547 lines
16 KiB
Text
547 lines
16 KiB
Text
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C
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C User element accessing Abaqus materials
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C Heat Transfer -- conduction
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C
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c*****************************************************************
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subroutine uelmat(rhs, amatrx, svars, energy, ndofel, nrhs,
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1 nsvars, props, nprops, coords, mcrd, nnode, u, du, v, a, jtype,
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2 time, dtime, kstep, kinc, jelem, params, ndload, jdltyp, adlmag,
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3 predef, npredf, lflags, mlvarx, ddlmag, mdload, pnewdt, jprops,
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4 njpro, period, materiallib)
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c
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include 'aba_param.inc'
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C
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dimension rhs(mlvarx,*), amatrx(ndofel, ndofel), props(*),
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1 svars(*), energy(*), coords(mcrd, nnode), u(ndofel),
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2 du(mlvarx,*), v(ndofel), a(ndofel), time(2), params(*),
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3 jdltyp(mdload,*), adlmag(mdload,*), ddlmag(mdload,*),
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4 predef(2, npredf, nnode), lflags(*), jprops(*)
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c
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c local arrays
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c
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parameter (zero=0.d0, one=1.d0)
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parameter (ndim=2, ndof=1, ninpt=4, nnodemax=4)
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c
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c ndim ... number of spatial dimensions
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c ndof ... number of degrees of freedom per node
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c ninpt ... number of integration points
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c
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dimension stiff(ndof*nnodemax,ndof*nnodemax),
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1 force(ndof*nnodemax), shape(nnodemax), dshape(ndim,nnodemax),
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2 xjaci(ndim,ndim), bmat(nnodemax*ndim), wght(ninpt)
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dimension coords_ip(3),dfgrd0(3,3),dfgrd1(3,3),
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1 drot(3,3)
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dimension coords_new(mcrd,nnodemax)
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c
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dimension predef_loc(npredf),dpredef_loc(npredf),xx1(3,3),
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1 xx1Old(3,3)
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dimension xjaci_new(ndim,ndim),bmat_new(nnodemax*ndim)
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dimension dtemdx(ndim),rhoUdotdg(3),flux(ndim),dfdt(ndim),
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1 dfdg(ndim,ndim)
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c
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data wght /one, one, one, one/
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c
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c********************************************************************
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c
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c U1 = first-order, plane strain, full integration
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c
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c********************************************************************
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if (lflags(3).eq.4) goto 999
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c
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c Preliminaries
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c
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pnewdtLocal = pnewdt
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if(jtype .ne. 1) then
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write(7,*)'Incorrect element type'
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call xit
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endif
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c
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c initialize rhs and lhs
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c
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do k1=1, ndof*nnode
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rhs(k1, 1)= zero
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do k2=1, ndof*nnode
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amatrx(k1, k2)= zero
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end do
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end do
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c
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do k1=1,nnode
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do k2=1,mcrd
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kk = (k1-1)*mcrd + k2
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coords_new(k2,k1) = coords(k2,k1) + u(kk)
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end do
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end do
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c
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c loop over integration points
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c
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do kintk = 1, ninpt
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c
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c initialization
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c
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rho = zero
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rhoUdot = zero
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rhoUdotdt = zero
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rhoUdotdg = zero
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do i=1, 3
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rhoUdotdg(i) = zero
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end do
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do i=1, ndim
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flux(i) = zero
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dfdt(i) = zero
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end do
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do i=1, ndim
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do j=1, ndim
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dfdg(i,j) = zero
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end do
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end do
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c
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c evaluate shape functions and derivatives
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c
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call shapefcn(kintk,ninpt,nnode,ndim,shape,dshape)
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c
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c compute coordinates at the integration point
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c
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do k1=1, 3
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coords_ip(k1) = zero
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end do
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do k1=1,nnode
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do k2=1,mcrd
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coords_ip(k2)=coords_ip(k2)+shape(k1)*coords(k2,k1)
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end do
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end do
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c
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if(npredf.gt.0) then
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call tempfv(kintk,ninpt,nnode,ndim,shape,predef,
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* npredf,predef_loc,dpredef_loc)
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end if
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c
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c form B-matrix
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c
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djac = one
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djac_new = one
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call jacobian(jelem,mcrd,ndim,nnode,coords,dshape,
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1 djac,xjaci,pnewdt,coords_new,xjaci_new,djac_new)
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c
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if (pnewdt .lt. pnewdtLocal) pnewdtLocal = pnewdt
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c
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call bmatrix(xjaci,dshape,nnode,ndim,bmat,xjaci_new,
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1 bmat_new)
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c
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c compute temp. and temp. gradient
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c
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temp = zero
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dtemp = zero
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call settemp(ndofel,ndof,ndim,nnode,mlvarx,bmat,du,
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* dstran,u,xx1,xx1Old,temp,dtemp,dtemdx,shape)
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c
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c get Abaqus material
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c
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rpl = zero
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drpldt = zero
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celent = one
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call material_lib_ht(materiallib,rhoUdot,rhoUdotdt,rhoUdotdg,
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* flux,dfdt,dfdg,rpl,drpldt,kintk,djac,predef_loc,
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* dpredef_loc,npredf,temp,dtemp,dtemdx,celent,coords_ip)
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c
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c
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c form stiffness matrix and internal force vector
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c
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call rhsjacobian(nnode,ndim,ndof,
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1 wght(kintk),djac,rhoUdot,rhoUdotdt,rhoUdotdg,flux,
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2 dfdt,dfdg,shape,bmat,stiff,force,dtime,lflags)
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c
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c assemble rhs and lhs
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c
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do k1=1, ndof*nnode
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rhs(k1, 1) = rhs(k1, 1) - force(k1)
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do k2=1, ndof*nnode
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amatrx(k1, k2) = amatrx(k1, k2) + stiff(k1,k2)
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end do
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end do
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end do ! end loop on material integration points
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pnewdt = pnewdtLocal
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c
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999 continue
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c
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return
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end
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c*****************************************************************
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c
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c Compute shape fuctions
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c
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subroutine shapefcn(kintk,ninpt,nnode,ndim,dN,dNdz)
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c
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include 'aba_param.inc'
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c
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parameter (dmone=-1.0d0,one=1.0d0,four=4.0d0,eight=8.0d0,
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1 gaussCoord=0.577350269d0)
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parameter (maxElemNode=8,maxDof=3,i2d4node=24,i3d8node=38)
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dimension dN(*),dNdz(ndim,*),coord24(2,4),coord38(3,8)
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c
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data coord24 /dmone, dmone,
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2 one, dmone,
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3 one, one,
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4 dmone, one/
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c
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data coord38 /dmone, dmone, dmone,
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2 one, dmone, dmone,
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3 one, one, dmone,
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4 dmone, one, dmone,
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5 dmone, dmone, one,
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6 one, dmone, one,
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7 one, one, one,
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8 dmone, one, one/
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C
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iCode = 0
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if (ninpt.eq.4.and.nnode.eq.4.and.ndim.eq.2) then
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iCode = 24
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else if (ninpt.eq.8.and.nnode.eq.8.and.ndim.eq.3) then
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iCode = 38
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else
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write (6,*) '***ERROR: The shape fuctions cannot be found'
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end if
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C
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C 3D 8-nodes
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C
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if (iCode.eq.i3d8node) then
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c
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c determine (g,h,r)
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c
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g = coord38(1,kintk)*gaussCoord
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h = coord38(2,kintk)*gaussCoord
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r = coord38(3,kintk)*gaussCoord
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c
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c shape functions
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dN(1) = (one - g)*(one - h)*(one - r)/eight
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dN(2) = (one + g)*(one - h)*(one - r)/eight
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dN(3) = (one + g)*(one + h)*(one - r)/eight
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dN(4) = (one - g)*(one + h)*(one - r)/eight
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dN(5) = (one - g)*(one - h)*(one + r)/eight
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dN(6) = (one + g)*(one - h)*(one + r)/eight
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dN(7) = (one + g)*(one + h)*(one + r)/eight
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dN(8) = (one - g)*(one + h)*(one + r)/eight
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c
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c derivative d(Ni)/d(g)
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dNdz(1,1) = -(one - h)*(one - r)/eight
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dNdz(1,2) = (one - h)*(one - r)/eight
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dNdz(1,3) = (one + h)*(one - r)/eight
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dNdz(1,4) = -(one + h)*(one - r)/eight
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dNdz(1,5) = -(one - h)*(one + r)/eight
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dNdz(1,6) = (one - h)*(one + r)/eight
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dNdz(1,7) = (one + h)*(one + r)/eight
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dNdz(1,8) = -(one + h)*(one + r)/eight
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c
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c derivative d(Ni)/d(h)
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dNdz(2,1) = -(one - g)*(one - r)/eight
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dNdz(2,2) = -(one + g)*(one - r)/eight
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dNdz(2,3) = (one + g)*(one - r)/eight
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dNdz(2,4) = (one - g)*(one - r)/eight
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dNdz(2,5) = -(one - g)*(one + r)/eight
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dNdz(2,6) = -(one + g)*(one + r)/eight
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dNdz(2,7) = (one + g)*(one + r)/eight
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dNdz(2,8) = (one - g)*(one + r)/eight
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c
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c derivative d(Ni)/d(r)
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dNdz(3,1) = -(one - g)*(one - h)/eight
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dNdz(3,2) = -(one + g)*(one - h)/eight
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dNdz(3,3) = -(one + g)*(one + h)/eight
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dNdz(3,4) = -(one - g)*(one + h)/eight
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dNdz(3,5) = (one - g)*(one - h)/eight
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dNdz(3,6) = (one + g)*(one - h)/eight
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dNdz(3,7) = (one + g)*(one + h)/eight
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dNdz(3,8) = (one - g)*(one + h)/eight
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C
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C 2D 4-nodes
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C
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else if (iCode.eq.i2d4node) then
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c
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c determine (g,h)
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c
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g = coord24(1,kintk)*gaussCoord
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h = coord24(2,kintk)*gaussCoord
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c
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c shape functions
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dN(1) = (one - g)*(one - h)/four;
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dN(2) = (one + g)*(one - h)/four;
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dN(3) = (one + g)*(one + h)/four;
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dN(4) = (one - g)*(one + h)/four;
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c
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c derivative d(Ni)/d(g)
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dNdz(1,1) = -(one - h)/four;
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dNdz(1,2) = (one - h)/four;
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dNdz(1,3) = (one + h)/four;
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dNdz(1,4) = -(one + h)/four;
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c
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c derivative d(Ni)/d(h)
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dNdz(2,1) = -(one - g)/four;
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dNdz(2,2) = -(one + g)/four;
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dNdz(2,3) = (one + g)/four;
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dNdz(2,4) = (one - g)/four;
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end if
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c
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return
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end
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c*****************************************************************
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c Get local predefined fileds
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c
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subroutine tempfv(kintk,ninpt,nnode,ndim,shape,predef,
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* npredf,predef_loc,dpredef_loc)
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c
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include 'aba_param.inc'
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c
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dimension shape(nnode),predef(2,npredf,nnode)
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dimension predef_loc(npredf),dpredef_loc(npredf)
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parameter (zero=0.d0)
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c
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do k1=1,npredf
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predef_loc(k1) = zero
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dpredef_loc(k1) = zero
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do k2=1,nnode
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predef_loc(k1) = predef_loc(k1)+
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& (predef(1,k1,k2)-predef(2,k1,k2))*shape(k2)
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dpredef_loc(k1) = dpredef_loc(k1)+predef(2,k1,k2)*shape(k2)
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end do
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end do
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c
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return
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end
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c*****************************************************************
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c Compute jacobian matrix
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c
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subroutine jacobian(jelem,mcrd,ndim,nnode,
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1 coords,dshape,djac,xjaci,pnewdt,coords_new,xjaci_new,
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2 djac_new)
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c
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c Notation: ndim ....... element dimension
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c nnode ..... number of nodes
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c coords ..... coordinates of nodes
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c dshape ..... derivs of shape fcn
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c djac ....... determinant of Jacobian
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c xjaci ...... inverse of Jacobian matrix
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c
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c
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include 'aba_param.inc'
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parameter(zero=0.d0, fourth=0.25d0, maxDof=3)
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dimension xjac(maxDof,maxDof), xjaci(ndim,*), coords(mcrd,*)
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dimension dshape(ndim,*),coords_new(mcrd,*)
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dimension xjac_new(maxDof,maxDof), xjaci_new(ndim,*)
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c
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do i = 1, ndim
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do j = 1, ndim
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xjac(i,j) = zero
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xjaci(i,j) = zero
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xjac_new(i,j) = zero
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xjaci_new(i,j) = zero
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|
|
end do
|
||
|
|
end do
|
||
|
|
c
|
||
|
|
do inod= 1, nnode
|
||
|
|
do idim = 1, ndim
|
||
|
|
do jdim = 1, ndim
|
||
|
|
xjac(idim,jdim) = xjac(idim,jdim) +
|
||
|
|
1 dshape(jdim,inod)*coords(idim,inod)
|
||
|
|
end do
|
||
|
|
end do
|
||
|
|
end do
|
||
|
|
C
|
||
|
|
C ndim == 3
|
||
|
|
C
|
||
|
|
if (ndim.eq.3) then
|
||
|
|
djac = xjac(1,1)*xjac(2,2)*xjac(3,3) +
|
||
|
|
& xjac(2,1)*xjac(3,2)*xjac(1,3) +
|
||
|
|
& xjac(3,1)*xjac(2,3)*xjac(1,2) -
|
||
|
|
& xjac(3,1)*xjac(2,2)*xjac(1,3) -
|
||
|
|
& xjac(2,1)*xjac(1,2)*xjac(3,3) -
|
||
|
|
& xjac(1,1)*xjac(2,3)*xjac(3,2)
|
||
|
|
if (djac .gt. zero) then
|
||
|
|
! jacobian is positive - o.k.
|
||
|
|
xjaci(1,1) = (xjac(2,2)*xjac(3,3)-xjac(2,3)*xjac(3,2))/djac
|
||
|
|
xjaci(1,2) = (xjac(1,3)*xjac(3,2)-xjac(1,2)*xjac(3,3))/djac
|
||
|
|
xjaci(1,3) = (xjac(1,2)*xjac(2,3)-xjac(1,3)*xjac(2,2))/djac
|
||
|
|
!
|
||
|
|
xjaci(2,1) = (xjac(2,3)*xjac(3,1)-xjac(2,1)*xjac(3,3))/djac
|
||
|
|
xjaci(2,2) = (xjac(1,1)*xjac(3,3)-xjac(1,3)*xjac(3,1))/djac
|
||
|
|
xjaci(2,3) = (xjac(1,3)*xjac(2,1)-xjac(1,1)*xjac(2,3))/djac
|
||
|
|
!
|
||
|
|
xjaci(3,1) = (xjac(2,1)*xjac(3,2)-xjac(2,2)*xjac(3,1))/djac
|
||
|
|
xjaci(3,2) = (xjac(1,2)*xjac(3,1)-xjac(1,1)*xjac(3,2))/djac
|
||
|
|
xjaci(3,3) = (xjac(1,1)*xjac(2,2)-xjac(1,2)*xjac(2,1))/djac
|
||
|
|
else
|
||
|
|
! negative or zero jacobian
|
||
|
|
write(7,*)'WARNING: element',jelem,'has neg.
|
||
|
|
1 Jacobian'
|
||
|
|
pnewdt = fourth
|
||
|
|
endif
|
||
|
|
C
|
||
|
|
C ndim == 2
|
||
|
|
C
|
||
|
|
else if (ndim.eq.2) then
|
||
|
|
djac = xjac(1,1)*xjac(2,2) - xjac(1,2)*xjac(2,1)
|
||
|
|
djac_new = xjac_new(1,1)*xjac_new(2,2)
|
||
|
|
* - xjac_new(1,2)*xjac_new(2,1)
|
||
|
|
if (djac .gt. zero) then
|
||
|
|
! jacobian is positive - o.k.
|
||
|
|
xjaci(1,1) = xjac(2,2)/djac
|
||
|
|
xjaci(2,2) = xjac(1,1)/djac
|
||
|
|
xjaci(1,2) = -xjac(1,2)/djac
|
||
|
|
xjaci(2,1) = -xjac(2,1)/djac
|
||
|
|
else
|
||
|
|
! negative or zero jacobian
|
||
|
|
write(7,*)'WARNING: element',jelem,'has neg.
|
||
|
|
1 Jacobian'
|
||
|
|
pnewdt = fourth
|
||
|
|
endif
|
||
|
|
end if
|
||
|
|
|
||
|
|
return
|
||
|
|
end
|
||
|
|
c*****************************************************************
|
||
|
|
c
|
||
|
|
c Compute the B matrix
|
||
|
|
c
|
||
|
|
subroutine bmatrix(xjaci,dshape,nnode,ndim,bmat,
|
||
|
|
* xjaci_new,bmat_new)
|
||
|
|
c
|
||
|
|
c Notation:
|
||
|
|
c bmat(i) .....dN1/dx, dN1/dy, dN2/dx, dN2/dy..
|
||
|
|
c xjaci ...... inverse Jabobian matrix
|
||
|
|
c dshape ......derivative of shape functions
|
||
|
|
c
|
||
|
|
include 'aba_param.inc'
|
||
|
|
c
|
||
|
|
parameter (zero=0.d0)
|
||
|
|
dimension bmat(*), dshape(ndim,*)
|
||
|
|
dimension xjaci(ndim,*)
|
||
|
|
dimension xjaci_new(ndim,*),bmat_new(*)
|
||
|
|
|
||
|
|
|
||
|
|
do i = 1, nnode*ndim
|
||
|
|
bmat(i) = zero
|
||
|
|
bmat_new(i) = zero
|
||
|
|
end do
|
||
|
|
|
||
|
|
do inod = 1, nnode
|
||
|
|
do ider = 1, ndim
|
||
|
|
do idim = 1, ndim
|
||
|
|
irow = idim + (inod - 1)*ndim
|
||
|
|
bmat(irow) = bmat(irow) +
|
||
|
|
1 xjaci(idim,ider)*dshape(ider,inod)
|
||
|
|
|
||
|
|
end do
|
||
|
|
end do
|
||
|
|
end do
|
||
|
|
|
||
|
|
return
|
||
|
|
end
|
||
|
|
c*****************************************************************
|
||
|
|
c
|
||
|
|
c Set temperatures
|
||
|
|
c
|
||
|
|
subroutine settemp(ndofel,ndof,ndim,nnode,
|
||
|
|
1 mlvarx,bmat,du,dstran,u,xx1,xx1Old,temp,dtemp,dtemdx,dN)
|
||
|
|
c
|
||
|
|
c
|
||
|
|
c
|
||
|
|
include 'aba_param.inc'
|
||
|
|
parameter(zero=0.d0, one=1.d0)
|
||
|
|
|
||
|
|
dimension dstran(*), bmat(ndim,*),
|
||
|
|
1 du(mlvarx, *), xdu(3), xx1(3,*),
|
||
|
|
2 u(ndofel), utmp(3),
|
||
|
|
3 utmpOld(3),xx1Old(3,*),eps(3,3),dInvFold(3,3)
|
||
|
|
dimension dtemdx(*),dN(*)
|
||
|
|
C
|
||
|
|
c
|
||
|
|
c****************************************************************
|
||
|
|
c Compute temp, dtemp, and temp gradient at the material point
|
||
|
|
c****************************************************************
|
||
|
|
c
|
||
|
|
|
||
|
|
temp = zero
|
||
|
|
dtemp = zero
|
||
|
|
do iNode=1, nnode
|
||
|
|
temp = temp + dN(iNode)*u(iNode)
|
||
|
|
dtemp = dtemp + dN(iNode)*du(iNode,1)
|
||
|
|
end do
|
||
|
|
do iDof = 1, ndim
|
||
|
|
dtemdx(iDof) = zero
|
||
|
|
do iNode=1, nnode
|
||
|
|
dtemdx(iDof) = dtemdx(iDof) + bmat(idof,iNode)*u(iNode)
|
||
|
|
end do
|
||
|
|
end do
|
||
|
|
c
|
||
|
|
return
|
||
|
|
end
|
||
|
|
c*****************************************************************
|
||
|
|
c
|
||
|
|
c Compute element jacobian and nodal forces
|
||
|
|
c
|
||
|
|
subroutine rhsjacobian(nnode,ndim,ndof,
|
||
|
|
1 weight,djac,rhoUdot,rhoUdotdt,rhoUdotdg,flux,dfdt,
|
||
|
|
2 dfdg,dN,bmat,stiff,force,dtime,lflags)
|
||
|
|
c
|
||
|
|
c Stiffness matrix and internal force contributions at
|
||
|
|
c material integration point
|
||
|
|
c
|
||
|
|
include 'aba_param.inc'
|
||
|
|
|
||
|
|
parameter(zero=0.d0,maxDof=3)
|
||
|
|
|
||
|
|
dimension stiff(ndof*nnode,*)
|
||
|
|
dimension force(*)
|
||
|
|
dimension flux(*),dfdt(*),dfdg(ndim,*),rhoUdotdg(*)
|
||
|
|
dimension dN(*),bmat(ndim,*),lflags(*)
|
||
|
|
|
||
|
|
do i = 1, ndof*nnode
|
||
|
|
force(i) = zero
|
||
|
|
do j = 1, ndof*nnode
|
||
|
|
stiff(j,i) = zero
|
||
|
|
end do
|
||
|
|
end do
|
||
|
|
|
||
|
|
dvol=weight*djac
|
||
|
|
do nodj=1, nnode
|
||
|
|
if (lflags(1).eq.32.or.lflags(1).eq.33)
|
||
|
|
& force(nodj) = dN(nodj)*rhoUdot*dvol
|
||
|
|
ccc force(nodj) = dN(nodj)*(rhoUdot-rpl)*dvol
|
||
|
|
do jDof=1, ndim
|
||
|
|
force(nodj) = force(nodj)+bmat(jDof,nodj)*flux(jDof)*dvol
|
||
|
|
do nodi=1, nnode
|
||
|
|
ccc stiff(nodj,nodi) = stiff(nodj,nodi) +
|
||
|
|
ccc * bmat(jDof,nodj)*dN(nodi)*dfdt(jDof)*dvol
|
||
|
|
do iDof=1, ndim
|
||
|
|
stiff(nodj,nodi) = stiff(nodj,nodi) +
|
||
|
|
* bmat(jDof,nodj)*bmat(iDof,nodi)*dfdg(jDof,iDof)*dvol
|
||
|
|
end do
|
||
|
|
end do
|
||
|
|
end do
|
||
|
|
end do
|
||
|
|
do nodj=1, nnode
|
||
|
|
do nodi=1, nnode
|
||
|
|
do iDof=1, ndim
|
||
|
|
ccc stiff(nodj,nodi) = stiff(nodj,nodi) +
|
||
|
|
ccc * dN(nodj)*bmat(iDof,nodi)*rhoUdotdg(iDof)*dvol
|
||
|
|
end do
|
||
|
|
end do
|
||
|
|
end do
|
||
|
|
c
|
||
|
|
if (lflags(1).eq.32.or.lflags(1).eq.33) then
|
||
|
|
do nodj=1, nnode
|
||
|
|
do nodi=1, nnode
|
||
|
|
stiff(nodj,nodi) = stiff(nodj,nodi) +
|
||
|
|
* rhoUdotdt*dN(nodj)*dN(nodi)*dvol/dtime
|
||
|
|
end do
|
||
|
|
end do
|
||
|
|
end if
|
||
|
|
c
|
||
|
|
return
|
||
|
|
end
|