加入VIP
  • 专属下载特权
  • 现金文档折扣购买
  • VIP免费专区
  • 千万文档免费下载

上传资料

关闭

关闭

关闭

封号提示

内容

首页 弹性力学

弹性力学

弹性力学

shiao
2010-02-09 0人阅读 举报 0 0 暂无简介

简介:本文档为《弹性力学pdf》,可适用于工程科技领域

ElasticityndEditionSOLIDMECHANICSANDITSAPPLICATIONSVolumeSeriesEditor:GMLGLADWELLDepartmentofCivilEngineeringUniversityofWaterlooWaterloo,Ontario,CanadaNLGIAimsandScopeoftheSeriesThefundamentalquestionsarisinginmechanicsare:Why,How,andHowmuchTheaimofthisseriesistoprovidelucidaccountswrittenbyauthoritativeresearchersgivingvisionandinsightinansweringthesequestionsonthesubjectofmechanicsasitrelatestosolidsThescopeoftheseriescoverstheentirespectrumofsolidmechanicsThusitincludesthefoundationofmechanicsvariationalformulationscomputationalmechanicsstatics,kinematicsanddynamicsofrigidandelasticbodies:vibrationsofsolidsandstructuresdynamicalsystemsandchaosthetheoriesofelasticity,plasticityandviscoelasticitycompositematerialsrods,beams,shellsandmembranesstructuralcontrolandstabilitysoils,rocksandgeomechanicsfracturetribologyexperimentalmechanicsbiomechanicsandmachinedesignThemedianlevelofpresentationisthefirstyeargraduatestudentSometextsaremonographsdefiningthecurrentstateofthefieldothersareaccessibletofinalyearundergraduatesbutessentiallytheemphasisisonreadabilityandclarityForalistofrelatedmechanicstitles,seefinalpagesElasticityndEditionbyJRBARBERDepartmentofMechanicalEngineering,UniversityofMichigan,AnnArbor,USAKLUWERACADEMICPUBLISHERSNEWYORK,BOSTON,DORDRECHT,LONDON,MOSCOWeBookISBN:PrintISBN:©KluwerAcademicPublishersNewYork,Boston,Dordrecht,London,MoscowPrint©KluwerAcademicPublishersAllrightsreservedNopartofthiseBookmaybereproducedortransmittedinanyformorbyanymeans,electronic,mechanical,recording,orotherwise,withoutwrittenconsentfromthePublisherCreatedintheUnitedStatesofAmericaVisitKluwerOnlineat:http:kluweronlinecomandKluwer'seBookstoreat:http:ebookskluweronlinecomDordrechtContentsPrefacetotheSecondEditionPrefacetotheFirstEditionIGENERALCONSIDERATIONSINTRODUCTIONNotationforstressanddisplacementStressStrainsandtheirrelationtodisplacementsStressstrainrelationsPROBLEMSEQUILIBRIUMANDCOMPATIBILITYEquilibriumequationsCompatibilityequationsThesignificanceofthecompatibilityequationsEquilibriumequationsfordisplacementsPROBLEMSDilatationandbulkmodulusLamé’sconstantsDefinitionofshearstrainTransformationofcoördinatesRotationandshearstrainTensilestrainDisplacementPrincipalstressesandVonMisesstressVectors,tensorsandtransformationrulesIndexandvectornotationxvxviivCONTENTSIITWODIMENSIONALPROBLEMSPLANESTRAINANDPLANESTRESSPlanestrainThecorrectivesolutionSaintVenant’sprincipleOtherSaintVenantproblemsPROBLEMSTheeigenvalueproblemSeparatedvariablesolutionsThecorrectivesolutionDecayingsolutionsENDEFFECTSPROBLEMSFouriertransformsChoiceofformSeriesandtransformsolutionsRectangularbeamproblemsSecondandthirddegreepolynomialsBiharmonicpolynomialfunctionsPROBLEMSINRECTANGULARCOÖRDINATESPROBLEMSTRESSFUNCTIONFORMULATIONPROBLEMSRelationshipbetweenplanestressandplanestrainGeneralizedplanestressPlanestressTheconceptofascalarstressfunctionChoiceofasuitableformTheAirystressfunctionThegoverningequationTheequilibriumequationsNonzerobodyforcesThecompatibilityconditionMethodofsolutionReduceddependenceonelasticconstantsBendingofabeambyanendloadHigherorderpolynomialsageneralstrategyManualsolutionssymmetryconsiderationsviLoadingattheendsPurebendingForcetransmissionCURVEDBEAMPROBLEMSPROBLEMSDisplacementsfortheMichellsolutionThecircularholeDeflectionofthefreeendEquilibriumconsiderationsThecylindricalpressurevesselRigidbodydisplacementsandendconditionsThecantileverwithanendloadCALCULATIONOFDISPLACEMENTSPROBLEMSHoleinatensilefieldTheMichellsolutionDegeneratecasesCircularholeinashearfieldSatisfactionofboundaryconditionsExpressionsforstresscomponentsStraincomponentsFourierseriesexpansionPROBLEMSINPOLARCOÖRDINATESRotationalaccelerationThecirculardiskTherectangularbarWeakboundaryconditionsandtheequationofmotionPROBLEMSTherotatingrectangularbeamSolutionofthegoverningequationSolutionforthestressfunctionRigidbodykinematicsQuasistaticproblemsInertiaforcesGravitationalloadingParticularcasesThecompatibilityconditionConservativevectorfieldsBODYFORCESCONTENTSviiStressfunctionformulationviiiEigenvaluesandeigenfunctionsTheinhomogeneousproblemThenearsingularproblemBeamwithsinusoidalloadingSomegeneralconsiderationsConclusionsPROBLEMWEDGEPROBLEMSPowerlawtractionsUniformtractionsMoregeneraluniformloadingEigenvaluesforthewedgeangleWilliams’asymptoticmethodAcceptablesingularitiesEigenfunctionexpansionNatureoftheeigenvaluesThesingularstressfieldsOthergeometriesGeneralloadingofthefacesPROBLEMSPLANECONTACTPROBLEMSTheFlamantSolutionThehalfplaneThenormalforceThetangentialforceSummaryDistributednormaltractionsFrictionlesscontactproblemsMethodofsolutionTheflatpunchThecylindricalpunch(Hertzproblem)ProblemswithtwodeformablebodiesUncoupledproblemsContactofcylindersCombinednormalandtangentialloadingCattaneoandMindlin’sproblemSteadyrolling:Carter’ssolutionPROBLEMSCONTENTSSelfsimilarityIIITORSIONOFAPRISMATICBARPrandtl’sstressfunctionSolutionorthegoverningequationThemembraneanalogyThinwalledopensectionsTherectangularbarMultiplyconnected(closed)sectionsThinwalledclosedsectionsPROBLEMSENDLOADINGOFTHEPRISMATICBARPROBLEMSTransformationofcoordinatesBoundaryconditionsTherectangularbarTheconcentratedlineforceThescrewdislocationANTIPLANESHEARPROBLEMSDundurs’TheoremSteadystateproblemsHeatconductionExampleThegoverningequationTHERMOELASTICITYPROBLEMSPlanecrackinatensilefieldLinearElasticFractureMechanicsCrackproblemsStressconcentrationsDislocationsinMaterialsScienceSimilaritiesanddifferencesDislocationsasGreen’sfunctionsDislocationsBodyforceproblemsTheKelvinsolutionFORCES,DISLOCATIONSANDCRACKSCONTENTSixCONTENTSxSHEAROFAPRISMATICBARThesemiinversemethodStressfunctionformulationTheboundaryconditionIntegrabilityRelationtothetorsionproblemMethodsofsolutionPROBLEMSIVTHREEDIMENSIONALPROBLEMSDISPLACEMENTFUNCTIONSOLUTIONSTHEBOUSSINESQPOTENTIALSSolutionA:ThestrainpotentialSolutionBSolutionE:RotationaldeformationOthercoördinatesystemsCylindricalpolarcoördinatesSphericalpolarcoördinatesSolutionsobtainedbysuperpositionSolutionF:FrictionlessisothermalcontactproblemsSolutionG:ThesurfacefreeofnormaltractionTheplanestrainsolutionincomplexvariablesPROBLEMSExpressionsforstressesRepresentationofdisplacementRepresentationofvectorsPreliminarymathematicalresultsPROBLEMSNonconservativebodyforcefieldsConservativebodyforcefieldsBodyforcesMethodsofpartialintegrationCompletenessanduniquenessThePapkovichNeubersolutionTheGalerkinvectorThestrainpotentialThecircularbarTherectangularbarPROBLEMSCylindricalcantileverwithanendloadNonaxisymmetricproblemsUniformlyloadedplateonasimplesupportAxisymmetriccircularplatesThehollowcylinderThesolidcylinderAxisymmetricproblemsforcylindersCYLINDERSANDCIRCULARPLATESPROBLEMSNonaxisymmetriccylindricalpotentialsLogarithmicfunctionsforcylinderproblemsHarmonicpotentialswithlogarithmictermsCartesianandcylindricalpolarcoördinatesNonaxisymmetricharmonicsSingularsphericalharmonicsSpecialcasesSPHERICALHARMONICSPROBLEMSOthersingularsolutionsTheBoussinesqsolutionDimensionalconsiderationsTheKelvinsolutionThecentreofdilatationThesourcesolutionSINGULARSOLUTIONSPROBLEMSThermoelasticplanestressSteadystatetemperature:SolutionTThemethodofstrainsuppressionPlanestressAxisymmetricproblemsforthecylinderPlaneproblemsTHERMOELASTICDISPLACEMENTPOTENTIALSCONTENTSxiReductiontoLegendre’sequationAxisymmetricpotentialsandLegendrepolynomialsFourierseriessolutionPROBLEMSThermoelasticproblemsThepennyshapedcrackintensionTHEPENNYSHAPEDCRACKPROBLEMSChoiceofformIndentationbyaflatpunchIntegralrepresentationBasicformsandsurfacevaluesReductiontoanAbelequationExample–TheHertzproblemCollins’MethodHankeltransformmethodsTHEBOUNDARYVALUEPROBLEMPROBLEMSBoundaryconditionsMixedboundaryvalueproblemsFRICTIONLESSCONTACTPROBLEMSTheSaintVenantproblemThecentreofrotationCylindricalandconicalbarsThedisplacementfieldSolutionofthegoverningequationThegoverningequationThetransmittedtorqueAXISYMMETRICTORSIONPROBLEMSINSPHERICALCOÖRDINATESSolidandhollowspheresConicalbarsPROBLEMSConicalbartransmittinganaxialforceInhomogeneousproblemsNonaxisymmetricproblemsCONTENTSThesolidsphereintorsionSphericalholeinatensilefieldDeterminingthecontactareaxiiCONTENTSTHEINTERFACECRACKTheuncrackedinterfaceThecorrectivesolutionGlobalconditionsMixedconditionsTHERECIPROCALTHEOREMMaxwell’sTheoremBetti’sTheoremUseofthetheoremAtiltedpunchproblemIndentationofahalfspaceThermoelasticproblemsAUSINGMAPLEANDMATHEMATICAIndexxiiiReductiontoasingleequationOscillatorysingularitiesThepennyshapedcrackintensionThecontactsolutionImplicationsforFractureMechanicsThispageintentionallyleftblankPrefacetotheSecondEditionSincethefirsteditionofthisbookwaspublished,therehavebeenmajorimprovementsinsymbolicmathematicallanguagessuchasMaple™andMathematica™andthishasopenedupthepossibilityofsolvingconsiderablymorecomplexandhenceinterestingandrealisticelasticityproblemsasclassroomexamplesItalsoenablesthestudenttofocusontheformulationoftheproblem(egtheappropriategoverningequationsandboundaryconditions)ratherthanonthealgebraicmanipulations,withaconsequentimprovementininsightintothesubjectandinmotivationDuringthepastyearsIhavedevelopedfilesinMapleandMathematicatofacilitatethisprocess,notablyelectronicversionsoftheTablesinthepresentChaptersandandoftherecurrencerelationsforgeneratingsphericalharmonicsOnepurposeofthisneweditionistomakethiselectronicmaterialavailabletothereaderthroughtheKluwerwebsitewwwelasticityorgIhopethatreaderswillmakeuseofthisresourceandreportbacktomeanyaspectsoftheelectronicmaterialthatcouldbenefitfromimprovementorextensionSomehintsabouttheuseofthismaterialarecontainedinAppendixAThosewhohaveneverusedMapleorMathematicawillfindthatittakesonlyafewhoursoftrialanderrortolearnhowtowriteprogramstosolveboundaryvalueproblemsinelasticityIhavealsotakentheopportunitytoincludesubstantiallymorematerialinthesecondeditionnotablythreechaptersonantiplanestresssystems,includingSaintVenanttorsionandbendingandanexpandedsectiononthreedimensionalproblemsinsphericalandcylindricalcoördinatesystems,includingaxisymmetrictorsionofbarsofnonuniformcircularcrosssectionFinally,IhavegreatlyexpandedthenumberofendofchapterproblemsSomeoftheseproblemsarequitechallenging,indeedseveralwerethesubjectofsubstantialtechnicalpaperswithinthenottoodistantpast,buttheycanallbesolvedinafewhoursusingMapleorMathematicaAfullsetofsolutionstotheseproblemsisinpreparationandwillbemadeavailabletobonafideinstructorsonrequestJRBarberAnnArborThispageintentionallyleftblankxviiPrefacetotheFirstEditionThesubjectofElasticitycanbeapproachedfromseveralpointsofview,dependingonwhetherthepractitionerisprincipallyinterestedinthemathematicalstructureofthesubjectorinitsuseinengineeringapplicationsandinthelattercase,whetheressentiallynumericaloranalyticalmethodsareenvisagedasthesolutionmethodMyfirstintroductiontothesubjectwasinresponsetoaneedforinformationaboutaspecificprobleminTribologyAsapractisingEngineerwithabackgroundonlyinelementaryStrengthofMaterials,IapproachedthatprobleminitiallyusingtheconceptsofconcentratedforcesandsuperpositionToday,witharathermoreextensiveknowledgeofanalyticaltechniquesinElasticity,Istillfindithelpfultogobacktotheserootsintheelementarytheoryandthinkthroughaproblemphysicallyaswellasmathematically,wheneversomenewandunexpectedfeaturepresentsdifficultiesinresearchThiswayofthinkingwillbefoundtopermeatethisbookMyengineeringbackgroundwillalsorevealitselfinatendencytoworkexamplesthroughtofinalexpressionsforstressesanddisplacements,ratherthanleavethederivationatapointwheretheremainingmanipulationswouldberoutineWiththepracticalengineeringreaderinmind,IhaveendeavouredtokeeptoaminimumanydependenceonpreviousknowledgeofSolidMechanics,ContinuumMechanicsorMathematicsMostofthetextshouldbereadilyintelligibletoareaderwithanundergraduatebackgroundofoneortwocoursesinelementaryStrengthofMaterialsandarudimentaryknowledgeofpartialdifferentiationCartesiantensornotationandthesummationconventionareusedinafewplacestoshortenthederivationofsomegeneralresults,butthesesectionsarecarefullyexplained,soastobeselfexplanatoryThebookisbasedonaonesemestergraduatecourseonLinearElasticitythatIhavetaughtattheUniversityofMichigansinceInsucharestrictedformat,itisclearlynecessarytomakesomedifficultchoicesaboutwhichtopicstoincludeand,complexvariablesolutionoftwodimensionalElasticity,which,ifitweretobeadequatelytreatedincludingessentialmathematicalpreliminaries,wouldneedmostofabookofthislengthtoitselfInstead,Ihavechosentorestrictthetwodimensionaltreatmenttothemoretraditionalrealstressfunctionapproach,soastoleaveroomforasubstantialamountofmaterialonthreedimensionalproblems,whicharearguablyclosertothefrontierofcurrentresearchmoresignificantly,whichtoexcludeThemostsignificantexclusionistheclassicalxviiiCONTENTSModernpractitionersofElasticityarenecessarilyinfluencedbydevelopmentsinnumericalmethods,whichpromisetosolveallproblemswithnomoreinformationaboutthesubjectthanisneededtoformulatethedescriptionofarepresentativeelementofmaterialinarelativelysimplestateofstressAsaresearcherinSolidMechanics,withaprimaryinterestinthephysicalbehaviourofthesystemsIaminvestigating,ratherthaninthemathematicalstructureofthesolutions,IhavefrequentlyhadrecoursetonumericalmethodsofalltypesandhavetendedtoadoptthepragmaticcriterionthatthebestmethodisthatwhichgivesthemostconvincingandaccurateresultintheshortesttimeInthiscontext,‘convincing’meansthatthesolutionshouldbecapableofbeingcheckedagainstreliableclosedformsolutionsinsuitablelimitingcasesandthatitisdemonstrablystableandinsomesenseconvergentMeasuredagainstthesecriteria,the‘best’solutiontomanypracticalproblemsisoftennotadirectnumericalmethod,suchasthefiniteelementmethod,butratheroneinvolvingsomesignificantanalyticalstepsbeforethefinalnumericalevaluationThisisparticularlytrueinthreedimensionalproblems,wheredirectnumericalmethodsareextremelycomputerintensiveifanyreasonablyaccuracyisrequired,andinproblemsinvolvinginfiniteorsemiinfinitedomains,discontinuities,bondedorcontactingmaterialinterfacesortheoreticallysingularstressfieldsBycontrast,Iwouldimmediatelyoptforafiniteelementsolutionofanytwodimensionalprobleminvolvingfinitebodieswithrelativelysmoothcontours,unlessithappenedtofallintothe(surprisinglywide)classofproblemstowhichthesolutioncanbewrittendowninclosedformThereaderwillthereforefindmychoiceoftopicssignificantlybiassedtowardsthosefieldsidentifiedabovewhereanalyticalmethodsaremostusefulIhaveprovidedarepresentativeselectionofproblemssuitableforclassuseattheendofmostofthechaptersManytextsonElasticitycontainproblemswhichofferacandidatestressfunctionandinvitethestudentto‘verify’thatitdefinesthesolutiontoagivenproblemStudentsinvariablyraisethequestion‘Howwouldweknowtochoosethatform

用户评价(0)

关闭

新课改视野下建构高中语文教学实验成果报告(32KB)

抱歉,积分不足下载失败,请稍后再试!

提示

试读已结束,如需要继续阅读或者下载,敬请购买!

文档小程序码

使用微信“扫一扫”扫码寻找文档

1

打开微信

2

扫描小程序码

3

发布寻找信息

4

等待寻找结果

我知道了
评分:

/49

弹性力学

仅供在线阅读

VIP

在线
客服

免费
邮箱

爱问共享资料服务号

扫描关注领取更多福利