A two-step perturbation method in nonlinear analysis of beams, plates and shells PDF
Preview A two-step perturbation method in nonlinear analysis of beams, plates and shells
Red box rules are for proof stage only. Delete before final printing. SHen Hui-SHen SHen A Two-Step Perturbation Method in Nonlinear Analysis of Beams, NA Plates and Shells o T nw A Two-Step l io n Hui-SHen SHen, Shanghai Jiao Tong University, Shanghai, China - e S at Perturbation Method in re 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 su postbuckling and nonlinear vibration. i Beams, Plates and Shells sr A two-step perturbation method is firstly proposed by Shen and Zhang (1988) for b o a postbuckling analysis of isotropic plates. This approach gives parametrical analytical ft expressions of the variables in the postbuckling range and has been generalized to other i Bo plate postbuckling situations. This approach is then successfully used in solving many en 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 mM 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 h P lo a Z Concentrates on three types of nonlinear analyses: vibration, bending and postbuckling td e Z Presents not only the theoretical aspect of the techniques, but also engineering sin applications of the method a n d 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 l l s A TWO-STEP PERTURBATION METHOD IN NONLINEAR ANALYSIS OF BEAMS, PLATES AND SHELLS INFORMATION SECURITYSERIES TheWiley-HEPInformationSecuritySeriessystematicallyintroducesthefundamentalsofinformation securitydesignandapplication.ThegoalsoftheSeriesare: (cid:1) toprovidefundamentalandemergingtheoriesandtechniquestostimulatemoreresearchincryptol- ogy,algorithms,protocols,andarchitectures (cid:1) toinspireprofessionalstounderstandtheissuesbehindimportantsecurityproblemsandtheideas behindthesolutions (cid:1) togivereferencesandsuggestionsforadditionalreadingandfurtherstudy TheSeriesisajointprojectbetweenWileyandHigherEducationPress(HEP)ofChina.Publications consistofadvancedtextbooksforgraduatestudentsaswellasresearcherandpractitionerreferences coveringthekeyareas,includingbutnotlimitedto: – ModernCryptography – CryptographicProtocolsandNetworkSecurityProtocols – ComputerArchitectureandSecurity – DatabaseSecurity – MultimediaSecurity – ComputerForensics – IntrusionDetection LEADEDITORS SongY.Yan London, UK Moti Yung Columbia University,USA JohnRief Duke University,USA EDITORIALBOARD LizBacon UniversityofGreenwich, UK Kefei Chen Shanghai Jiaotong University, China Matthew Franklin UniversityofCalifornia, USA Dieter Gollmann Hamburg Universityof Technology,Germany Yongfei HanBeijing UniversityofTechnology, China ONETS Wireless &Internet Security Tech. Co.,Ltd.Singapore KwangjoKim KAIST-ICC,Korea David Naccache Ecole NormaleSup(cid:1)erieure,France DingyiPei Guangzhou University,China Peter Wild UniversityofLondon, UK A TWO-STEP PERTURBATION METHOD IN NONLINEAR ANALYSIS OF BEAMS, PLATES AND SHELLS Hui-ShenShen ShanghaiJiaoTongUniversity,Shanghai,China This edition first published 2013 # 2013 Higher Education Press. All rights reserved. Published by John Wiley & Sons Singapore Pte. Ltd., 1 Fusionopolis Walk, #07-01 Solaris South Tower, Singapore 138628, under exclusive license by Higher Education Press in all media and all languages throughout the world excluding Mainland China and excluding Simplified and Traditional Chinese languages. For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com. All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as expressly permitted by law, without either the prior written permission of the Publisher, or authorization through payment of the appropriate photocopy fee to the Copyright Clearance Center. Requests for permission should be addressed to the Publisher, John Wiley & Sons Singapore Pte. Ltd., 1 Fusionopolis Walk, #07-01 Solaris South Tower, Singapore 138628, tel: 65-66438000, fax: 65-66438008, email: [email protected]. Wileyalsopublishesitsbooksinavarietyofelectronicformats.Somecontentthatappearsinprintmaynotbe availableinelectronicbooks. Designationsusedbycompaniestodistinguishtheirproductsareoftenclaimedastrademarks.Allbrandnames andproductnamesusedinthisbookaretradenames,servicemarks,trademarksorregisteredtrademarksoftheir respectiveowners.ThePublisherisnotassociatedwithanyproductorvendormentionedinthisbook.This publicationisdesignedtoprovideaccurateandauthoritativeinformationinregardtothesubjectmattercovered. ItissoldontheunderstandingthatthePublisherisnotengagedinrenderingprofessionalservices.Ifprofessional adviceorotherexpertassistanceisrequired,theservicesofacompetentprofessionalshouldbesought. LimitofLiability/DisclaimerofWarranty:Whilethepublisherandauthorhaveusedtheirbesteffortsinpreparing thisbook,theymakenorepresentationsorwarrantieswithrespecttotheaccuracyorcompletenessofthecontentsof thisbookandspecificallydisclaimanyimpliedwarrantiesofmerchantabilityorfitnessforaparticularpurpose.Itis soldontheunderstandingthatthepublisherisnotengagedinrenderingprofessionalservicesandneitherthe publishernortheauthorshallbeliablefordamagesarisingherefrom.Ifprofessionaladviceorotherexpert assistanceisrequired,theservicesofacompetentprofessionalshouldbesought. 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
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