有限元编程算例(fortran)

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Fortran语言编写弹性力学平面问题3节点三角形单元或4节点等参单元的有限元程序

Fortran语言编写弹性力学平面问题3节点三角形单元或4节点等参单元的有限元程序：c--------------------------------------------------------------------------c.....FEA2DP---A finite element analysis program for2D elastic problemscc Tangent matrix is stored with varioud band methodc This program is used to demonstrte the usage of vrious bandc Storage schem of symmetric and unsymmetric tangent matrixcc Wang shunjinc At chongqing vniversity(06/06/2013)c-------------------------------------------------------------------------program FEA2DPcc a(1)-a(n1-1):x(ndm,nummnp);a(n1)-a(n2-1):f(ndf,numnp)c a(n2)-a(n3-1):b(neq);a(n3)-a(n4-1):ad(neq)c a(n4)-a(n5-1):al(nad);a(n5)-a(n6-1):nu(nad)cc ia(1)-ia(n1-1):ix(nen1,numel);ia(n1)-ia(n2-1):id(ndf,numnp)c ia(n2)-ia(n3-1):jd((ndf*numnp);ia(n3)-ia(n4-1):idl(nen*numel*ndf)cimplicit real*8(a-h,o-z)dimension a(100000),ia(1000)character*80headcommon/cdata/numnp,numel,nummat,nen,neqcommon/sdata/ndf,ndm,nen1,nstcommon/iofile/ior,iowcnmaxm=100000imaxm=1000ior=1iow=2cc Open files for data input and outputcopen(ior,file='input.dat',form='formatted')open(iow,file='output.dat')cc.....Read titlecread(ior,'(a)')headwrite(iow,'(a)')headcc.....Read and print control informationcc numnp:number of nodesc numel:number of elementsc nummat:number of material typesc nload:number of loadsc ndm:number of coordinats of each nodec ndf:number of degrees of freedomc nen:number of nodes in each elementcread(ior,'(7i5)')numnp,numel,nummat,nload,ndm,ndf,nenwrite(iow,2000)numnp,numel,nummat,nload,ndm,ndf,nen cc.....Set poiters for allocation of data arrayscnen1=nen+4nst=nen*ndfnneq=ndf*numnpcn1=ndm*numnp+1n2=n1+ndf*numnp+1ci1=nen1*numel+1i2=i1+ndf*numnp+1i3=i2+ndf*numnp+1i4=i3+numel*nen*ndf+1cc.....Call mesh input subroutine to read all mesh dataccall pmesh(a(1),a(n1),ia(1),ia(i1),ndf,ndm,nen1,nload)cpute profileccall profil(ia(i2),ia(i3),ia(i1),ia(1),ndf,nen1,nad)cn3=n2+neq+1n4=n3+neq+1n5=n4+nad+1n6=n5+nad+1cc The lengthes of real and integer arrayscwrite(iow,2222)n6,i4cc The lengthes of array exceeds the limitationcif(n6>nmaxm.or.i4>imaxm)thenif(n6>nmaxm)write(iow,3333)n6,nmaxmif(i4>nmaxm)write(iow,4444)i4,imaxmstopend ifctute and aseemble element arraysccall assem(nad,ia(1),ia(i1),ia(i2),a(1),a(n2),a(n3),1a(n4),a(n5))cc Form load vectorccall pload(ia(i1),a(n1),a(n2),nneq,neq)cc.....Triangular decomposition of a matrix stored in profile formccall datri(ndf,numnp,ia(i2),neq,nad,.false.,a(n3),a(n5),a(n5))cc For unsymmtric tangent matirxc Call datri(ndf,numnp,ia(i2),neq,nad,.true.,a(n3),a(n4),a(n5))cc Solve equationsccall dasol(ndf,numnp,a(n2),ia(i2),neq,nad,aengy,a(n3),a(n5),a(n5)) cc For unsymmetric tangent matrixc Call dasol(ndf,numnp,a(n2),ia(i2),neq,nad,aengy,a(n3),a(n5),a(n5)) cc Output nodal displacementsccall prtdis(ia(i1),a(n2),ndf,numnp,neq)cc.....Close input and output files;destroy temporary disk filescclose(ior)close(iow)cc.....Input/output formatsc1000format(20a4)2000format(//x5x,'number of nodal points=',i6/15x,'number of elements=',i6/25x,'number of material sets=',i6/35x,'number of nodal loads=',i6/45x,'dimension of coordinate space=',i6/55x,'degree of freedoms/node=',i6/65x,'nodes per element(maximum)=',i6)2222format(//,10x,'the lengthe of real array is',i10,/,110x,'the lengthe of integer array is',i10)3333format(//,10x,'the lengthe of real array',i10,'exceed the',1'maximun value',i10)4444format(//,10x,'the lengthe of integer array',i10,'exceed the',1'maximun value',i10)cstopendccsubroutine pmesh(x,f,ix,id,ndf,ndm,nen1,nload)cc......Data input routine for mesh descriprioncimplicit real*8(a-h,o-z)dimension x(ndm,numnp),f(ndf,numnp),id(ndf,numnp),ix(nen1,numel)common/bdata/head(20)common/cdata/numnp,numel,nummat,nen,neqcommon/mater/ee,xnu,itypecommon/iofile/ior,iowcc.....Input constrain codes and nodal coordinate datacc id(k,j):constrain code of kth degree of freedom of node j,=0:free,=1:fixed c x(k,j):kth coordinate of node jcdo i=1,numnpread(ior,'(3i5,2f10.4)')j,(id(k,j),k=1,ndm),(x(k,j),k=1,ndm) end docwrite(iow,'(//17hnodal coordinates,/)')do i=1,numnpwrite(iow,'(3i5,2f10.4)')i,(id(k,i),k=1,ndm),(x(k,i),k=1,ndm) end docc.....element data inputcc ix(k,j):global node number of kth node in element jcdo i=1,numelread(ior,'(9i5)')j,(ix(k,j),k=1,nen)end docwrite(iow,'(//,18helement definition,/)')do i=1,numelwrite(iow,'(9i5)')j,(ix(k,j),k=1,nen)end docc.....Material data inputcc ee:young's modulus,xnu:poisson ratioc itype:type of problem,=1,:plane stress,=2:plane strain,=3:axi-symmetric cread(ior,'(2f10.4,i5)')ee,xnu,itypewrite(iow,'(//,19hmateial properties,/)')write(iow,'(2(e10.4,5x),i5)')ee,xnu,itypecc.....force/disp data inputcc f(k,j):concentrate load at node j in k directioncf=0.0d0do i=1,nloadread(ior,'(i5,2f10.4)')j,(f(k,j),k=1,ndf)end docwrite(iow,'(//,20happlied nodal forces,/)')do i=1,nloadwrite(iow,'(i5,2f10.4)')j,(f(k,j),k=1,ndf)end docreturncc format statementsc2000format('mesh1>',$)3000format(1x,'**warning**element connections necessary'1'to use block in macro program')4000format('**current problem valies**'/i6,'nodes,',1i5,'elmts,',i3,'matls,',i2,'dims,',i2,'dof/node,',2i3,'nodes/elmt')endccsubroutine assem(nad,ix,id,jd,x,b,ad,al,au)cc Call element subroutine and assemble global tangent matrixcimplicit real*8(a-h,o-z)dimension ilx(nen),xl(ndf,nen),ld(ndf,nen),s(nst,nst),p(nst)dimension ix(nen1,numel),id(ndf,numnp),jd(ndf*numnp)dimension x(ndm,numnp),b(neq),ad(neq),al(nad),au(nad)common/cdata/numnp,numel,nummat,nen,neqcommon/sdata/ndf,ndm,nen1,nstcnel=nencc elenment loopcdo320n=1,numels=0.0d0!element stiffness matrixp=0.0d0!nodal forcene=ndo310i=1,nenilx(i)=ix(i,ne)!current element definitiondo k=1,ndmxl(k,i)=x(k,ilx(i))!nodal coords in current elementend dokk=ilx(i)do k=1,ndfld(k,i)=id(k,kk)!equation numbersend do310continuecc Call element libccall elmt01(xl,ilx,s,p,ndf,ndm,nst)cc Asemmble tangent matrix and load vector if neededccall dasbly(ndf,nad,s,p,ld,jd,nst,b,ad,al,au)c320continue!end element loopcreturnendccsubroutine dasbly(ndf,nad,s,p,ld,jp,ns,b,ad,al,au)cc.....Assemble the symmetric or unsymmetric arrays for'dasol'cimplicit real*8(a-h,o-z)c logical alfl,aufl,bfldimension ad(neq),al(nad),au(nad)dimension ld(ns),jp(ndf*numnp),b(neq),s(ns,ns),p(ns)common/cdata/numnp,numel,nummat,nen,neqcommon/iofile/ior,iowcc alfl=true:for unsymmetric matirx assemblec alfl=false:for symmetric matirx assemblec s:element stiffness matrixc p:load or internal force vectorc ad:diagonal elementsc au:upper triangle elementsc al:lower triangle elementsc jp:pointer to last element in each row/column of al/au respectivec ld:equation numbers of each freedom degree in an element(get from id) cc.....Loop through the rows to perform the assemblycdo200i=1,nsii=ld(i)if(ii.gt.0)thenc if(aufl)then!assemble stiffness matrixcc.....Loop through the columns to perform the assemblycdo100j=1,nsif(ld(j).eq.ii)thenad(ii)=ad(ii)+s(i,j)elseif(ld(j).gt.ii)thenjc=ld(j)jj=ii+jp(jc)-jc+1au(jj)=au(jj)+s(i,j)c if(alfl)al(jj)=al(jj)+s(j,i)!unsymmetricendif100continueendifc if(bfl)b(ii)=b(ii)+p(i)!assemble nodal forcec endif200continuecreturnendccsubroutine dasol(ndf,numnp,b,jp,neq,nad,energy,ad,al,au)cc.....Solution of symmetric equations in profile formc.....Coeficient matrix must be decomposed into its triangularc.....Factor using datri beforce using dasol.cc jp:pointer to last element in each row/column of al/au respecive ccimplicit real*8(a-h,o-z)dimension ad(neq),al(nad),au(nad)dimension b(neq),jp(ndf*numnp)common/iofile/ior,iowdata zero/0.0d0/cc.....Find the first nonzero entry in the ring hand sidecdo is=1,neqif(b(is).ne.zero)go to200end dowrite(iow,2000)returnc200if(is.lt.neq)thencc.....Reduce the right hand sidecdo300j=is+1,neqjr=jp(j-1)jh=jp(j)-jrif(jh.gt.0)thenb(j)=b(j)-dot(al(jr+1),b(j-jh),jh)end if300continueend ifcc.....Multiply inverse of diagonal elementscenergy=zerodo400j=is,neqbd=b(j)b(j)=b(j)*ad(j)energy=energy+bd*b(j)400continuecc.....backsubstitutioncif(neq.gt.1)thendo500j=neq,2,-1jr=jp(j-1)jh=jp(j)-jrif(jh.gt.0)thencall saxpb(au(jr+1),b(j-jh),-b(j),jh,b(j-jh))end if500continueend ifcreturnc2000format('**dasol warning1**zero right-hand-side vector') endccsubroutine datest(au,jh,daval)cc.....test for rankcimplicit real*8(a-h,o-z)dimension au(jh)cdaval=0.0d0cdo j=1,jhdaval=daval+abs(au(j))end docreturnendccsubroutine datri(ndf,numnp,jp,neq,nad,flg,ad,al,au)cc.....Triangular decomposiontion of a matrix stored in profile form cimplicit real*8(a-h,o-z)logical flgdimension jp(ndf*numnp),ad(neq),al(nad),au(nad)common/iofile/ior,iowcc.....n.b.tol should be set to approximate half-word precision.cdata zero,one/0.0d0,1.0d0/,tol/0.5d-07/cc.....Set initial values for contditioning checkcdimx=zerodimn=zerocdo j=1,neqdimn=max(dimn,abs(ad(j)))end dodfig=zerocc.....Loop through the columns to perform the triangular decomposition cjd=1do200j=1,neqjr=jd+1jd=jp(j)jh=jd-jrif(jh.gt.0)thenis=j-jhie=j-1cc.....If diagonal is zeor compute a norm for singularity testcif(ad(j).eq.zero)call datest(au(jr),jh,daval)do100i=is,iejr=jr+1id=jp(i)ih=min(id-jp(i-1),i-is+1)if(ih.gt.0)thenjrh=jr-ihidh=id-ih+1au(jr)=au(jr)-dot(au(jrh),al(idh),ih)if(flg)al(jr)=al(jr)-dot(al(jrh),au(idh),ih)end if100continueend ifcc.....Reduce the diagonalcif(jh.ge.0)thendd=ad(j)jr=jd-jhjrh=j-jh-1call dredu(al(jr),au(jr),ad(jrh),jh+1,flg,ad(j))cc.....Check for possible errors and print warningscif(abs(ad(j)).lt.tol*abs(dd))write(iow,2000)jif(dd.lt.zero.and.ad(j).gt.zero)write(iow,2001)jif(dd.gt.zero.and.ad(j).lt.zero)write(iow,2001)jif(ad(j).eq.zero)write(iow,2002)jif(dd.eq.zero.and.jh.gt.0)thenif(abs(ad(j)).lt.tol*daval)write(iow,2003)jendifendifcc.....Stroe reciprocal of diagonal,compute condition checkscif(ad(j).ne.zero)thendimx=max(dimx,abs(ad(j)))dimn=min(dimn,abs(ad(j)))dfig=max(dfig,abs(dd/ad(j)))ad(j)=one/ad(j)end if200continuecc.....Print conditioning informationcdd=zeroif(dimn.ne.zero)dd=dimx/dimnifig=dlog10(dfig)+0.6write(iow,2004)dimx,dimn,dd,ifigcreturncc.....formatsc2000format('**datri warning1**loss of at least7digits in', 1'reducing diagonal of equation',i5)2001format('**datri warning2**sign of changed when', 1'reducing equation',i5)2002format('**datri warning3**reduced diagonal is zero zeri for', 1'equation',i5)2003format('**datri warning4**rank failure ffo zero unreduced', 1'diagonal in equation',i5)2004format(//'conditon check:d-max',e11.4,';d-min',e11.4, 1';ratio',e11.4/'maximim no.diagonal digits lost:',i3) 2005format('cond ck:dmax',1p1e9.2,';dmin',1p1e9.2,1';ratio',1p1e9.2)endccsubroutine dredu(al,au,ad,jh,flg,dj)cc.....Reduce diagonal element in triangular decompositioncimplicit real*8(a-h,o-z)logical flgdimension al(jh),au(jh),ad(jh)cdo j=1,jhud=au(j)*ad(j)dj=dj-al(j)*udau(j)=udend docc.....Finish computation of column of al for unsymmetric matricescif(flg)thendo j=1,jhal(j)=al(j)*ad(j)end doend ifcreturnendccsubroutine profil(jd,idl,id,ix,ndf,nen1,nad)cpute profile of global arrayscimplicit real*8(a-h,o-z)dimension jd(ndf*numnp),idl(numel*nen*ndf),id(ndf,numnp),1ix(nen1,numel)common/cdata/numnp,numel,nummat,nen,neqcommon/frdata/maxfcommon/iofile/ior,iowcc jd:column hight(address of diagonal elements)c id:boudary condition codes before this bubroutine's runningc id:equation numbers in global array(excluded restrained nodes)after running c idl:element strech orderc nad:total number of non-zero elements except diagonal elementsc in global tangent matrixcc.....Set up the equation numberscneq=0cdo10k=1,numnpdo10n=1,ndfj=id(n,k)if(j.eq.0)thenneq=neq+1id(n,k)=neqelseid(n,k)=0endif10continuecpute column heightsccall pconsi(jd,neq,0)cdo50n=1,numelmm=0nad=0do30i=1,nenii=iabs(ix(i,n))if(ii.gt.0)thendo20j=1,ndfjj=id(j,ii)if(jj.gt.0)thenif(mm.eq.0)mm=jjmm=min(mm,jj)nad=nad+1idl(nad)=jjendif20continueend if30continueif(nad.gt.0)thendo40i=1,nadii=idl(i)jj=jd(ii)jd(ii)=max(jj,ii-mm)40continueendif50continuecpute diagongal pointers for profilecnad=0jd(1)=0if(neq.gt.1)thendo60n=2,neqjd(n)=jd(n)+jd(n-1)60continuenad=jd(neq)end ifcc.....Set element search order to sequentialcdo70n=1,numelidl(n)=n70continuecc.....equation summarycmaxf=0mm=0if(neq.gt.0)mm=(nad+neq)/neqwrite(iow,2001)neq,numnp,mm,numel,nad,nummatcreturnc2001format(5x,'neq=',i5,5x,'numnp=',i5,5x,'mm=',i5,/5x, 1'numel=',i5,5x,'nad=',i5,5x,'nummat=',i5/) endcsubroutine saxpb(a,b,x,n,c)cc.....Vector times scalar added to second vectorcimplicit real*8(a-h,o-z)dimension a(n),b(n),c(n)cdo k=1,nc(k)=a(k)*x+b(k)end docreturnendcsubroutine pconsi(iv,nn,ic)cc.....Zero integer arraycdimension iv(nn)cdo n=1,nniv(n)=icend docreturnendcsubroutine elmt01(xl,ilx,s,p,ndf,ndm,nst)cc.....plane linear elastic element routinec ityp=1:plane stressc=2:plane strainc=3:axisymmetriccimplicit real*8(a-h,o-z)dimension xl(ndm,nen),ilx(nen),sigr(6)dimension d(18),s(nst,nst),p(nst),shp(3,9),sg(16),tg(16),wg(16)character wd(3)*12common/cdata/numnp,numel,nummat,nen,neqcommon/mater/ee,xnu,itypecommon/iofile/ior,iowdata wd/'plane stress','plane strain','axisymmetric'/cc xl(ndm,nen):coords of each node in current elementc ilx(nen):element definition of current elementc d(18):materials propertiesc s(nst,nst):element stiffness matrixc p(ns):nodal force and internal forcec shp(3,9):shape function and its derivativesc sg(16),tg(16),wg(16):weight coefficients of guass intergtation c l,k:integration pointscl=2k=2e=eenel=nencc d(14):thickness;d(11),d(12):body forcesc.....Set material patameter type and flagscityp=max(1,min(ityp,3))j=min(ityp,2)cd(1)=e*(1.+(1-j)*xnu)/(1.+xnu)/(1.-j*xnu)d(2)=xnu*d(1)/(1.+(1-j)*xnu)d(3)=e/2./(1.+xnu)d(13)=d(2)*(j-1)if((d(14).le.0.0d0).or.ityp.ge.2)d(14)=1.0d(15)=itypd(16)=ed(17)=xnud(18)=-xnu/el=min(4,max(1,l))k=min(4,max(1,k))d(5)=ld(6)=kc d(9)=t0c d(10)=e*alp/(1.-j*xnu)lint=0cwrite(iow,2000)wd(ityp),d(16),d(17),d(4),l,k,d(14),1d(11),d(12)cc.....stiffness/residual computationcl=kcc Compute cordinates and weights of integtation pointc`sg,tg:cootds;wg=wp*wqcif(l*l.ne.lint)call pguass(l,lint,sg,tg,wg)cpute integrals of shape functionscdo340l=1,lintcc Compute shape function and their derivatives to local and global coordinate systemccall shape(sg(l),tg(l),xl,shp,xsj,ndm,nen,ilx,.false.)cc Compute global coordinates of integration pointscxx=0.0yy=0.0do j=1,nenxx=xx+shp(3,j)*xl(1,j)yy=yy+shp(3,j)*xl(2,j)end doxsj=xsj*wg(l)*d(14)!xsj+|j|(sp,tq)*wp*wq*tcpute jacobian correction for plane stress and strain problemscif(ityp.le.2)thendv=xsjxsj=0.0zz=0.0c sigr4=-d(11)*dv!d(11)body forceelsecc For anisymmetric problemcdv=xsj*xx*3.1415926*2.zz=1./xxc sigr4=sigr(4)*xsj-d(11)*dvendifj1=1cc.....Loop over rowscdo330j=1,nelw11=shp(1,j)*dvw12=shp(2,j)*dvw22=shp(3,j)*xsjw22=shp(3,j)*dv*zzccpute the internal forces out of balancecc p(j1)=p(j1)-(shp(1,j)*sigr(1)+shp(2,j)*sigr(2))*dvc1-shp(3,j)*sigr4c p(j1+1)=p(j1+1)-(shp(1,j)*sigr(2)+shp(2,j)*sigr(3))*dvc1+d(12)*shp(3,j)*dv!d(12)body force cc.....Loop over columns(symmetry noted)c Compute stiffness matrixck1=j1a11=d(1)*w11+d(2)*w22a21=d(2)*w11+d(1)*w22a31=d(2)*(w11+w22)a41=d(3)*w12a12=d(2)*w12a32=d(1)*w12a42=d(3)*w11do320k=j,nelw11=shp(1,k)w12=shp(2,k)w22=shp(3,k)*zzs(j1,k1)=s(j1,k1)+w11*a11+w22*a21+w12*a41s(j1+1,k1)=s(j1+1,k1)+(w11+w22)*a12+w12*a42s(j1,k1+1)=s(j1,k1+1)+w12*a31+w11*a41s(j1+1,k1+1)=s(j1+1,k1+1)+w12*a32+w11*a42k1=k1+ndf320continuej1=ndf+j1330continue340continuecc.....Make stiffness symmetriccdo360j=1,nstdo360k=j,nsts(k,j)=s(j,k)360continuecreturncc.....Formats for input-outputc1000format(3f10.0,3i10)1001format(8f10.0)2000format(/5x,a12,'linear elastic element'//110x,'modulus',e18.5/10x,'poission ratio',f8.5/10x,'density',e18.5/ 210x,'guass ptr/dir',i3/10x,'stress pts',i6/10x,'thickness',e16.5/310x,'1-gravity',e16.5/10x,'2-gtavity',e16.5/10x,'alpha',e20.5/410x,'base temp',e16.5/)2001format(5x,'element stresses'//'elmt1-coord',2x,'11-stress',2x, 1'12-stress',2x,'22-stress',2x,'33-stress',3x,'1-coord',2x,3x,2'2-stress'/'matl2-coord',2x,'11-strain',2x,'12-strain'2x,3'22-strain',2x,'33-strain',6x,'angle'/39('-'))2002format(i4,0p1f9.3,1p6e11.3/i4,0p1f9.3,1p4e11.3,0p1f11.2/) 5000format('input:e,nu,rho,pts/stiff,pts/stre',1',type(1=stress,2=strain,3=axism)',/3x,'>',$)5001format('input:thickness,1-body force,1-body force,alpha,' 1,'temp-base'/3x,'>',$)endcsubroutine shape(ss,tt,xl,shp,xsj,ndm,nel,ilx,flg)cc.....Shape function routine for two dimension elementscimplicit real*8(a-h,o-z)logical flgdimension xl(ndm,nel),s(4),t(4),x(nel)dimension shp(3,nel),xs(2,2),sx(2,2)data s/-0.5d0,0.5d0,0.5d0,-0.5d0/,1t/-0.5d0,-0.5d0,0.5d0,0.5d0/cc.....Form4-node quatrilateral shape functionscc nel:nuber of nodes per elementcdo100i=1,4shp(3,i)=(0.5+s(i)*ss)*(0.5+t(i)*tt)shp(1,i)=s(i)*(0.5+t(i)*tt)shp(2,i)=t(i)*(0.5+s(i)*ss)100continuecc.....Form triangge bu adding their and fourth together for triangle element cif(nel.eq.3)thendo i=1,3shp(i,3)=shp(i,3)+shp(i,4)enddoendifcc.....Add quatratic terms if necessary for element with more than4nodes cif(nel.gt.4)call shap2(ss,tt,shp,ilx,nel)cc.....Construct jacobian and its inversecdo125i=1,2do125j=1,2xs(i,j)=0.0do120k=1,nelxs(i,j)=xs(i,j)+xl(i,k)*shp(j,k)120continue125continuecc xsj:determinate of jacob matrixcxsj=xs(1,1)*xs(2,2)-xs(1,2)*xs(2,1)cif(flg)returnc flg=false:form global derivativescif(xsj.le.0.0d0)xsj=1.0sx(1,1)=xs(2,2)/xsjsx(2,2)=xs(1,1)/xsjsx(1,2)=-xs(1,2)/xsjsx(2,1)=-xs(2,1)/xsjcc....Form global derivativescdo130i=1,neltp=shp(1,i)*sx(1,1)+shp(2,i)*sx(2,1)shp(2,i)=shp(1,i)*sx(1,2)+shp(2,i)*sx(2,2)shp(1,i)=tp130continuecreturnendcsubroutine shap2(s,t,shp,ilx,nel)cc....Add quadtatic function as necessarycimplicit real*8(a-h,o-z)dimension shp(3,9),ilx(nel)cs2=(1.-s*s)/2.t2=(1.-t*t)/2.do100i=5,9do100j=1,3shp(j,i)=0.0100continuecc.....Midsize nodes(serenipity)cif(ilx(5).eq.0)go to101shp(1,5)=-s*(1.-t)shp(2,5)=-s2shp(3,5)=s2*(1.-t)101if(nel.lt.6)go to107if(ilx(6).eq.0)go to102shp(1,6)=t2shp(2,6)=-t*(1.+s)shp(3,6)=t2*(1.+s)102if(nel.lt.7)go to107if(ilx(7).eq.0)go to103shp(1,7)=-s*(1.+t)shp(2,7)=s2shp(3,7)=s2*(1.+t)103if(nel.lt.8)go to107if(ilx(8).eq.0)go to104shp(1,8)=-t2shp(2,8)=-t*(1.-s)shp(3,8)=t2*(1.-s)cc.....Interior node(lagragian)c104if(nel.lt.9)go to107if(ilx(9).eq.0)go to107shp(1,9)=-4.*s*t2shp(2,9)=-4.*t*s2shp(3,9)=4.*s2*t2cc.....Correct edge nodes for interior node(lagrangian) cdo106j=1,3do105i=1,4105shp(j,i)=shp(j,i)-0.25*shp(j,9)do106i=5,8106if(ilx(i).ne.0)shp(j,i)=shp(j,i)-.5*shp(j,9)cc.....Correct corner nodes for presense of midsize nodes c107do108i=1,4k=mod(i+2,4)+5l=i+4do108j=1,3108shp(j,i)=shp(j,i)-0.5*(shp(j,k)+shp(j,l))returnendcsubroutine pguass(l,lint,r,z,w)cc.....Guass points and weights for two dimensionscimplicit real*8(a-h,o-z)dimension lr(9),lz(9),lw(9),r(16),z(16),w(16)c common/eldtat/dm,n,ma,mct,iel,neldata lr/-1,1,1,-1,0,1,0,-1,0/,lz/-1,-1,1,1,-1,0,1,0,0/data lw/4*25,4*40,64/cc lint:number of integration pointsc r,z:coordinates of integration pointsc w:wp*wq,product of the two weightsclint=l*lcc.....1x1integerationc1r(1)=0.z(1)=0.w(1)=4.creturncc.....2x2integerationc2g=1.0/sqrt(3.d0)do i=1,4r(i)=g*lr(i)z(i)=g*lz(i)w(i)=1.end docreturncc.....3x3integerationc3g=sqrt(0.60d0)h=1.0/81.0d0cdo i=1,9r(i)=g*lr(i)z(i)=g*lz(i)w(i)=h*lw(i)enddocreturncendcsubroutine pload(id,f,b,nneq,neq) cc.....Form load vector in compact formcimplicit real*8(a-h,o-z)dimension f(nneq),b(neq),id(nneq)common/iofile/ior,iowcb=0.0d0cj=id(n)if(j.gt.0)thenb(j)=f(n)endifenddocreturnendcsubroutine prtdis(id,b,ndf,numnp,neq)cc Print out nodal displacementscimplicit real*8(a-h,o-z)dimension id(ndf,numnp),b(neq),u(ndf,numnp)common/iofile/ior,iowcu=0.0d0do100i=1,numnpdo j=1,ndfn=id(j,i)if(n>0)u(j,i)=b(n)end do100continuecc Out nodal displacementscwrite(iow,'(//,19hnodal displacements,/)')do i=1,numnpwrite(iow,'(5x,i5,2x,3(e12.4,3x))')i,(u(k,i),k=1,ndf) end docreturnendcdouble precision function dot(a,b,n)implicit real*8(a-h,o-z)dimension a(n),b(n)cc.....Dot product functioncdot=0.0d0do10k=1,ndot=dot+a(k)*b(k)10continuereturn end。

Fortran平面钢架有限元分析

1 有限元分析软件的开发1.1 程序功能该程序为平面刚架静力分析程序，能针对平面刚架间问题进行有限元计算，计算杆端位移及杆端力大小。

程序从磁盘文件中读取单元编号、节点编号及坐标、材料属性、荷载、边界条件等信息；将杆端位移，杆端力等计算结果以磁盘文件的形式输出，采用等带宽二维数组存储整体刚度矩阵并使用高斯消去法进行求解。

1.2 程序结构及流程1.3 程序的输入与输出详细介绍输入输出数据的格式。

如：数据文件分几个部分，各有几行，分别包含哪些内容及其类型、先后次序，等等。

输入，共有九行。

第一行：7,13,5,1,2,2。

分别为，7个结点，13个自由度，5个单元，1个类型，2个结点荷载，2个非结点荷载。

第二行：1,2,3,0.0,0.0,0,0,,6.0,0.0。

分别为：一号结点的位移序号，x方向为1，y方向为2，转角为3，坐标为(0.0,0.0)，因为二号结点固结在地面，所以二号结点的位移序号，x方向为0，y方向为0，转角为0，坐标为(6.0,0.0)。

第三行：4,5,6,0.0,6.0,4,5,7,0.0,6.0。

分别为：三号结点的位移序号，x方向为4，y方向为5，转角为6，坐标为(0.0,6.0), 四号结点位移序号x方向和y相同，转角为7，坐标为(,0.0,6.0)。

第四行：8,9,10,6.0,6.0,0,0,11,0.0,12.0.五号结点位移序号，x方向为8，y方向为9，转角为10，坐标为（6.0,6.0）。

因为六号结点铰接在地面，所以六号结点的位移序号，x方向和y方向为0，转角为11，坐标为（0.0,12.0）。

第五行：12,0,13,6.0,12.0. 因为七号结点与地面用滑动支座固定，所以七号结点的位移序号，x方向为12，y方向为0，转角为13，坐标（6.0,12.0）.第六行：1,2,1,1,3,1,4,5,1,3,6,1,5,7,1,分别为，1号和2号结点组成的单元为1号类型。

1号和3号结点组成的单元为1号类型，4号和5号结点组成的为1号类型，3号和6号结点组成的单元为1号类型，5号和7号结点组成的单元为1号类型。

Fortran语言-有限元程序分析-平面钢架

程序框图：程序特点：问题类型：可用于计算结构力学的平面刚架问题单元类型：直接利用杆单元载荷类型：节点载荷及非节点载荷，其中非节点载荷包括均布荷载和垂直于杆件的集中荷载材料性质：所有杆单元几何性质相同，且由相同的均匀材料组成方程求解：结构刚度矩阵采用满阵存放，Gauss消元过程采用《数值分析》中的列主元素消去法输入文件：按先处理法的要求，由手工生成输入数据文件1.主要变量：ne: 单元个数nj: 结点个数n: 自由度e: 弹性模量（单位：KN/m2）a: 杆截面积zi: 惯性矩np: 结点荷载个数nf: 非结点荷载个数x(nj): 存放结点的x轴坐标y(nj): 存放结点的y轴坐标ij(ne,2): 存放单元结点编号，其中ij(nj,1)存放起始结点编号，ij(nj,2)存放终止结点编号jn(nj,3): 存放结点位移编号，以组成单元定位数组pj(np,3): 存放结点荷载信息，其中pj(np,1)存放结点荷载作用结点号，pj(np,2)存放荷载方向代码(1—x方向；2—y方向；3—转角)，pj(np,3)存放荷载大小pf(ne,4): 存放非结点荷载信息，其中pf(ne,1)存放荷载作用单元号，pf(ne,2)存放荷载代码(1—均布荷载，2—垂直集中荷载)，pf(ne,3)存放荷载大小，pf(ne,4)荷载作用距离（均布荷载，集中荷载均以单元起始结点为计算起始位置）。

2.子例行子程序哑元信息：第一部分：基本部分I. subroutine lsc(Length & Sin & Cos):输入哑元：m(单元号),nj,ne,x,y,ij输出哑元：bl(杆件长度),si(正弦值),co(余弦值)II. subroutine elv(Element Location Vector):输入哑元：m,ne,nj,ij,jn输出哑元：lv(单元定位数组)III. subroutine esm(Element Stiffness Matrix):输入哑元：e,a,zi,bl,si,co输出哑元：ek(整体坐标系下的单刚矩阵)IV. subroutine eff(Element Fixed-end Forces)输入哑元：i,pf,nf,bl输出哑元：fo(局部坐标系下单元固端力)第二部分：主程序直接调用部分I. subroutine tsm(Total Stiffness Matrix 计算总刚矩阵)输入哑元：ne,nj,n,e,x,y,ij,a,zi,jn输出哑元：tkII. subroutine jlp(Joint Load Vector 计算结点荷载)输入哑元：ne,nj,n,np,nf,x,y,ij,jn,pj,pf输出哑元：p(结点荷载列矩阵)III. subroutine gauss(带列主元素消去的高斯法)输入(输出)哑元：tk,p,n ;(注意，算出位移后，直接存储到结点荷载列矩阵)IV. subroutine mvn(Member-end forces of elements 计算各单元的杆端力)输入哑元：ne,nj,n,nf,e,x,y,ij,a,zi,jn,pf,p3.文件管理：源程序文件：pff.for程序需读入的数据文件：input.txt程序输出的数据文件：output4.数据文件格式：【输出文件格式】： 1. 第1部分：每行数据依次为：结点号，结点x 方向位移，结点y 方向位移，结点转角位移 2. 第2部分：每行数据依次为：单元号，xi F ，yi F ，i M ，xj F ，yj F ，j M源程序：program PFF implicit nonereal tk(100,100),x(50),y(50),p(100),pj(50,3),pf(50,4) integer ij(50,2),jn(50,3) integer ne,nj,n,np,nf real e,a,ziopen(1,file="input.txt",status="old") open(2,file="output.txt",status="old")read(1,*) ne,nj,n,e,a,zi,np,nfcall input(ne,nj,x,y,ij,jn,np,nf,pj,pf)call tsm(ne,nj,n,e,x,y,ij,a,zi,jn,tk)call jlp(ne,nj,n,np,nf,x,y,ij,jn,pj,pf,p)call gauss(tk,p,n)call mvn(ne,nj,n,nf,e,x,y,ij,a,zi,jn,pf,p)endsubroutine input(ne,nj,x,y,ij,jn,np,nf,pj,pf)dimension x(nj),y(nj),ij(ne,2),jn(nj,3),pj(np,3),pf(nf,4) read(1,*)(x(i),y(i),i=1,nj)read(1,*)(ij(i,1),ij(i,2),i=1,ne)read(1,*)((jn(i,j),j=1,3),i=1,nj)if (np>0) read(1,*)((pj(i,j),j=1,3),i=1,np)if (nf>0) read(1,*)((pf(i,j),j=1,4),i=1,nf)endsubroutine tsm(ne,nj,n,e,x,y,ij,a,zi,jn,tk)dimension x(nj),y(nj),ij(ne,2),jn(nj,3),tk(n,n),ek(6,6),lv(6) do i=1,ndo j=1,ntk(i,j)=0enddoenddodo m=1,necall lsc(m,ne,nj,x,y,ij,bl,si,co)call esm(e,a,zi,bl,si,co,ek)call elv(m,ne,nj,ij,jn,lv)do l=1,6i=lv(l)if (i/=0) thendo k=1,6j=lv(k)if (j/=0) tk(i,j)=tk(i,j)+ek(l,k)enddoendifenddoenddoendsubroutine lsc(m,ne,nj,x,y,ij,bl,si,co) dimension x(nj),y(nj),ij(ne,2)i=ij(m,1)j=ij(m,2)dx=x(j)-x(i)dy=y(j)-y(i)bl=sqrt(dx*dx+dy*dy)si=dy/blco=dx/blendsubroutine esm(e,a,zi,bl,si,co,ek) dimension ek(6,6)c1=e*a/blc2=2.0*e*zi/blc3=3.0*c2/blc4=2.0*c3/bls1=c1*co*co+c4*si*sis2=(c1-c4)*si*cos3=c3*sis4=c1*si*si+c4*co*cos5=c3*cos6=c2ek(1,1)=s1ek(1,2)=s2ek(1,3)=-s3ek(1,4)=-s1ek(1,5)=-s2ek(1,6)=-s3ek(2,2)=s4ek(2,3)=s5ek(2,4)=-s2ek(2,5)=-s4ek(2,6)=s5ek(3,3)=2*s6ek(3,4)=s3ek(3,5)=-s5ek(3,6)=s6ek(4,4)=s1ek(4,5)=s2ek(4,6)=s3ek(5,5)=s4ek(5,6)=-s5ek(6,6)=2.0*s6do i=1,5do j=i+1,6ek(j,i)=ek(i,j)enddoenddoendsubroutine elv(m,ne,nj,ij,jn,lv)dimension ij(ne,2),jn(nj,3),lv(6)i=ij(m,1)j=ij(m,2)do k=1,3lv(k)=jn(i,k)lv(k+3)=jn(j,k)enddoendsubroutine jlp(ne,nj,n,np,nf,x,y,ij,jn,pj,pf,p)dimension x(nj),y(nj),ij(ne,2),jn(nj,3),pj(np,3),pf(nf,4),p(n),fo(6),pe(6),lv(6) do i=1,np(i)=0.0enddoif (np>0) thendo i=1,npj=int(pj(i,1))k=int(pj(i,2))l=jn(j,k)if (l/=0) p(l)=pj(i,3)enddoendifif(nf>0) thendo i=1,nfm=int(pf(i,1))call lsc(m,ne,nj,x,y,ij,bl,si,co)call eff(i,pf,nf,bl,fo)call elv(m,ne,nj,ij,jn,lv)pe(1)=-fo(1)*co+fo(2)*sipe(2)=-fo(1)*si-fo(2)*cope(3)=-fo(3)pe(4)=-fo(4)*co+fo(5)*sipe(5)=-fo(4)*si-fo(5)*cope(6)=-fo(6)do j=1,6l=lv(j)if (l/=0) p(l)=p(l)+pe(j) enddoenddoendifendsubroutine eff(i,pf,nf,bl,fo) dimension pf(nf,4),fo(6)no=int(pf(i,2))q=pf(i,3)c=pf(i,4)b=bl-cc1=c/blc2=c1*c1c3=c1*c2do j=1,6fo(j)=0.0enddogoto(10,20),no10 fo(2)=-q*c*(1.0-c2+c3/2.0)fo(3)=-q*c*c*(0.5-2.0*c1/3.0+0.25*c2) fo(5)=-q*c*c2*(1.0-0.5*c1)fo(6)=q*c*c*c1*(1.0/3.0-0.25*c1) return20 fo(2)=-q*b*b*(1.0+2.0*c1)/bl/blfo(3)=-q*c*b*b/bl/blfo(5)=-q*c2*(1.0+2.0*b/bl)fo(6)=q*c2*breturnendsubroutine gauss(e,d,n)dimension e(n,n),d(n),a(n,n+1)do i=1,ndo j=1,na(i,j)=e(i,j)enddoenddodo i=1,na(i,n+1)=d(i)enddodo k=1,n-1do i=k+1,nif (abs(a(i,k))>abs(a(k,k))) thendo j=1,n+1c=a(k,j)a(k,j)=a(i,j)a(i,j)=cenddoelseendifenddodo i=k+1,na(i,k)=a(i,k)/a(k,k)do j=k+1,n+1a(i,j)=a(i,j)-a(i,k)*a(k,j)enddoenddoenddoa(n,n+1)=a(n,n+1)/a(n,n)do i=n-1,1,-1do j=i+1,np=p+a(i,j)*a(j,n+1)enddoa(i,n+1)=(a(i,n+1)-p)/a(i,i)p=0enddodo i=1,nd(i)=a(i,n+1)enddoendsubroutine mvn(ne,nj,n,nf,e,x,y,ij,a,zi,jn,pf,p)dimension x(nj),y(nj),ij(ne,2),jn(nj,3),pf(nf,4),lv(6),fo(6),d(6),fd(6),f(6),ek(6,6),p(n) write(2,10)10 format(//2x,"结点位移"/5x,"结点号",9x,"u向位移",9x,"v向位移",9x,"角位移") do j=1,njdo i=1,3d(i)=0.0l=jn(j,i)if (l/=0) d(i)=p(l)enddowrite(2,20)j,d(1),d(2),d(3)20 format(2x,i6,4x,3e15.6)enddowrite(2,30)30 format(/2x,"单元杆端力及弯矩"/4x,"单元号",13x,"Fx",17x,"Fy",17x,"弯矩") do m=1,necall lsc(m,ne,nj,x,y,ij,bl,si,co)call esm(e,a,zi,bl,si,co,ek)call elv(m,ne,nj,ij,jn,lv)do i=1,6l=lv(i)d(i)=0.0if(l/=0) d(i)=p(l)enddodo i=1,6fd(i)=0.0do j=1,6fd(i)=fd(i)+ek(i,j)*d(j)enddoenddof(1)=fd(1)*co+fd(2)*sif(2)=-fd(1)*si+fd(2)*cof(3)=fd(3)f(4)=fd(4)*co+fd(5)*sif(5)=-fd(4)*si+fd(5)*cof(6)=fd(6)if (nf>0) thendo i=1,nfl=int(pf(i,1))if (m==l) thencall eff(i,pf,nf,bl,fo)do j=1,6f(j)=f(j)+fo(j)enddoendifenddoendifwrite(2,40)m,f40format(2x,i8,4x,"Ix=",f12.4,3x,"Iy=",f12.4,3x,"Mi=",f12.4/14x,"Jx=",f12.4,3x,"J y=",f12.4,3x,"Mj=",f12.4)enddoend【算例】：课题二：平面刚架有限元程序分析题目一：分析如图所示结构，其中5AB BC CD m ===， 3.5ED EF FG m ===，40GPa E =，20.02m A =，44410m I -=⨯。

读有限元Fortran程序笔记范文

读有限元程序笔记1.ALLOCATABLE::COORD(:,:),PROPS(:,:,:) !声明两个可变大小的数组，COORD(:,:)是二维数组，PROPS(:,:,:)是三维数组。

2.Fortran程序行首为C代表改行为注释，不会被编译3.全局变量（common），不同的程序之间，也就是在不同的函数之间或者是主程序跟函数之间，除了可以通过传递参数的方法来共享内存，还可以通过“全局变量”来让不同程序中声明出来的变量使用相同的内存位置。

4.Dimensional维的，viscoplastic塑性的，elastic有弹力的，finite有限的，element元素，program程序。

5.THREE DIMENSIONAL ELASTIC-VISCOPLASTIC FINITE ELEMENT PROGRAM三维弹塑性有限元程序6.Module可以用来封装程序模块，通常是用来把程序中，具备相关功能的函数及变量封装在一起。

程序在开始定义了一个module模块，在模块中定义了MXKKK=，MXGSJ=1000，MXGSJ=1000三个常量（PARAMETER表示常量），并且每个常量都赋了值。

在module模块中定义了NELEM,NPOIN,NPROP,MXDFN,NSTEP,IDEVP,IDDP,LTYPE以及NFIX1,NPL,NVL,NSL,NHL,NTL,IDCVG,NTOTV,NKK以及DTIME,TOLER,SCALE,DSCALE这些全局变量（common表示全局变量），定义了ICM(3,8),CGAUS(2),VSHAP(8,8),DERIV(3,8,8)以及POSGP(3),COPG(3),EJ(3,3),EJACI(3,3),R(8,8)这些维数与大小都确定的全局数组变量，定义了COORD(:,:),PROPS(:,:,:)以及STRSG(:,:,:),DJ(:,:),CARTD(:,:,:,:)以及TRANJ(:,:,:,:),DJRMX(:,:,:)以及DREMX(:,:,:),DJEMX(:,:,:,:)以及CREMX(:,:,:),CJEMX(:,:,:,:)以及MELEM(:,:),MPROP(:),ISSOR(:,:),NNDEX(:)以及MPFIX(:,:),MPSJ(:),MMATP(:),MPIV(:)以及TSTIF(:)以及ADISP(:),TDISP(:),ALOAD(:)以及PSNBR(:,:,:),PSNBJ(:,:)以及PSTNR(:,:,:),PSTNJ(:,:)以及STRSP(:,:),STRSJ(:,:)这些维数确定但是大小不确定的可变大小的数组，ALLOCATABLE表示可变大小的数组变量。

读有限元Fortran程序笔记

读有限元程序笔记1.ALLOCATABLE::COORD(:,:),PROPS(:,:,:) !声明两个可变大小的数组，COORD(:,:)是二维数组，PROPS(:,:,:)是三维数组。

4.Dimensional维的，viscoplastic塑性的，elastic有弹力的，finite有限的，element元素，program程序。

程序在开始定义了一个module模块，在模块中定义了MXKKK=50000000，MXGSJ=1000，MXGSJ=1000三个常量（PARAMETER表示常量），并且每个常量都赋了值。

Fortran---平面四边形八结点等参元有限元程序

% -------------------------------------------------------------------------% 这是一个平面四边形八结点等参元有限元主程序，本程序具有以下功能：% 1,本程序能计算平面应力问题。

% 2，自动画出变形图和荷载图。

% 3，输出节点位移，节点力,节点应力，和节点主应力。

% 时间：2004年12月%--------------------------------------------------------------------------function N8plane% 变量说明列表:% NfreeNum 节点自由度数(本程序为2);EleNodeNum 单元节点数(本程序为8) % ---------------------------单变量---------------------------------------% FP1 数据文件指针(输入);NPOIN 节点总数;NELEM 单元总数;NVFIX 约束自由度数;% E 弹性模量;POISSON 泊松比;h 单元厚度;method 问题类型(1.单元应力 2.单元应变)% ----------------------------数组----------------------------------------% LNODS 单元定义;COORD 坐标;FPOIN 点荷载定义;k 单刚矩阵;K 总刚矩阵% Oxy 单元中点应力;O12单元中点主应力% ----------------------------矢量----------------------------------------% FIXED 约束信息;NFORCE 荷载信息;ASLOD 等效节点荷载;Ecoord 单元坐标% DISP 总体位移;EDisp 单元位移% ------------------------------------------------------------------------% 主调函数:% N8ek 生成单刚N8Assemble 组装总刚;N8stress 求解应力;% ------------------------------------------------------------------------%%%clear%-----输入数据存储的文件名------------file_in = input('数据输入的文件: ', 's' ) ;file_out = input( '数据输出的文件: ', 's') ;%--------------------------------------------------------------------------% 打开文件读取数据%--------------------------------------------------------------------------FP1=fopen(file_in,'r');NfreeNum=2;EleNodeNum=8;NPOIN=fscanf(FP1,'%d',1); NELEM=fscanf(FP1,'%d',1); NVFIX=fscanf(FP1,'%d',1);E=fscanf(FP1,'%f',1);POISSON=fscanf(FP1,'%f',1);h=fscanf(FP1,'%f',1);method=fscanf(FP1,'%d' ,1);%-------读取结构信息--------LNODS=fscanf(FP1,'%f',[8,NELEM])'; %单元定义COORD=fscanf(FP1,'%f',[2,NPOIN])'; %坐标FIXED=fscanf(FP1,'%f',NVFIX)'; %约束信息NFORCE=fscanf(FP1,'%d',2)'; %荷载信息if NFORCE(1)~=0FPOIN=fscanf(FP1,'%f',[3,NFORCE(1)])'; %节点力end%--------------定义非结点力-------------------------------------------------if NFORCE(2)~=0NF=NFORCE(1);np_number=fscanf( FP1, '%d', 1 ) ; % 读入均布侧压的单元边数PBorder=zeros(np_number,6);for i=1:np_numberPBorder(i,1)=fscanf( FP1, '%d', 1 ) ; % 单元编号PBorder(i,2)=fscanf( FP1, '%d', 1 ) ; % 侧压边左结点号PBorder(i,3)=fscanf( FP1, '%d', 1 ) ; % 侧压边中结点号PBorder(i,4)=fscanf( FP1, '%d', 1 ) ; % 侧压边右结点号PBorder(i,5)=fscanf( FP1, '%f', 1 ) ; % 侧压力的大小PBorder(i,6)=fscanf( FP1, '%d', 1 ) ; % 侧压力的方向：1--x方向，2--y方向%--------------------------------------------------------------------------% 以下语句将均布荷载转化为集中力%--------------------------------------------------------------------------if PBorder(i,6)==1 % 判断均布力的方向1--x方向，2--y方向xi=COORD(PBorder(i,2),1); % 提取侧压边两端点坐标yi=COORD(PBorder(i,2),2);xj=COORD(PBorder(i,4),1);yj=COORD(PBorder(i,4),2);Blength=sqrt((xj-xi)^2+(yj-yi)^2); % 边界长度FPOIN(NF+1,1)=PBorder(i,2); % 给侧压力下端点分配力，并输入到节点力矩阵中FPOIN(NF+1,2)=PBorder(i,5)*Blength*h/6;FPOIN(NF+1,3)=0;FPOIN(NF+2,1)=PBorder(i,3); % 给侧压力中端点分配力，并输入到节点力矩阵中FPOIN(NF+2,2)=PBorder(i,5)*Blength*h*2/3;FPOIN(NF+2,3)=0;FPOIN(NF+3,1)=PBorder(i,4); % 给侧压力上端点分配力，并输入到节点力矩阵中FPOIN(NF+3,2)=PBorder(i,5)*Blength*h/6;FPOIN(NF+3,3)=0;NF=NF+3;elsexi=COORD(PBorder(i,2),1); % 提取侧压边两端点坐标，为计算边界长度作准备yi=COORD(PBorder(i,2),2);xj=COORD(PBorder(i,4),1);yj=COORD(PBorder(i,4),2);Blength=sqrt((xj-xi)^2+(yj-yi)^2); % 边界长度FPOIN(NF+1,1)=PBorder(i,2); % 给侧压力左端点分配力，并输入到节点力矩阵中FPOIN(NF+1,2)=0;FPOIN(NF+1,3)=PBorder(i,5)*Blength*h/6;FPOIN(NF+2,1)=PBorder(i,3); % 给侧压力中端点分配力，并输入到节点力矩阵中FPOIN(NF+2,2)=0;FPOIN(NF+2,3)=PBorder(i,5)*Blength*h*2/3;FPOIN(NF+3,1)=PBorder(i,3); % 给侧压力右端点分配力，并输入到节点力矩阵中FPOIN(NF+3,2)=0;FPOIN(NF+3,3)=PBorder(i,5)*Blength*h/6;NF=NF+3; % NF为转化后集中力的个数endendend%--------------------------------------------------------------------------% 均布荷载转化完毕%--------------------------------------------------------------------------fclose(FP1);K=zeros(2*NPOIN,2*NPOIN);%-----生成单刚,组装总刚-----for i=1:NELEMfor j=1:EleNodeNumEcoord((j-1)*NfreeNum+1:j*NfreeNum)=COORD(LNODS(i,j),1:NfreeNum); % 提取i单元各节点的坐标endk=N8ek(E,POISSON,h,Ecoord,method); % 高斯积分求解单刚K=N8Assemble(K,k,LNODS,NfreeNum,EleNodeNum,i); % 叠加总刚if k~=k'error('单刚矩阵不对称，请检查') % 判断刚度对称性endendif K~=K'error('总刚矩阵不对称，请检查')end%-------生成荷载向量---------ASLOD(1:2*NPOIN)=0;ASLOD1(1:2*NPOIN)=0;for i=1:NF % NF为转化后集中力的个数ASLOD1((FPOIN(i,1)*2-1):FPOIN(i,1)*2)=FPOIN(i,2:3);ASLOD=ASLOD+ASLOD1; % 实现相同节点力的叠加ASLOD1(1:2*NPOIN)=0;%NPOIN(i,1)为作用点,NPOIN(i,2:3)为x,y方向的节点力end%----------------------------------------------K1=K;%-----------加约束-----------for j=1:NVFIXa=FIXED(j);K1(1:NfreeNum*NPOIN,a)=0; K1(a,1:NfreeNum*NPOIN)=0; K1(a,a)=1;ASLOD(a)=0;endDISP=K1\ASLOD'; % 求出节点位移%-----------------Fnode=K*DISP; % 求出节点力%------求单元节点应力--------EDisp=zeros(16,1);sigma=zeros(NPOIN,3);nodetimes=zeros(NPOIN); % 统计节点求解的次数,因不同单元可能共用某个节点for i=1:NELEMfor j=1:EleNodeNumEDisp(j*2-1:j*2)=DISP(2*LNODS(i,j)-1:2*LNODS(i,j));endfor j=1:EleNodeNumEcoord((j-1)*NfreeNum+1:j*NfreeNum)=COORD(LNODS(i,j),1:NfreeNum);endEnodesigma=N8stress(E,POISSON,Ecoord,EDisp,method); % 求解i单元的节点应力for j=1:EleNodeNumnum=LNODS(i,j);nodetimes(num)=nodetimes(num)+1;if nodetimes(num)==0sigma(num,1:3)=Enodesigma(j,1:3);elsesigma(num,1:3)=sigma(num,1:3)+Enodesigma(j,1:3); % 公共节点处应力叠加endendendfor i=1:NPOINsigma(i,1:3)=sigma(i,1:3)/nodetimes(i); % i节点应力mainsigma(i,1:3)=mainstress2d(sigma(i,1:3)); % i节点主应力end%-------------------------------------------------------------------------%%%--------------------------------------------------------------------------% 程序输出部分%--------------------------------------------------------------------------%FP2 = fopen( file_out, 'w' ); % 打开输出文件fprintf( FP2,'----------------------------------------------------------------------------------------\n');fprintf( FP2,'这是一个平面四边形八结点等参元有限元主程序，本程序具有以下功能：\n'); fprintf( FP2,' 1,本程序能计算平面应力问题。

有限元方法(有FORTRAN程序)飞箭系列

§4.2 元件程序的结构………………………………………………………81
4.2.1 START 元件程序…………………………………………………………81 4.2.1.1 功能………………………………………………………………82 4.2.1.2 命令行参数说明…………………………………………………82 4.2.1.3 参数及数组说明…………………………………………………83
2.2.1 导数之间的变换………………………………………………………46
§2.3 数值积分………………………………………………………………49
2.3.1 高斯积分……………………………………………………………49 2.3.2 节点积分……………………………………………………………51
第三章有限元输入数据形式
Γ 0
图 1.1.1
x
要求解的未知函数 u 可以是标量函数场(例如温度)，也可以是几个变量组成的向量函数场(例如位移、应变、应力等)。 A, B 是表示对于独立变量(例如空间坐标、时间坐标等)的微分算子。偏微分方程数应和未知场函数的数目相对应，因此，上述偏微分方程可以是单个的方程，也可以是一组方程。所以在式(1.1.1) 和(1.1.2)中采用了矩阵形式。对于工程或物理学中遇到的偏微分方程一般是没有理论解的，即未知函数没有解析表达式。而工程上又需要了解这些未知函数，所以我们一般用数值的方法来求解这些偏微分方程。有限元方法就是一种数值求解偏微分方程的方法，它实
§1.4 求解解梯度的最小二乘法………………………………………27
1.4.1 已知位移求应力………………………………………………………28 1.4.2 已知温度求热流密度…………………………………………………29 1.4.3 已知电势求电场强度…………………………………………………30

有限元计算结构力学fortran程序

有限元计算结构力学fortran程序计算结构力学程序计算结构力学编程大作业时间,2007年6月!!!***************************************************************** ***********!!! 关于程序的说明!!!***************************************************************** ***********!一、功能:! 1、可计算包括节点力，一般非节点力，支座沉降、温度荷载作用、制造误差的平! 面桁架、梁、刚架及其组合结构的节点位移与杆端力;! 2、可同时计算多种工况下的节点位移与杆端力。

!******************************************************************* **********!******************************************************************* ***********!! 二、变量说明:! NE——单元数;! N——结构中自由度数;! NJ——节点数;! NS——特殊节点数，包括支座节点、主从节点(1节点不做主节点)、连接桁架的铰节点(没有转角);! NAI——结构的单元截面类型数;! MT——单元截面类型号;! NL——荷载工况数;! H——截面高度;! E——弹性模量;! JC——单元定位向量数组;! X(NJ),Y(NJ)——节点的X，Y坐标值;! JE(NE,2)——单元两端节点码数组;! AI(NAI,2)——按单元类型顺序存放A与I，AI(I，1)—第I类单元的截面积，AI(I，2)—第I类单元的! 惯性矩;! MT(NE)——单元所属单元类型号;! JS(NS,4)——特殊节点信息，JS(I,1)—结点码;JS(I,2)，JS(I,3)，JS(I,4)—U，V，CETA约束信息，! 有约束为1，没有约束为0;从节点某位移同主节点时位移时，该位移约束信息填主节点码;!! PJ(NP,3)——节点荷载信息数组;PJ(I，1)—节点力所在节点号;PJ(I，2)—节点力作用坐标方向:! 坐标方向U，V，M分别为1，2，3; PJ(I，3)—节点力的大小(含正负号);U，V方向集中力时，! 与坐标轴正向同向为正，M按右手法则为正;本程序推导过程取y轴向下为正。

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有限元编程算例(Fortran)本程序通过Fortran语言编写，程序在Intel Parallel Studio XE 2013 with VS2013中成功运行，程序为《计算力学》（龙述尧等编）一书中的源程序，仅作研究学习使用，省去了敲写的麻烦。

源程序为：!Page149COMMON/X1/NJ,NE,NZ,NDD,NPJ,IND,NJ2,EO,UN,GAMA,TE,AECOMMON/X2/JM(100,3),NZC(50),CJZ(100,2),PJ(100,2),B(3,6),D(3,3),S(3,6),TKZ(200,20),EKE(6,6),P(200) OPEN(5,FILE='DATAIN')!OPEN(6,FILE='DATAOUT',STATUS='NEW')CALL DATAIF(IND.EQ.0)GOTO 10EO=EO/(1.0-UN*UN)UN=UN/(1.0-UN)10 CALL TOTSTICALL LOADCALL SUPPORCALL SOLVEQCALL STRESSPAUSE!STOPENDSUBROUTINE DATACOMMON/X1/NJ,NE,NZ,NDD,NPJ,IND,NJ2,EO,UN,GAMA,TE,AECOMMON/X2/JM(100,3),NZC(50),CJZ(100,2),PJ(100,2),B(3,6),D(3,3),S(3,6),TKZ(200,20),EKE(6,6),P(200)READ(5,*)NJ,NE,NZ,NDD,NPJ,INDNJ2=NJ*2NPJ1=NPJ+1READ(5,*)EO,UN,GAMA,TEREAD(5,*)((JM(I,J),J=1,3),I=1,NE)READ(5,*)((CJZ(I,J),J = 1,2),I=1,NJ)!Page150READ(5,*)(NZC(I),I=1,NZ)READ(5,*)((PJ(I,J),J=1,2),I=1,NPJ1)WRITE(6,10)(I,(CJZ(I,J),J=1,2),I=1,NJ)10 FORMA T(4X,2HNO,6X,1HX,6X,1HY/(I6,2X,F7.2,F7.2))RETURNENDSUBROUTINE ELEST(MEO,IASK)COMMON/X1/NJ,NE,NZ,NDD,NPJ,IND,NJ2,EO,UN,GAMA,TE,AECOMMON/X2/JM(100,3),NZC(50),CJZ(100,2),PJ(100,2),B(3,6),D(3,3),S(3,6),TKZ(200,20),EKE(6,6),P(200) IE=JM(MEO,1)JE=JM(MEO,2)ME=JM(MEO,3)CM=CJZ(JE,1)-CJZ(IE,1)BM=CJZ(IE,2)-CJZ(JE,2)CJ=CJZ(IE,1)-CJZ(ME,1)BJ=CJZ(ME,2)-CJZ(IE,2)AE=(BJ*CM-BM*CJ)/2.0IF(IASK.LE.1) GOTO 50DO 10 I=1,3DO 10 J=1,6B(I,J)=0.010 CONTINUEB(1,1)=-BJ-BMB(1,3)=BJB(1,5)=BMB(2,2)=-CJ-CMB(2,4)=CJB(2,6)=CMB(3,1)=B(2,2)B(3,2)=B(1,1)B(3,3)=B(2,4)B(3,4)=B(1,3)B(3,5)=B(2,6)!Page151B(3,6)=B(1,5)DO 20 I=1,3DO 20 J=1,6B(I,J)=B(I,J)/(2.0*AE) 20 CONTINUED(1,1)=EO/(1.0-UN*UN)D(1,2)=EO*UN/(1.0-UN*UN) D(2,1)=D(1,2)D(2,2)=D(1,1)D(1,3)=0.0D(2,3)=0.0D(3,1)=0.0D(3,2)=0.0D(3,3)=EO/(2.0*(1.0+UN))DO 30 I=1,3DO 30 J=1,6S(I,J)=0.0DO 30 K=1,3S(I,J)=S(I,J)+D(I,K)*B(K,J)30 CONTINUEIF(IASK.LE.2) GOTO 50DO 40 I=1,6DO 40 J=1,6EKE(I,J)=0.0DO 40 K=1,3!**********************************Exchange B And S***********************************************EKE(I,J)=EKE(I,J)+B(K,I)*S(K,J)*AE*TE40 CONTINUE50 CONTINUERETURNENDSUBROUTINE TOTSTICOMMON/X1/NJ,NE,NZ,NDD,NPJ,IND,NJ2,EO,UN,GAMA,TE,AECOMMON/X2/JM(100,3),NZC(50),CJZ(100,2),PJ(100,2),B(3,6),D(3,3),S(3,6),TKZ(200,20),EKE(6,6),P(200)!Page152DO 20 I=1,NJ2DO 20 J=1,NDDTKZ(I,J)=0.020 CONTINUE!*************Not Understanded*****************************DO 30 MEO=1,NECALL ELEST(MEO,3)DO 30 I=1,3DO 30 II=1,2LH=2*(I-1)+IILDH=2*(JM(MEO,I)-1)+IIDO 30 J=1,3DO 30 JJ=1,2L=2*(J-1)+JJLZ=2*(JM(MEO,J)-1)+JJLD=LZ-LDH+1IF(LD.LE.0) GOTO 30TKZ(LDH,LD)=TKZ(LDH,LD)+EKE(LH,L)30 CONTINUERETURNENDSUBROUTINE LOADCOMMON/X1/NJ,NE,NZ,NDD,NPJ,IND,NJ2,EO,UN,GAMA,TE,AECOMMON/X2/JM(100,3),NZC(50),CJZ(100,2),PJ(100,2),B(3,6),D(3,3),S(3,6),TKZ(200,20),EKE(6,6),P(200)DO 10 I=1,NJ2P(I)=0.010 CONTINUEIF(NPJ.EQ.0) GOTO 30DO 20 I=1,NPJI1=I+1J=IFIX(PJ(I1,2))P(J)=PJ(I1,1)20 CONTINUE30 IF(GAMA.LE.0.0) GOTO 50!Page153DO 40 MEO=1,NECALL ELEST(MEO,1)PE=-GAMA*AE*TE/3.0IE=JM(MEO,1)JE=JM(MEO,2)ME=JM(MEO,3)P(2*IE)=P(2*IE)+PEP(2*JE)=P(2*JE)+PEP(2*ME)=P(2*ME)+PE40 CONTINUE50 CONTINUERETURNENDSUBROUTINE SUPPORCOMMON/X1/NJ,NE,NZ,NDD,NPJ,IND,NJ2,EO,UN,GAMA,TE,AECOMMON/X2/JM(100,3),NZC(50),CJZ(100,2),PJ(100,2),B(3,6),D(3,3),S(3,6),TKZ(200,20),EKE(6,6),P(200)DO 60 I=1,NZMZ=NZC(I)TKZ(MZ,1)=1.0DO 10 J=2,NDDTKZ(MZ,J)=0.010 CONTINUEIF(MZ-NDD)20,20,3020 JO=MZGOTO 4030 JO=NDD40 DO 50 J = 2,JOJ1=MZ-JTKZ(J1+1,J)=0.050 CONTINUEP(MZ)=0.060 CONTINUERETURNEND!Page154SUBROUTINE SOLVEQCOMMON/X1/NJ,NE,NZ,NDD,NPJ,IND,NJ2,EO,UN,GAMA,TE,AECOMMON/X2/JM(100,3),NZC(50),CJZ(100,2),PJ(100,2),B(3,6),D(3,3),S(3,6),TKZ(200,20),EKE(6,6),P(200)NJ1=NJ2-1DO 50 K=1,NJ1IF(NJ2-K-NDD+1)10,10,2010 IM=NJ2GOTO 3020 IM=K+NDD-130 K1=K+1DO 50 I=K1,IML=I-K+1C=TKZ(K,L)/TKZ(K,1)LD1=NDD-L+1DO 40 J=1,LD1M=J+I-KTKZ(I,J)=TKZ(I,J)-C*TKZ(K,M)40 CONTINUEP(I)=P(I)-C*P(K)50 CONTINUEP(NJ2)=P(NJ2)/TKZ(NJ2,1)DO 100 I1 = 1,NJ1I=NJ2-I1!************************************************************************下面一行可能出错IF(NDD-NJ2+I-1)60,60,7060 JO=NDDGOTO 8070 JO=NJ2-I+180 DO 90 J=2,JOLH=J+I-1P(I)=P(I)-TKZ(I,J)*P(LH)90 CONTINUEP(I)=P(I)/TKZ(I,1)100 CONTINUE!Page155WRITE(6,110)(I,P(2*I-1),P(2*I),I=1,NJ)!************************************************************************************ 110 FORMA T(2X,3HJD=,3X,2HU=,12X,2HV=/(I4,3X,F16.7,3X,F16.7))RETURNENDSUBROUTINE STRESSCOMMON/X1/NJ,NE,NZ,NDD,NPJ,IND,NJ2,EO,UN,GAMA,TE,AECOMMON/X2/JM(100,3),NZC(50),CJZ(100,2),PJ(100,2),B(3,6),D(3,3),S(3,6),TKZ(200,20),EKE(6,6),P(200) DIMENSION WY(6),YL(3)DO 60 MEO=1,NECALL ELEST(MEO,2)DO 10 I=1,3DO 10 J=1,2LH=2*(I-1)+JLDH=2*(JM(MEO,I)-1)+JWY(LH)=P(LDH)10 CONTINUEDO 20 I=1,3YL(I)=0.0DO 20 J=1,6YL(I)=YL(I)+S(I,J)*WY(J)20 CONTINUESIGX=YL(1)SIGY=YL(2)TOXY=YL(3)PYL=(SIGX+SIGY)/2.0SIG=(SIGX-SIGY)**2/4.0+TOXY*TOXYRYL=SQRT(SIG)SIG1=PYL+RYLSIG2=PYL-RYLIF(SIGY.EQ.SIG2) GOTO 30CETA1=TOXY/(SIGY-SIG2)CETA=90.0-57.29578*ATAN(CETA1)GOTO 40!Page15630 CETA=0.040 WRITE(6,50)MEO,SIGX,SIGY,TOXY,SIG1,SIG2,CETA50FORMA T(4X,2HE=,I3/2X,3HSX=,F11.3,3X,3HSY=,F11.3,3X,4HTAU=,F11.3/2X,3HS1=,F11.3,3X,3HS2=,F11. 3,3X,4HCET=,F11.3)!50FORMA T(4X,2HE=,I3/2X,3HSX=,Fll.3,3X,3HSY=,F11.3,3X,4HTAU=,F11.3/2X,3HSl=,Fll.3,3X,3HS2=,F11.3,3 X,4HCET=,F11.3)60 CONTINUERETURNEND输入文件为datain28,36,9,10,4,01,0.17,0,11,5,22,5,62,6,33,6,73,7,44,7,85,9,66,9,106,10,77,10,117,11,88,11,129,13,1010,13,1410,14,11 11,14,15 11,15,12 12,15,16 13,17,14 14,17,18 14,18,15 15,18,19 15,19,16 16,19,20 17,21,18 18,21,22 18,22,19 19,22,23 19,23,20 20,23,24 21,25,22 22,25,26 22,26,23 23,26,27 23,27,24 24,27,28 0,61,62,63,60,51,52,53,50,41,42,43,40,31,32,33,30,21,22,23,20,11,12,13,10,01,02,03,07,15,23,31,39,47,49,50,550,0-5E4,2-10E4,4-10E4,6-5E4,8输出结果为：DATAOUTNO X Y1 0.00 6.002 1.00 6.003 2.00 6.004 3.00 6.005 0.00 5.006 1.00 5.007 2.00 5.008 3.00 5.009 0.00 4.0010 1.00 4.0011 2.00 4.0012 3.00 4.0013 0.00 3.0014 1.00 3.0015 2.00 3.0016 3.00 3.0017 0.00 2.0018 1.00 2.0019 2.00 2.0020 3.00 2.0021 0.00 1.0022 1.00 1.0023 2.00 1.0024 3.00 1.0025 0.00 0.0026 1.00 0.0027 2.00 0.0028 3.00 0.00JD= U= V=1 -29766.873 -1173917.7502 -14003.185 -1174018.8753 -3753.270 -1179518.1254 0.000 -1181719.7505 -26382.471 -1072681.5006 -10746.993 -1073615.0007 -2064.593 -1082360.7508 0.000 -1085873.2509 -13536.995 -964010.12510 3372.794 -970055.12511 7268.415 -989269.12512 0.000 -998401.81213 7816.581 -835383.43814 27176.234 -861713.93815 22063.230 -905726.12516 0.000 -927165.18817 29514.479 -665602.87518 53419.637 -747340.43819 34876.832 -839806.81220 0.000 -881219.12521 29580.273 -416288.71922 52944.918 -632601.12523 17504.195 -803765.68824 0.000 -859481.93825 0.000 0.00026 -120102.820 -583505.37527 -76202.375 -787347.18828 0.000 -829170.812E= 1SX= -1489.530 SY=-101489.383 TAU= -1489.531 S1= -1467.348 S2=-101511.562 CET= 179.147 E= 2SX= -1475.844 SY=-100654.875 TAU= -1790.500 S1= -1443.531 S2=-100687.188 CET= 178.966 E= 3SX= -7021.670 SY=-101597.672 TAU= -3741.688 S1= -6873.875 S2=-101745.469 CET= 177.738 E= 4SX= -8067.500 SY= -98528.750 TAU= -4459.156 S1= -7848.227 S2= -98748.023 CET= 177.185 E= 5SX= -13143.328 SY= -99391.750 TAU= -1662.500 S1= -13111.293 S2= -99423.781 CET= 178.896 E= 6SX= -14652.781 SY= -98337.500 TAU= -1501.062S1= -14625.867 S2= -98364.414 CET= 178.973 E= 7SX= -2923.122 SY=-109168.297 TAU= -5888.469 S1= -2597.762 S2=-109493.656 CET= 176.837 E= 8SX= -716.078 SY=-103681.562 TAU= -8617.406 S1= 0.148 S2=-104397.789 CET= 175.249 E= 9SX= -9188.316 SY=-105121.867 TAU= -9771.594 S1= -8203.125 S2=-106107.062 CET= 174.243 E= 10SX= -12285.000 SY= -95180.250 TAU= -12199.594 S1= -10526.887 S2= -96938.359 CET= 171.799 E= 11SX= -14170.516 SY= -95500.750 TAU= -5489.531 S1= -13801.664 S2= -95869.602 CET= 176.156 E= 12SX= -22797.406 SY= -91347.000 TAU= -3902.844 S1= -22575.914 S2= -91568.492 CET= 176.752 E= 13SX= -5104.269 SY=-129494.438 TAU= -11708.750 S1= -4011.727 S2=-130586.977 CET= 174.669 E= 14SX= 969.672 SY=-108176.375 TAU= -21424.750 S1= 5024.582 S2=-112231.281 CET= 169.283 E= 15SX= -14954.572 SY=-110883.469 TAU= -18383.531 S1= -11552.273 S2=-114285.766 CET= 169.515 E= 16SX= -19890.141 SY= -86924.312 TAU= -25131.188 S1= -11514.844 S2= -95299.609 CET= 161.569 E= 17SX= -22109.688 SY= -87301.625 TAU= -10225.406 S1= -20543.453 S2= -88867.859 CET= 171.292 E= 18SX= -35190.453 SY= -77219.000 TAU= -9162.000 S1= -33280.023 S2= -79129.430 CET= 168.222 E= 19SX= -9785.850 SY=-171444.172 TAU= -20524.969 S1= -7220.594 S2=-174009.422 CET= 172.876 E= 20SX= 4594.438 SY=-113592.375 TAU= -46145.688 S1= 20477.398 S2=-129475.336 CET= 161.007 E= 21SX= -25287.307 SY=-118672.312 TAU= -30023.750 S1= -16467.512 S2=-127492.109 CET= 163.629 E= 22SX= -30634.422 SY= -71127.188 TAU= -44991.469 S1= -1543.715 S2=-100217.891 CET= 147.114 E= 23SX= -34259.609 SY= -71743.438 TAU= -14637.906 S1= -29220.699 S2= -76782.344 CET= 161.005 E= 24SX= -43958.047 SY= -53418.938 TAU= -17697.562 S1= -30369.627 S2= -67007.359 CET= 142.482 E= 25SX= -19028.160 SY=-252549.000 TAU= -34958.688 S1= -13907.055 S2=-257670.094 CET= 171.666 E= 26SX= 3973.812 SY=-114063.750 TAU= -92238.344 S1= 54459.047 S2=-164548.984 CET= 151.307 E= 27SX= -39180.809 SY=-121400.055 TAU= -39312.688 S1= -23409.074 S2=-137171.781 CET= 158.140 E= 28SX= -42804.766 SY= -43317.938 TAU= -65723.062 S1= 22662.211 S2=-108784.914 CET= 135.112 E= 29SX= -42224.094 SY= -43219.188 TAU= -10273.375 S1= -32436.225 S2= -53007.055 CET= 136.386 E= 30SX= -21830.422 SY= -25448.312 TAU= -23810.344 S1= 239.594 S2= -47518.328 CET= 137.172 E= 31SX= -48815.199 SY=-424587.344 TAU= -79800.078 S1= -32570.844 S2=-440831.688 CET= 168.494 E= 32SX=-132271.750 SY= -71582.000 TAU=-175409.250 S1= 76087.781 S2=-279941.531 CET= 130.093 E= 33SX= -45090.102 SY= -56761.105 TAU= 804.781 S1= -45034.867 S2= -56816.336 CET= 3.926 E= 34SX= 42332.711 SY= -9221.938 TAU= -47066.344 S1= 70218.328 S2= -37107.555 CET= 149.354 E= 35SX= -20899.344 SY= -19971.375 TAU= 16235.219 S1= -4193.512 S2= -36677.207 CET= 45.819E= 36SX= 73163.914 SY= -17873.250 TAU= -17873.344 S1= 76547.250 S2= -21256.586 CET= 169.281。