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1、求解无限大弹性体扁平椭圆状裂纹的一种等效方法第26卷第1期Vo1.26No.1宁夏大学(自然科学版)JournalofNingxiaUniversity(NaturalScienceEdition)2005年3月Mar.2005ArticleID:0253—2328(2005)O1—0045—03ASimpleWaytoSolvetheFlatEllipticalCrackinInfiniteElasticBodyHeLijun,CaiShengqing(Schoo1ofPhysicsandElectricalInformation
2、Science,NingxiaUniversity,Yinchuan750021,China)Abstract:Stressintensityfactor(SIF)alongthecrackfrontofaflatellipticalcrackininfiniteelasticbodyisinvestigated.Byusinganequivalentmethod,theellipticalcrackcanbetreatedasapennyshapecrackatlocaldomain.Themaximumopeningdispla
3、cementofthesepennyshapecracks'surfaceissame,whichisequaltotheopeningdisplacementofellipticalcrack'ssurface.ComparedwitholdmethodgivenbyGreenandSneddon'thenewapproachisverysimpleandeasytounderstandanddoinmathematics.Keywords:SIF;ellipticalcrack;pennyshapecrackCLCnumber:
4、V214.35;TU313.1Documentcode;ATheembeddedellipticalcrackinanelasticsolidbodyhasbeeninvestigatedbyGreenandSneddonE,theyhavebasedtheiranalysisonexistingsolutionsofthefluidmechanicsbecauseoftheproblems'similarities.FanC]gavethedetailedprocedurebyusingGreenandSneddon'smetho
5、dandcorrectedseveralmistakesofSneddonandLowengrub:引.ButtheEllipticfunctionmethod,whichwasused,madethesolvingproceduretoocomplicated.Here,wewil1giveanapproach,comparedwiththeoldmethodmentionedabove,itisstraightforwardandtheinclosedformsolutionhasbeenderivedwithoutunduel
6、abor.Let'sconsideraflatellipticalcrackembeddedininfiniteelasticbody(Figure1),thecrackplane1ieson:roycoordinateplane,farfieldunif~)I'ITIloadisparallelto2coordinateaxis.脚1Anellipticalera~.eisembeddedinilff'mitebodyLengthofthelongaxisoftheellipticalcrackis2a,andtheshortax
7、lsproblemonxoyplane(Figure2).Shapeofthecrackisgivenby+:1.(1)口.6"…Consideranarbitrarypoint(aeosO,bsinO)ontheellipseinthefirstquadrant,thepositionvectorRcanbewrittenasis2b,weinvestigatetheFigure2EllipticalcrackliesoilxoyplaneR:(aCOS0,bsin),(2)where,0istheparameterange1.T
8、henthetangentvectorfandthenormalvector,lcanbewrittenasf:(一asin0,bcos),(3),l:(bcos0,asin).(4)Fromequation(4)wecanderiv
