国立成功大学土木工程研究所硕士论文

::I(Meshfreemethod)(DifferentialReproducingKernelApproximation,DRKM)(stressintensityfactor)II927III……………………………………………………………………..……………………………………………………………………..……………………………………………………………………..…………………………………………………………………..…………………………………………………………………..………………………………………………………….….11.1…………………………………………………..…….……11.2………………………………………..………….21.3……………………………………………..………….4…………………………………………….………….62.1……………………………………..……….62.2DRKM………………………..………82.3...……………………………………….….…122.3.1Free-FreeWedge………………………………………….152.3.2Free-FixedWedge………………………………………...16………………………………….……193.1…………………………………..……19IV3.2…………………………………………………....…213.2.1……………………………………….…………..223.2.2……………………………………….…………..233.2.3……………………………………….…………..243.3……………………………………..………..…25..………………………………………….………….284.1………………………………….………...284.2………………………………….………...364.3…………………………………………….………...484.4…………………………………….………...53……..……………………………………………………..56………………………………………………………………..581…………………………………………………………………...602…………………………………………………………………...66V2.1Free-FixedWedge/2…………………………………….……..174.1a310d-=()……………………….324.1b610d-=()…………………….…324.2a310d-=()…………………….334.2b610d-=()…………………….334.3a310d-=()…………………….394.3b610d-=()…………………….394.4a310d-=()…………………….404.4b610d-=()…………………….404.5K……………………………….504.6NA……………………………55VI2.1……………………………………….143.1in-planeforce……………………………………..193.2…………………………………….223.3…………………………………….233.3……………………………………………….264.1…………………………………….284.2……………………………………….294.3……………………………………….304.4a…………………………………………...314.4b………………………………………...314.5aK(x)…………………………….…..344.5bK(y)………………………….……..344.5cK(x)………………………………...354.5dK(y)………………………….……..354.6…………………………………….364.7a………………………………………..384.7b………………………………………...38VII4.8aK(x)…………………………….…....414.8bK(y)……………………………...…..414.8cK(x)……………………………..…...424.8dK(y)………………………….………424.9ax………………….………...444.9bx………………….………...444.10ay…………………..………454.10by…………………..………454.11axy…………………….……464.11bxy…………………….……464.12………………………………………….….…...484.13………………………….……494.14……………………………………….……494.15…………………………51,524.16a=2(a/b=0.4)NA………..……541meshlessmethodDifferentialReproducingKernelApproximationMethod,DRKMstressintensityfactor2DRKMDRKMDRKMLucy(smoothparticlemethod)[1]3Nayroles[2](diffuseelementmethod)GalerkinMethodBelytschko[3]NayrolesMLSElementFreeGalerkin[4]Element-FreeGalerkinpartitionsofunityLiu[5](reproducingkernelapproximation)Chen[6](ReproducingKernelParticleMethod,RKPM)Li[7]RKPMOñate[8](finitepointmethod)(pointcollocationmethod)OñateZhu[9](LBIE)Belytschko[10][11]4(EFG)DRKMDRKM56DRKM2.1(DiscreteReproducingKernelApproximation)()uxNP{}12,,...,NPxxx()iiuux=()ux11()(;)NPNPRaIIIIIIuxxxxuu===Φ-=Ψ∑∑(2.1)(2.1)()(;)()(;)aIIaIIxxxxxxCxxxΨ≡Φ-=Φ--(2.2)()aIxxΦ-(weightingfunction)(;)()()TIICxxxbxHxx-=-(correctionfunction)(2.3)012()[(),(),(),...,()]Tnbxbxbxbxbx=2()[1,(),(),...,()]TnIIIIHxxxxxxxx-=---7()bx()uxn(2.1)()ux()()Ruxux=1()NPmmIIIxxx=Ψ=∑m=0,1,2,…,n(2.4)(2.4)11112222211111()1()()()()0()()()2()()20()()0NPIINPNPNPIIIIIIIINPNPNPNPIIIIIIIIIINPnIIIxxxxxxxxxxxxxxxxxxxxxxxxxx=========Ψ=-Ψ=Ψ-Ψ=-=-Ψ=Ψ-Ψ+Ψ=-×+=-Ψ=∑∑∑∑∑∑∑∑∑M11()()()()()()(0)NPNPTIIIaIIIIHxxxHxxxxHxxbxH==-Ψ=-Φ--=∑∑(2.5)[](0)1,0,0,...,0TH=(2.5)()()(0)MxbxH=(2.6)1()()()()NPTIaIIIMxHxxxxHxx==-Φ--∑(2.7)8(2.6)(2.7)010121112()()()()1()()()()0()()()()0nnnnnnmxmxmxbxmxmxmxbxmxmxmxbx++⎡⎤⎡⎤⎡⎤⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥=⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥⎣⎦⎣⎦⎣⎦LLMMOMMML(2.8)1()()()NPijijIaIImxxxxx++==-Φ-∑(2.9)1()()(0)bxMxH-=(2.10)(2.10)(2.2)(2.3)(ReproducingKernelshapefunction)1()()()()(0)TIaIIxxxHxxMxH-Ψ=Φ--(2.11)2.2DRKM(2.11)(2.11)11()()()()()(0)()()(0)TTaIIIIaIxxxHxxHxxMxHxxMxHxxx--∂Φ-∂Ψ∂-=-+Φ-∂∂∂91()()()(0)TaIIMxxxHxxHx-∂+Φ--∂111()()()()MxMxMxMxxx---∂∂=-∂∂DRKM(2.1)1()NPRIIIuxu==Ψ∑1()RNPIIIuxux=∂′=Ψ∂∑(2.12)(2.4)I′Ψ11()NPmmIIIxxmx-=′Ψ=∑,m=0,1,2,…,n(2.13)(2.13)I′Ψ*()()(;)IaIIxxxCxxx′Ψ=Φ--(2.14)10(2.14)**(;)()()TIICxxxbxHxx-=-(2.15)(2.13)1111222211111()0()()()()011()()()2()()0220()()0NPIINPNPNPIIIIIIIINPNPNPNPIIIIIIIIIIINPnIIIxxxxxxxxxxxxxxxxxxxxxxxxx=========′Ψ=′′′-Ψ=Ψ-Ψ=×-=-′′′′-Ψ=Ψ-Ψ+Ψ=×-+=′-Ψ=∑∑∑∑∑∑∑∑∑M*11()()()()()()(0)NPNPTIIIaIIIHxxxHxxxHxxbxH==′′-Ψ=-Φ-=∑∑(2.16)[](0)0,1,0,0,...,0TH′=-(2.16)*()()(0)MxbxH′=(2.17)*1()()(0)bxMxH-′=(2.18)(2.18)(2.14)(2.15)1()()()()(0)TIaIIxxxHxxMxH-′′Ψ=Φ--(2.19)[](0)0,1,0,0,...,0TH′=-11(2.13)[]1()()()()(0)(0)0,0,2,0,...,0TIaIIxxxHxxMxHH-′′′′Ψ=Φ--′′=(2.20)n()1()()()()()(0)nTnIaIIxxxHxxMxH-Ψ=Φ--(2.21)()()(0)InInIxxHxxHx=∂-=∂(2.22)n(,)(;)(,;,)IaIIIIxyxxyyCxyxxyyΨ=Φ----(2.23)12(,;,)(,)(,)TIIIICxyxxyybxyHxxyy--=--(2.24)22(,)[1,(),(),(),(),()(),TIIIIIIIIHxxyyxxyyxxyyxxyy--=------3322(),(),()(),()(),...]IIIIIIxxyyxxyyxxyy------(2.25)()1()(,)(,)(,)(,)(0)mnTmnIaIIIIxyxxyyHxxyyMxyH+-+Ψ=Φ----(2.26)n()(0)mnH+()(),(,)(0)IImnmnIImnIIxxyyHxxyyHxy++==∂--=∂∂(2.27)2.3Eshelby-Stroh[1](two-dimensionaldeformation)u=u(12,xx)3x13%*12*(,)()()uxxAfzqAfzq=+(2.28)%12**(,)()()xxBfzqBfzqΩ=+(2.29)AB*()fz()fzaz%,qqWilliams(1952)[12]rd-1Re[]0*()fz1**1**()()fzzfzzdd++==%11**uAzqAzqdd++=+(2.30)%11**BzqBzqdd++Ω=+(2.31)2.1(12,xx)1412()zxpxaaq-=+=r(,)azqq-(2.32)cos()sin()()cos()sin()pppaaaqqqqq-----⋅-=+⋅(,)cos()()sin()paazqqqqqqq----=-+-2(2.32)(2.30)(2.31)%{}111**(,)(,)urAqAqdddzqqzqq+++--=+(2.33)%{}111