3 PostbucklingofShearDeformableLaminatedPlatesunder
CompressionandRestingonTensionlessElasticFoundations 163
5.4 ThermalPostbucklingofShearDeformableLaminatedPlatesRestingon
TensionlessElasticFoundations 171
5.5 ThermomechanicalPostbucklingofShearDeformableLaminatedPlates
RestingonTensionlessElasticFoundations 178
5.6 PostbucklingofFunctionallyGradedFiberReinforcedCompositePlates
underCompression 185
5.7 ThermalPostbucklingofFunctionallyGradedFiberReinforced
CompositePlates 194
5.8 PostbucklingofShearDeformableHybridLaminatedPlateswithPFRC
Actuators 200
References 211
6 NonlinearVibrationAnalysisofCylindricalShells 215
6.1 Introduction 215
6.2 Reddy’sHigherOrderShearDeformationShellTheoryandGeneralized
K(cid:1)arm(cid:1)an-typeMotionEquations 216
Contents vii
6.3 NonlinearVibrationofShearDeformableCross-plyLaminated
CylindricalShells 219
6.4 NonlinearVibrationofShearDeformableAnisotropicCylindricalShells 233
6.5 HygrothermalEffectsontheNonlinearVibrationofFunctionally
GradedFiberReinforcedCompositeCylindricalShells 252
6.6 NonlinearVibrationofShearDeformableLaminatedCylindricalShells
withPFRCActuators 257
Appendix6.G 263
References 269
7 PostbucklingAnalysisofCylindricalShells 273
7.1 Introduction 273
7.2 PostbucklingofFunctionallyGradedFiberReinforcedComposite
CylindricalShellsunderAxialCompression 274
7.3 PostbucklingofFunctionallyGradedFiberReinforcedComposite
CylindricalShellsunderExternalPressure 295
7.4 ThermalPostbucklingofFunctionallyGradedFiberReinforced
CompositeCylindricalShells 312
7.5 PostbucklingofAxiallyLoadedAnisotropicCylindricalShells
SurroundedbyanElasticMedium 320
7.6 PostbucklingofInternalPressureLoadedAnisotropicCylindrical
ShellsSurroundedbyanElasticMedium 325
Appendix7.H 331
Appendix7.I 339
Appendix7.J 341
References 344
Index 349