基于XFEM的混凝土开裂1数值模拟研究

281()Vol.28No.120092JOURNALOFCHONGQINGJIAOTONGUNIVERSITY(NATURALSCIENCE)Feb.2009XFEM:2008207207;:2008210217:(50539030);(SLK2008B04):(19742),,,,,E2mail:[e-mail];Tel:[phone],2(1.,400074;2.,210098):(XFEM)(),,,,,,,,:;;;:TV642.3:A:167420696(2009)0120036205StudyonNumericalSimulationofCrackGrowthofConcreteBasedonXFEMDONGYu2wen1,RENQing2wen2(1.SchoolofRiver&OceanEngineering,ChongqingJiaotongUniversity,Chongqing400074,China;2.SchoolofCivilEngineering,HehaiUniversity,JiangsuNanjing210098,China)Abstract:Extendedfiniteelementmethod(XFEM)isanewandeffectivemethodforanalyzingdiscontinuityproblemariseninrecentfewyears,speciallytheproblemoffracture.ThebasictheoryofXFEMisintroducedandthemethodofanalyzingconcretefractureandcrackgrowthispresented.Finally,thefracturingprocessoftwosamplesincludinginitialcracksandthecrackgrowthprocessoftheconcretegravitydamaresimulatedbyXFEM.Thedisciplineofdisplacementandstressfielddistributionofthesamplesareanalyzed.Comparingwithclassicalfiniteelementmethod,thecrackgrowthofconcretecanbesimulatedbyXFEMwithoutmakingthecracksurfaceassociatedtothemesh,withoutsettingdensemeshnearthecracktipandwithoutre2meshingaftercrackgrowth.Thusthecumbersomeworksanddisadvantagesinfracturinganalysisarea2voidedbytheapplicationofXFEM.TheuniqueadvantageofXFEMinconcretefracturinganalysisisdisplayed.Keywords:XFEM(ExtendedFiniteElementMethod);concrete;crackgrowth;numericalsimulation1,,,(292m)(278m)(305m)(284m)(216m)(161m)(175m)(156m),,,,,,,,,,,,:,,,,©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(XFEM)Be2lytschko1999[1-2],,,,[3-6],,,22.1uh(x)=ni=1Niui(1),Nii;uii(x,y),:nei=1Ni(x,y)1DuarteOden[7],,,Belytschko[1-2],,uh(x)=iNNi(x)ui+H(x)aiiN+4=1biiN(2),N;N(1);N(1);H(x)Heaviside,,+1-1,,H(x)=sign((x))=1,(x)0-1,(x)0(3),,(r,)(2),4:=rsin2,cos2,sin2sin,cos2sin(=14)(4)1XXFEM22.23,,(2),XFEM:Kd=f(5),d,{d}i={ui},(1),{d}i={ui,b1i,b2i,b3i,b4i},Heaviside(1),{d}i={ui,ai}(5),f,:fei={fuifaifb1ifb21fb3ifb4i}T(6):fui=eNibd+CNi€td(7)fai=eNiHbd+CNiH€td(8)fbi=eNibd+CNi€td(9)731,:XFEM©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(7)(9),b,€t(3)(5),K,:keij=kuuijkuaijkubijkauijkaaijkabijkbuijkbaijkbbij(10)(10):krsij=e(Bri)TDBsjd,(r,s=u,a,b)(11)D,Bui,Bai,Bbi,,:Bui=Ni,x00Ni,yNi,yNi,x(12)Bai=(NiH),x00(NiH),y(NiH),y(NiH),x(13)Bbi=(Ni),x00(Ni),y(Ni),y(Ni),x=14(14)32.3H(x)(x),,,[3,7],(4),Gauss:x=3i=1Ni()xi,x=x-1(),(8)(11)Gauss,,(5),,,433.1:Ke=12cos02[K(1+cos0)-3Ksin0]KC(15),Ke;KIC;KK,M[8];0,KK,3.2,,F,:1),P2)PF,,nF,;PF,P,nF-P,,,,(15),0,,,,,P,:xn+1=xn-xn-xn-1f(xn)-f(xn-1)f(xn)(16),xn-1,xn,xn+1;f(x)=Ke(x)-KC,x=0,,f(0)=-83()28©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(16),,f(x)(),xn+1,P=xn+1F44.15,L=3mw=1.5m,,=1104Pa,,,(0,1.5)(0.8,1.5)E=2.21010Pa,=0.167,KC=575314Pam5,,2041=820,8824.1.1[9]K=Ca(17),C=1.12-0.231aW+10.55aW2-21172aW3+30.39aW4(18)5XFEMM,,,,R()M,11(K/K)R=2AR=3AR=4AR=5A102101948019680198501990204101981019850199611001408101991019940199601999:A1:1),(2041),;2)R,R,,R=34A4.1.26,7,,,,,,,x,y,xy8(a)8(c)6/m7931,:XFEM©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.=575314Pam,,1,,,10100m,(0100,1315)(10100,1315),,,1900,20169XFEM101110XFEM,,,,,;112015m,,12,,,,,,,,(155)04()28©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.[2],,.[J].,2007(5):76279.[3].()[D].:,2005.[4],.[J].,2004(1):1152119.[5].CS()[D].:,2005.[6],.[J].,2006,4(2):1132114.[7],.[M].:,2006.(40)125,,,,,,,,,,,,,,:[1]BelytschkoT,BlackT.Elasticcrackgrowthinfiniteele2mentswithminimalremeshing[J].InternationalJournalforNumericalMethodinEngineering,1999(45):6012620.[2]MoÊsN,DolbowJ,BelytschkoT.Afiniteelementmeth2odforcrackgrowthwithoutremeshing[J].InternationalJournalforNumericalMethodinEngineering,1999(46):1312150.[3]DolbowJ,MoÊsN,BelytschKT.Anextendedfiniteel2ementmethodformodelingcrackgrowthwithfrictionalcontact[J].ComputerMethodsinAppliedMechanicsandEngineering,2001(190):682526846.[4]MoÊsN,BelytschkoT.Extendedfiniteelementmethodforcohesivecrackgrowth[J].EngineeringFractureMe2chanics,2002(69):8132833.[5].[J].[J].2005,24(24):443424439.[6]SukumarN,PrvostJ2H.Modelingquasi2staticcrackgrowthwiththeextendedfiniteelementmethodPartI:Computerimplementation[J].InternationalJournalofSolidsandStructures,2003(40):751327537.[7]DuarteCA,OdenJT.AnH2Padaptivemethodusingclouds[J].ComputerMethodsinAppliedMechanicsandEngineering,1996(139):2372262.[8],.[M].:,2001.[9].[M].:,2003.5511,:©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.