多体动力学的休斯敦方法及其发展

©1994-2009ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.Ò(2000)06-0601-07:(),,,,:;;;:O313.7:A:19991210:(PD9521910),,,2050,,,,,,,,,,(Huston),1[14]1.1,RB0,1B1;B1,,,,1K,J,L(K)=J(1),L,Ln(K)=L(Ln-1(K))(2)L0(K)=K(3)L(0)=0(4)11L(K),1Ln(K)K123456789L0(K)123456789L(K)011315676L2(K)000101565L3(K)000000151L4(K)000000010L5(K)000000000106©1994-2009ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.:nj1,nj2,nj3Rk:nk1,nk2,nk3,BjBk,nk1,nk2,nk3nj1,nj2,nj3BkBj33[SJK]SJKmnSJKmn=njmõnknm,n=1,2,3(5)[SJK],njm=SJKmnnkn(6)[SOK]BkR,[SOK]=0t=u[SSV](7),0t=u,V=Lt(K),S=L(V),K=k,J=j,Lu(K)=11.3N,6N,3N3N,nf6NnfxlK,6,xkn(k=1,2,,N;n=1,2,3),xkn(k=1,2,,N;n=4,5,6),,xl=x3(k-1)+n(l=1,2,,3N),xl=x3(N+k-1)+n(l=3N+1,,6N)AkBkCksk1sk2sk3,,,,4,Ekn(n=1,2,3,4)BkBjX^k=X^k1nj1+X^k2nj2+X^k3nj3=X^kmnjn(8)sõk=sõk1nj1+sõk2nj2+sõk3nj3=sõknnjn(9)6Nyl,yl=X^knl=3(k-1)+n(10)yl=sõknl=3(N+k-1)+n(11),dlpxõp=yll=1,,6N,p=1,,6N7N(12)1.4(1),BkXkXk=0t=uX^vv=Lt(K)(13),0t=u,Lu(K)=1,V=v(6)(8),X^k=X^knSOJmnnom(14)X^kl=5X^k5yl=X^klmnom(15)(10),,(13)Xk=Xklmylnom(16),Xklm,,(2)Ak=dXkdt=(Xõklmyl+Xklmyõl)nom(17)(3)GBk(2),pk=0t=u(qv+sv)+rk={0t=u[SOSmn(qvn+svn)]+SOKmnrkn}nom(18),v=V=Lt(K);S=L(V);Lu(K)=1vk=dpkdt={0t=u[SOaSmn(qvn+svn)+SOSmnsõvn]+SOaKmnrkn}nom(19)yl=X^vnl=13Nsõvnl=3N+16N,vk=vklmylnom(20)20611620006©1994-2009ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(4)ak=dvkdt=(võklmyl+vklmyõl)nom(21)1.5Fl+F3l=0l=1,,nf(22),FlF3lxlBkFkMk,Fl=Fkõ5vk5yl+Mkõ5Xk5ylk=1,,N(23)FkMkFkmMkm,(16)(20),Fl=vklmFkm+XklmMkmk=1,,N;m=1,2,3(24)BkF3kM3kF3k=-mkak(25)M3k=-I=kõAk-Xk(I=kõXk)(26),mkBk;I=kBkF3l=vklmF3km+XklmM3km(27)(22),alpyõp=fll,p=1,,6N(28)fl=Fl-hlAlp=mkvklmvkpm+IkmnXklmXkpnhl=mkvklmvõkpmyp+IkmnXklmXõkpnyp+ersmIksnXklmXkprXkqnypyq(29)(29)k=1,,N,lpq=1,,6N,mnr,s=1,2,3(28)(12),2Ayõ=f(30)Dxõ=y(31),A6N6N;yõfy6N1;D6N6N7N;xõ6N7N11.6,gu,u=1,2,,m,mgugu=nfp=1bupypu=1,,m(32)nf,nf-m(32)g=By(33),gm1;Bmnf;ynf1Ku,Fp=mu=1Kubupp=1,2,,nf(34)F=BTK,Fnf1;Km1Fp+F3p+Fp=0p=1,2,,nf(35)F+F3+BTK=0(36)(36)(33)nfypmKuCB,BC=0CTBT=0(37)CT(36),CTF+CTF3=0(38)Kl+K3l=0l=1,2,,nf-m(39)(39),KlFlm,,(33),nfyp22.1[5,6],336,,N,BkNk,Skii,:xl(l=1,2,,6N),;GkK(k=1,2,,N,K=1,2,,6Nk),(K=1,2,,3Nk)(K=3Nk+1,2,,6Nk)ylxl,306©1994-2009ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.=yl0L6NGõkK6N+k-1j=16NjL6N+kj=16Njk=1,,N(40)BkSk1,SkiBkSKSkiSKSki=100010001+iS=10-Gk3(S-1)+3Gk3(S-1)+2Gk3(S-1)+30-Gk3(S-1)+1-Gk3(S-1)+2Gk3(S-1)+10(41)SOSki=SOKõSKSki(42),SkiBkX^kiX^ki=X^kiKmGõkKnkmK=1,2,,6Nkm=1,2,3(43)SkiXki=Xk+X^ki=(Xklmyl+XkiKmGõkK)nom(44)Xki=8iiLmYLnom(45)Aki=[8õkiLmYL+8kiLmYõL]nom(46),vki=VkiLmYLnom(47)aki=[VõkiLmYL+VkiLmYõL]nom(48),ALpYõp=FL-HL(49)ALp=mkiVkiLmVkipm+Ikimn8kiLm8kipnHL=mkiVkiLmVõkipmYp+Ikimn8kiLm8õkipnYp+eghmIkihn8kiLm8kipg8kiQnYpYQ,mkiIkimnSki;FL,FL=FlL=lFkKL=6N+k-1j=16Nj+K(50),FlFkKylGõkK()(),[4],,[5,6]Ski()Fkij(j=1,2,,6)Uki,Fkij=5Uki5Gkijj=1,2,,6(51),FkijGkij,j=1,2,33;j=4,5,63{Fki}=-[Kki]{Gki}(52),[Kki]2;{Fki}{Gki}FkijGkij,()(49)FL,GkK,,(49)(28)(29)2,2.2[7,8],,,,,,,,,(1)BBR,3B^B,OB^,BB^3PB,B,PP^(P^B^)B,uPP^,,rP^OvPvOXB^POB^R(),vP=vO+XB^(r+u)+uõ(53)bi(i=1,2,3),(53)vP=[vOi+eimkXB^m(rk+uk)+uõi]bi=vPibii(54),vOivObi,,,ui40611620006©1994-2009ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.=Nijqj+12Hipjqpqj(i=1,2,3;p,j=1,,nj)(55),qj(j=1,,nj),;Nij(i=1,2,3;j=1,,nj);Hipj(i=1,2,3;p,j=1,,nj)Nij(55),(54)vP={vOi+eimkXB^m[rk+Nkjqj+12Hkpjqpqj]+[Nij+Hipjqp]qõj}bi(56)(2)B()E,E^EEHi(i=1,2,3)E^B^,,E^B^BõXE^=(Hõ1+Hõ3H2)b1+(Hõ2-Hõ3H1)b2+(Hõ3+Hõ2H1)b3(57)Hi=(ijqj+125ipjqpqj(58)XE^E^R,XE^=[XB^i+((ij+5ipjqp)qõj]bi(59)(56)(59)(3)yl=XB^ii=1,2,3;l=ivOii=1,2,3;l=3+iqõjj=1,2,,nj;l=6+j(60),BPRvP=vPliylbi(61)XE^=XE^liylbi(62)vPl=5vP5yl(63)XE^l=5XE^5yl(64)vPliXE^libi6+njvPliXE^li,,,,(55)(59),,,,,[7],,(56)(59),PRE^RvP=vPliylbi(65)XE^=XE^liylbi(66)(4)(65)(66)R,aP=(UPliyl+vPliyõl)bi(67)AE^=(8E^liyõl+XE^liyõl)bi(68)vPliXE^libi,UPli8E^li(5)EP,,PE^,EPF3EM3EF3E=-mEazP(69)M3E=-I=EõAE^-XE^(I=EõXE^)(70),mEI=EEF3El=vPlõF3E+XE^lõM3El=1,2,,nj+6(71)(6)Fl,UFl=-5U5q(l-6)l=7,8,,nj+6(72),U,U=K(l-6)jq(1-6)qjl=7,8,,nj+6;j=1,2,,nj(73),Kij,Fl=0L=1,2,,6-K(l-6)jqjl=7,8,,nj+6(74)(7)Fl+F3l=0l=1,2,,nj+6(75),F3lylF3l=KEF3Ell=1,2,,nj+6(76)(76),,alhyõh=fll,h=1,2,,nj+6(77)alh=E(mEvPlivPhi+IEijXE^liXE^hi)fl=Fl-E(mEvPliUPhiyh+IEijXE^li8^E^hiyh+ejkiIEkmXE^liXE^PiXE^hmyPyh)506©1994-2009ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(77)(49)(28),,,,[9][10],,[11],[12],,[13],[14,15],3[16]3.1,,1,6,PUMA760,,,711NmöA,,,FFT,10167Hz16133Hz,,,3.2,,22149,,MAKINOFNC86-A2114%8715%,5318%9512%,4,38%64%,,,,3.3,;,,,,,,,,,3.4,,,,,;,,,,,,,()60611620006©1994-2009ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.:[1]HustonRL,PasserelloCE,HarlowMW.Dynam2icsofMultirigid-bodySystem.ASMEJournalofAppliedMechanics,1978,45(4):889894[2]HustonRL,PasserelloCE.MultibodyStructuralDynamicsIncludingTranslationBetweentheBo