James R. Rice__Foundations of Solid Mechanics.pdf

James R. Rice__Foundations of Solid Mechanics.pdf

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时间:2019-03-14

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1、ManuscriptforpublicationasChapter2ofthebookMechanicsandMaterials:FundamentalsandLinkages(eds.M.A.Meyers,R.W.Armstrong,andH.Kirchner),Wiley,publicationexpected1998.FoundationsofSolidMechanicsJamesR.RiceDivisionofEngineeringandAppliedSciencesandDepartmentofEarthandPlanetarySciencesHa

2、rvardUniversityJanuary,19981.IntroductionThischapterisdevotedtoareviewoffoundationsofsolidmechanics.Itisbasedonaneditedtranscriptoftwolecturesbytheauthoronthatsubjectata1993summerschooloftheNSFInstituteforMechanicsandMaterials.Inuniversitycourses,itusuallytakesahealthypartoftheseme

3、stertogooverthematerial.So,itishopedthatthestudentwillappreciatethatthisisindeedareview.Itisassumedthatthematerialhastosomeextentbeenencounteredbefore,anditishopedthatthisquickreviewwillhelpthereaderputthingstogetherinhisorherownmind.Pleaseseethebibliographyforreferencesonthehistor

4、yofthesubject,andforfurtherreadings.Figure1showsanorthogonalCartesianreferenceframe,whichweconsidertobeaNewtonianframe.Coordinatesinspacearedenoted1,2,3;thee'sareunitvectorsalongthesecoordinatedirections.Thevectorx,whichdenotesapositioninspace,hascomponentsx1,x2,x3.visthevelocityve

5、ctorforthisposition.1Wefocusonanarbitrarilychosenregionofsomebody.ThatregionhasvolumeV;itssurfaceisdenotedbyS.WeseeinFig.1anelementofsurface,dS,aunitnormaltothesurface,n,andanelementofvolume,dV.Thequantitieswhicharegoingtoentertheequationsofmotionare,ofcourse,thelinearandangularmom

6、entum.Thesearetakenasintegralsovertheregionofmassdensitytimesvelocityintegratedovervolume,andfortheangularmomentum,thecrossproductofmassdensitytimesvelocityintegratedovervolume:Linearmomentum≡P=∫ρvdV(1)VAngularmomentum(relativetothecoordinateorigin)≡H=∫ρx×vdV(2)VThestudentmayreason

7、ablyask:"Inmicroscopicterms,whatdothesequantitiesmean?"Ofcourse,massdensityisanaverageofmassperunitvolume,andweassumeinatheoryofthetypetobediscussedthatitistakenoverspatialandtemporalscalesthatarelargeenoughtobeindependentofanyfluctuationsatthemicroscopiclevel.Ifweask"Whatdoesveloc

8、itymean?",especiallywhenwe

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