弧长法算法

2000127fxF∆=∆)(1x∆f∆iifxF∆=∆)(x∆f∆—f∆x∆f∆12Ncr,Ncr3SAP-StructureAnalysisProgramσε—2.12.1.1iifxF∆=∆)(λiifxF∆=∆λ)(2n+1nRx∈∆λn222222Sxf=∆+∆λ3S()()11'+×+∈nnRFλ2.1.22kkkkRfxxK+∆=∆λ)(4)(kxK)('kxFkx∆kkλkλkR∆∆=xfr2λ23Sr=25ii+1)1(+∆iλ)1(+∆iu2)1()()1(++∆+=iiiurr65()()2)1()()1()(Sururiiii=∆+⋅∆+++72)()(Srrii=⋅80)2()()1()1(=+∆∆++iiiruu9[][]()22)1()1()1()1()1(fxxuuiiTiii∆∆+∆∆=∆⋅∆+++++λ10[][]()22)()()()()(fxxrriiTiii∆+=⋅λ11[][][]0)2(2(2)(2)1(2)1()()1()1(=∆+∆∆∆∆++∆∆++++fffxxxiiiiiTiλλλ12[])1(+∆ix[][][]IIiIiiixxx)1()1()1()1(++++∆+∆∆=∆λ13[][][]fxKIii∆=∆+)1()(14[][][])()1()(iIIiiRxK=∆+151312)1(+∆iλ()02)1(2)1(=+∆+∆++caiiλλ16[][]IiTIixxa)1()1(1++∆∆+=[][][])()()1()1()(iIIiTIiixxxb+∆∆+=++λ[][][])2()()1()1(iIIiTIIixxxc+∆∆=++16)1(+∆iλ)1(+∆iλ)(ir)1(+∆iu0)1()(=∆⋅+iiur17[][]022)1()()1()(=∆∆+∆++fxxiiiTiλλ18)1(+∆ix[][][][]22)()1()()1()()1(1ffxxxxiIiiIIiTii∆∆+∆∆−=∆+++λλ1913162)(iλiiff∆−=∆+12.1.2LancsozLancsozRitz1θnθnλθ≈2nλ02θ1subroutineArcLeng(TotalP,TotalU,F,ArcL)2subroutineJudge(PD,GK)3subroutineSolve(GK,Gload,Gdisp)fx∆x(1)∆x(i)∆x(i+1)r(1)r(i)r(i+1)∆u(i+1)λ(1)λ(i)λ(i+1)∆λ(i+1)∆λ(i)ArcLeng3nTotalFTotalUFArcLSetGK(GK,TotalU)SetGKGKJudgeJudge(PD,GK)Solve(GK,Gload,Gdisp)SolveGdispuuFFArcLtT∆∆+=2)(λFFλ=uuλ=GetRF(RF,TotalU+U)SetGK(GK,TotalU+U)GKRJudge(PD,GK)PPGKui111][−+=∆RGKui112][−+=∆λλ+∆∆−=∆++1212itituuuu1211++∆+∆∆=∆iiuuuλIPPPλ∆+=uuu∆+=ελ∆3ArcLengJudgeLanczosLanczos22×∈RBB1θ2θnλθ≈2nλ02θSolveIGKGKλ+=nGKabsval))((min1010−=λ2.22.2.1LancsozLancsoz1Lancsoz23PreConLanczosLanczosHilbertn5LanczosLancsoz2.2.2A3M=A3HilbertbHx=HHilbertx~2~xAb−11101.164153218269348E-0101.091393642127514E-010202.607703208923340E-0081.117587089538574E-008301.981854438781738E-0069.313225746154785E-0082.2.3IMSLDLSLXGDLSLXG4FF1X1F2X24X1,X222×∈RGK-]75.225.25.0[020300+−=iiiiiiiixxxxxxFF55-20102FF=F-(X2)66442-36-710-77734580.250.5900.511.522.533.500.511.522.533.5S/S0F/F067-00.511.522.533.544.550123456780123456780123456780.10.20.40.50.889180%-90%2GaussLancsoz150300312Lanczos3Lanczos4A35