!
!     CalculiX - A 3-dimensional finite element program
!              Copyright (C) 1998-2015 Guido Dhondt
!
!     This program is free software; you can redistribute it and/or
!     modify it under the terms of the GNU General Public License as
!     published by the Free Software Foundation(version 2);
!     
!
!     This program is distributed in the hope that it will be useful,
!     but WITHOUT ANY WARRANTY; without even the implied warranty of 
!     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 
!     GNU General Public License for more details.
!
!     You should have received a copy of the GNU General Public License
!     along with this program; if not, write to the Free Software
!     Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
!
      subroutine e_c3d(co,kon,lakonl,p1,p2,omx,bodyfx,nbody,s,sm,
     &  ff,nelem,nmethod,elcon,nelcon,rhcon,nrhcon,alcon,nalcon,alzero,
     &  ielmat,ielorien,norien,orab,ntmat_,
     &  t0,t1,ithermal,vold,iperturb,nelemload,
     &  sideload,xload,nload,idist,sti,stx,iexpl,plicon,
     &  nplicon,plkcon,nplkcon,xstiff,npmat_,dtime,
     &  matname,mi,ncmat_,mass,stiffness,buckling,rhsi,intscheme,
     &  ttime,time,istep,iinc,coriolis,xloadold,reltime,
     &  ipompc,nodempc,coefmpc,nmpc,ikmpc,ilmpc,veold,springarea,
     &  nstate_,xstateini,xstate,ne0,ipkon,thicke,
     &  integerglob,doubleglob,tieset,istartset,iendset,ialset,ntie,
     &  nasym,pslavsurf,pmastsurf,mortar,clearini,ielprop,prop,kscale)
!
!     computation of the element matrix and rhs for the element with
!     the topology in konl
!
!     ff: rhs without temperature and eigenstress contribution
!
!     nmethod=0: check for positive Jacobian
!     nmethod=1: stiffness matrix + right hand side
!     nmethod=2: stiffness matrix + mass matrix
!     nmethod=3: static stiffness + buckling stiffness
!     nmethod=4: stiffness matrix + mass matrix
!
      implicit none
!
      integer mass,stiffness,buckling,rhsi,coriolis
!
      character*1 entity
      character*8 lakonl
      character*20 sideload(*)
      character*80 matname(*),amat
      character*81 tieset(3,*)
!
      integer konl(26),ifaceq(8,6),nelemload(2,*),nbody,nelem,
     &  mi(*),iloc,jfaces,igauss,mortar,kon(*),ielprop(*),null,
     &  mattyp,ithermal,iperturb(*),nload,idist,i,j,k,l,i1,i2,j1,
     &  nmethod,k1,l1,ii,jj,ii1,jj1,id,ipointer,ig,m1,m2,m3,m4,kk,
     &  nelcon(2,*),nrhcon(*),nalcon(2,*),ielmat(mi(3),*),six,
     &  ielorien(mi(3),*),ilayer,nlayer,ki,kl,ipkon(*),indexe,
     &  ntmat_,nope,nopes,norien,ihyper,iexpl,kode,imat,mint2d,
     &  mint3d,ifacet(6,4),nopev,iorien,istiff,ncmat_,iface,
     &  ifacew(8,5),intscheme,n,ipointeri,ipointerj,istep,iinc,
     &  layer,kspt,jltyp,iflag,iperm(60),m,ipompc(*),nodempc(3,*),
     &  nmpc,ikmpc(*),ilmpc(*),iscale,nstate_,ne0,iselect(6),kscale,
     &  istartset(*),iendset(*),ialset(*),ntie,integerglob(*),nasym,
     &  nplicon(0:ntmat_,*),nplkcon(0:ntmat_,*),npmat_,nopered
!
      real*8 co(3,*),xl(3,26),shp(4,26),xs2(3,7),veold(0:mi(2),*),
     &  s(60,60),w(3,3),p1(3),p2(3),bodyf(3),bodyfx(3),ff(60),
     &  bf(3),q(3),shpj(4,26),elcon(0:ncmat_,ntmat_,*),t(3),
     &  rhcon(0:1,ntmat_,*),xkl(3,3),eknlsign,reltime,prop(*),
     &  alcon(0:6,ntmat_,*),alzero(*),orab(7,*),t0(*),t1(*),
     &  anisox(3,3,3,3),voldl(0:mi(2),26),vo(3,3),xloadold(2,*),
     &  xl2(3,9),xsj2(3),shp2(7,9),vold(0:mi(2),*),xload(2,*),
     &  xstate(nstate_,mi(1),*),xstateini(nstate_,mi(1),*),
     &  v(3,3,3,3),springarea(2,*),thickness,tlayer(4),dlayer(4),
     &  om,omx,e,un,al,um,xi,et,ze,tt,const,xsj,xsjj,sm(60,60),
     &  sti(6,mi(1),*),stx(6,mi(1),*),s11,s22,s33,s12,s13,s23,s11b,
     &  s22b,s33b,s12b,s13b,s23b,t0l,t1l,coefmpc(*),xlayer(mi(3),4),
     &  senergy,senergyb,rho,elas(21),summass,summ,thicke(mi(3),*),
     &  sume,factorm,factore,alp,elconloc(21),eth(6),doubleglob(*),
     &  weight,coords(3),dmass,xl1(3,9),term,clearini(3,9,*),
     &  plicon(0:2*npmat_,ntmat_,*),plkcon(0:2*npmat_,ntmat_,*),
     &  xstiff(27,mi(1),*),plconloc(802),dtime,ttime,time,tvar(2),
     &  sax(60,60),ffax(60),gs(8,4),a,stress(6),stre(3,3),
     &  pslavsurf(3,*),pmastsurf(6,*),xmass
!
      intent(in) co,kon,lakonl,p1,p2,omx,bodyfx,nbody,
     &  nelem,elcon,nelcon,rhcon,nrhcon,alcon,nalcon,alzero,
     &  ielmat,ielorien,norien,orab,ntmat_,
     &  t0,t1,ithermal,vold,iperturb,nelemload,
     &  sideload,nload,idist,sti,stx,iexpl,plicon,
     &  nplicon,plkcon,nplkcon,xstiff,npmat_,dtime,
     &  matname,mi,ncmat_,mass,stiffness,buckling,rhsi,intscheme,
     &  ttime,time,istep,iinc,coriolis,xloadold,reltime,
     &  ipompc,nodempc,coefmpc,nmpc,ikmpc,ilmpc,veold,
     &  nstate_,xstateini,ne0,ipkon,thicke,
     &  integerglob,doubleglob,tieset,istartset,iendset,ialset,ntie,
     &  nasym,pslavsurf,pmastsurf,mortar,clearini,ielprop,prop
!
      intent(inout) s,sm,ff,xload,nmethod,springarea,xstate
!
      include "gauss.f"
!
      ifaceq=reshape((/4,3,2,1,11,10,9,12,
     &            5,6,7,8,13,14,15,16,
     &            1,2,6,5,9,18,13,17,
     &            2,3,7,6,10,19,14,18,
     &            3,4,8,7,11,20,15,19,
     &            4,1,5,8,12,17,16,20/),(/8,6/))
      ifacet=reshape((/1,3,2,7,6,5,
     &             1,2,4,5,9,8,
     &             2,3,4,6,10,9,
     &             1,4,3,8,10,7/),(/6,4/))
      ifacew=reshape((/1,3,2,9,8,7,0,0,
     &             4,5,6,10,11,12,0,0,
     &             1,2,5,4,7,14,10,13,
     &             2,3,6,5,8,15,11,14,
     &             4,6,3,1,12,15,9,13/),(/8,5/))
      iflag=3
      null=0
      iperm=(/13,14,-15,16,17,-18,19,20,-21,22,23,-24,
     &            1,2,-3,4,5,-6,7,8,-9,10,11,-12,
     &            37,38,-39,40,41,-42,43,44,-45,46,47,-48,
     &            25,26,-27,28,29,-30,31,32,-33,34,35,-36,
     &            49,50,-51,52,53,-54,55,56,-57,58,59,-60/)
!
      tvar(1)=time
      tvar(2)=ttime+time
!
      summass=0.d0
!
      indexe=ipkon(nelem)
c     Bernhardi start
      if(lakonl(1:5).eq.'C3D8I') then
         nope=11
         nopev=8
         nopes=4
      elseif(lakonl(4:5).eq.'20') then
c     Bernhardi end
         nope=20
         nopev=8
         nopes=8
      elseif(lakonl(4:4).eq.'8') then
         nope=8
         nopev=8
         nopes=4
      elseif(lakonl(4:5).eq.'10') then
         nope=10
         nopev=4
         nopes=6
      elseif(lakonl(4:4).eq.'4') then
         nope=4
         nopev=4
         nopes=3
      elseif(lakonl(4:5).eq.'15') then
         nope=15
         nopev=6
      elseif(lakonl(4:4).eq.'6') then
         nope=6
         nopev=6
      elseif(lakonl(1:2).eq.'ES') then
         if(lakonl(7:7).eq.'C') then
            if(mortar.eq.0) then
               nope=ichar(lakonl(8:8))-47
               konl(nope+1)=kon(indexe+nope+1)
            elseif(mortar.eq.1) then
               nope=kon(indexe)
            endif
         else
            nope=ichar(lakonl(8:8))-47
         endif
      elseif(lakonl(1:4).eq.'MASS') then
         nope=1
      endif
!
!     material and orientation
!
      if(lakonl(7:8).ne.'LC') then
!
         imat=ielmat(1,nelem)
         amat=matname(imat)
         if(norien.gt.0) then
            iorien=ielorien(1,nelem)
         else
            iorien=0
         endif
!
         if(nelcon(1,imat).lt.0) then
            ihyper=1
         else
            ihyper=0
         endif
      elseif(lakonl(4:5).eq.'20') then
!
!        composite materials
!
!        determining the number of layers
!
         nlayer=0
         do k=1,mi(3)
            if(ielmat(k,nelem).ne.0) then
               nlayer=nlayer+1
            endif
         enddo
         mint2d=4
!
!        determining the layer thickness and global thickness
!        at the shell integration points
!
         iflag=1
         do kk=1,mint2d
            xi=gauss3d2(1,kk)
            et=gauss3d2(2,kk)
            call shape8q(xi,et,xl2,xsj2,xs2,shp2,iflag)
            tlayer(kk)=0.d0
            do i=1,nlayer
               thickness=0.d0
               do j=1,nopes
                  thickness=thickness+thicke(i,indexe+j)*shp2(4,j)
               enddo
               tlayer(kk)=tlayer(kk)+thickness
               xlayer(i,kk)=thickness
            enddo
         enddo
         iflag=3
!
         ilayer=0
         do i=1,4
            dlayer(i)=0.d0
         enddo
!
      elseif(lakonl(4:5).eq.'15') then
!
!        composite materials
!
!        determining the number of layers
!
         nlayer=0
         do k=1,mi(3)
            if(ielmat(k,nelem).ne.0) then
               nlayer=nlayer+1
            endif
         enddo
         mint2d=3
!
!        determining the layer thickness and global thickness
!        at the shell integration points
!
         iflag=1
         do kk=1,mint2d
            xi=gauss3d10(1,kk)
            et=gauss3d10(2,kk)
            call shape6tri(xi,et,xl2,xsj2,xs2,shp2,iflag)
            tlayer(kk)=0.d0
            do i=1,nlayer
               thickness=0.d0
               do j=1,6
                  thickness=thickness+thicke(i,indexe+j)*shp2(4,j)
               enddo
               tlayer(kk)=tlayer(kk)+thickness
               xlayer(i,kk)=thickness
            enddo
         enddo
         iflag=3
!
         ilayer=0
         do i=1,3
            dlayer(i)=0.d0
         enddo
!     
      endif
!
      if(intscheme.eq.0) then
         if(lakonl(4:5).eq.'8R') then
            mint2d=1
            mint3d=1
         elseif(lakonl(4:7).eq.'20RB') then
            if((lakonl(8:8).eq.'R').or.(lakonl(8:8).eq.'C')) then
               mint2d=4
               mint3d=50
            else
               mint2d=4
               call beamintscheme(lakonl,mint3d,ielprop(nelem),prop,
     &              null,xi,et,ze,weight)
            endif
         elseif((lakonl(4:4).eq.'8').or.(lakonl(4:6).eq.'20R')) then
            if((lakonl(7:7).eq.'A').or.(lakonl(7:7).eq.'S').or.
     &         (lakonl(7:7).eq.'E')) then
               mint2d=2
               mint3d=4
            else
               mint2d=4
               if(lakonl(7:8).eq.'LC') then
                  mint3d=8*nlayer
               else
                  mint3d=8
               endif
            endif
         elseif(lakonl(4:4).eq.'2') then
            mint2d=9
            mint3d=27
         elseif(lakonl(4:5).eq.'10') then
            mint2d=3
            mint3d=4
         elseif(lakonl(4:4).eq.'4') then
            mint2d=1
            mint3d=1
         elseif(lakonl(4:5).eq.'15') then
            if(lakonl(7:8).eq.'LC') then
               mint3d=6*nlayer
            else
               mint3d=9
            endif
         elseif(lakonl(4:4).eq.'6') then
            mint3d=2
         else
            mint3d=0
         endif
      else
         if((lakonl(4:4).eq.'8').or.(lakonl(4:4).eq.'2')) then
            mint3d=27
            if(lakonl(4:4).eq.'8') then
               if(lakonl(5:5).eq.'R') then
                  mint2d=1
               else
                  mint2d=4
               endif
            else
               if(lakonl(6:6).eq.'R') then
                  mint2d=4
               else
                  mint2d=9
               endif
            endif
         elseif((lakonl(4:5).eq.'10').or.(lakonl(4:4).eq.'4')) then
            mint3d=15
            if(lakonl(4:5).eq.'10') then
               mint2d=3
            else
               mint2d=1
            endif
         elseif((lakonl(4:5).eq.'15').or.(lakonl(4:4).eq.'6')) then
            mint3d=9
         else
            mint3d=0
         endif
      endif
!
!     computation of the coordinates of the local nodes
!
      do i=1,nope
        konl(i)=kon(indexe+i)
        do j=1,3
          xl(j,i)=co(j,konl(i))
        enddo
      enddo
!
!       initialisation for distributed forces
!
      if(rhsi.eq.1) then
        if(idist.ne.0) then
          do i=1,3*nope
            ff(i)=0.d0
          enddo
        endif
      endif
!
!     displacements for 2nd order static and modal theory
!
      if(((iperturb(1).eq.1).or.(iperturb(2).eq.1)).and.
     &          (stiffness.eq.1).and.(buckling.eq.0)) then
         do i1=1,nope
            do i2=1,3
               voldl(i2,i1)=vold(i2,konl(i1))
            enddo
         enddo
      endif
!
!     initialisation of sm
!
      if((mass.eq.1).or.(buckling.eq.1).or.(coriolis.eq.1)) then
        do i=1,3*nope
          do j=1,3*nope
            sm(i,j)=0.d0
          enddo
        enddo
      endif
!
!     initialisation of s
!
      do i=1,3*nope
        do j=1,3*nope
          s(i,j)=0.d0
        enddo
      enddo
!
!     calculating the stiffness matrix for the (contact) spring elements
!     and the mass matrix for the mass elements
!
      if(mint3d.eq.0) then
!
!        for a
!        first step in a displacement-driven geometrically nonlinear
!        calculation or a nonlinear calculation with linear strains
!        the next block has to be evaluated
!
         if(iperturb(2).eq.0) then
            do i1=1,nope
               do i2=1,3
                  voldl(i2,i1)=vold(i2,konl(i1))
               enddo
            enddo
         endif
!
         kode=nelcon(1,imat)
         if(lakonl(1:2).eq.'ES') then
            if(lakonl(7:7).ne.'C') then
               t0l=0.d0
               t1l=0.d0
               if(ithermal.eq.1) then
                  t0l=(t0(konl(1))+t0(konl(2)))/2.d0
                  t1l=(t1(konl(1))+t1(konl(2)))/2.d0
               elseif(ithermal.ge.2) then
                  t0l=(t0(konl(1))+t0(konl(2)))/2.d0
                  t1l=(vold(0,konl(1))+vold(0,konl(2)))/2.d0
               endif
            endif
!     
            if((lakonl(7:7).eq.'A').or.(lakonl(7:7).eq.'1').or.
     &         (lakonl(7:7).eq.'2').or.(mortar.eq.0)) then
               call springstiff_n2f(xl,elas,konl,voldl,s,imat,elcon,
     &              nelcon,ncmat_,ntmat_,nope,lakonl,t1l,kode,elconloc,
     &              plicon,nplicon,npmat_,iperturb,
     &              springarea(1,konl(nope+1)),nmethod,mi,ne0,nstate_,
     &              xstateini,xstate,reltime,nasym,ielorien,orab,norien,
     &              nelem)
            elseif(mortar.eq.1) then
               iloc=kon(indexe+nope+1)
               jfaces=kon(indexe+nope+2)
               igauss=kon(indexe+nope+1) 
               call springstiff_f2f(xl,elas,voldl,s,imat,elcon,nelcon,
     &              ncmat_,ntmat_,nope,lakonl,t1l,kode,elconloc,plicon,
     &              nplicon,npmat_,iperturb,springarea(1,iloc),nmethod,
     &              mi,ne0,nstate_,xstateini,xstate,reltime,
     &              nasym,iloc,jfaces,igauss,pslavsurf,
     &              pmastsurf,clearini,kscale)
            endif
         elseif(lakonl(1:4).eq.'MASS') then
!
!           mass matrix contribution
!
            if(mass.eq.1) then
               do i1=1,3
                  sm(i1,i1)=rhcon(1,1,imat)
               enddo
            endif
!
!           contribution to the rhs
!
            if(rhsi.eq.1) then
               if(nbody.ne.0) then
!
                  xmass=rhcon(1,1,imat)
!
                  do i1=1,3
                     ff(i1)=bodyfx(i1)*xmass
                  enddo
!
                  if(omx.gt.0.d0) then
!     
!                    omega**2 * mass
!     
                     om=omx*xmass
                     do i1=1,3
!     
!                   computation of the global coordinates of the
!                   mass node
!
                        if((iperturb(1).ne.1).and.(iperturb(2).ne.1)) 
     &                     then
                           q(i1)=xl(i1,1)
                        else
                           q(i1)=xl(i1,1)+voldl(i1,1)
                        endif
!     
                        q(i1)=q(i1)-p1(i1)
                     enddo
                     const=q(1)*p2(1)+q(2)*p2(2)+q(3)*p2(3)
!     
!                 inclusion of the centrifugal force into the body force
!
                     do i1=1,3
                        ff(i1)=ff(i1)+(q(i1)-const*p2(i1))*om
                     enddo
                  endif
               endif
            endif
!            
         endif
         return
      endif
!
!     computation of the matrix: loop over the Gauss points
!
      do kk=1,mint3d
         if(intscheme.eq.0) then
            if(lakonl(4:5).eq.'8R') then
               xi=gauss3d1(1,kk)
               et=gauss3d1(2,kk)
               ze=gauss3d1(3,kk)
               weight=weight3d1(kk)
            elseif(lakonl(4:7).eq.'20RB') then
               if((lakonl(8:8).eq.'R').or.(lakonl(8:8).eq.'C')) then
                  xi=gauss3d13(1,kk)
                  et=gauss3d13(2,kk)
                  ze=gauss3d13(3,kk)
                  weight=weight3d13(kk)
               else
                  call beamintscheme(lakonl,mint3d,ielprop(nelem),prop,
     &                 kk,xi,et,ze,weight)
               endif
            elseif((lakonl(4:4).eq.'8').or.(lakonl(4:6).eq.'20R')) 
     &              then
               if(lakonl(7:8).ne.'LC') then
                  xi=gauss3d2(1,kk)
                  et=gauss3d2(2,kk)
                  ze=gauss3d2(3,kk)
                  weight=weight3d2(kk)
               else
                  kl=mod(kk,8)
                  if(kl.eq.0) kl=8
!
                  xi=gauss3d2(1,kl)
                  et=gauss3d2(2,kl)
                  ze=gauss3d2(3,kl)
                  weight=weight3d2(kl)
!
                  ki=mod(kk,4)
                  if(ki.eq.0) ki=4
!
                  if(kl.eq.1) then
                     ilayer=ilayer+1
                     if(ilayer.gt.1) then
                        do i=1,4
                           dlayer(i)=dlayer(i)+xlayer(ilayer-1,i)
                        enddo
                     endif
                  endif
                  ze=2.d0*(dlayer(ki)+(ze+1.d0)/2.d0*xlayer(ilayer,ki))/
     &                 tlayer(ki)-1.d0
                  weight=weight*xlayer(ilayer,ki)/tlayer(ki)
!
!                 material and orientation
!
                  imat=ielmat(ilayer,nelem)
                  amat=matname(imat)
                  if(norien.gt.0) then
                     iorien=ielorien(ilayer,nelem)
                  else
                     iorien=0
                  endif
!     
                  if(nelcon(1,imat).lt.0) then
                     ihyper=1
                  else
                     ihyper=0
                  endif
               endif
            elseif(lakonl(4:4).eq.'2') then
               xi=gauss3d3(1,kk)
               et=gauss3d3(2,kk)
               ze=gauss3d3(3,kk)
               weight=weight3d3(kk)
            elseif(lakonl(4:5).eq.'10') then
               xi=gauss3d5(1,kk)
               et=gauss3d5(2,kk)
               ze=gauss3d5(3,kk)
               weight=weight3d5(kk)
            elseif(lakonl(4:4).eq.'4') then
               xi=gauss3d4(1,kk)
               et=gauss3d4(2,kk)
               ze=gauss3d4(3,kk)
               weight=weight3d4(kk)
            elseif(lakonl(4:5).eq.'15') then
               if(lakonl(7:8).ne.'LC') then
                  xi=gauss3d8(1,kk)
                  et=gauss3d8(2,kk)
                  ze=gauss3d8(3,kk)
                  weight=weight3d8(kk)
               else
                  kl=mod(kk,6)
                  if(kl.eq.0) kl=6
!
                  xi=gauss3d10(1,kl)
                  et=gauss3d10(2,kl)
                  ze=gauss3d10(3,kl)
                  weight=weight3d10(kl)
!
                  ki=mod(kk,3)
                  if(ki.eq.0) ki=3
!
                  if(kl.eq.1) then
                     ilayer=ilayer+1
                     if(ilayer.gt.1) then
                        do i=1,3
                           dlayer(i)=dlayer(i)+xlayer(ilayer-1,i)
                        enddo
                     endif
                  endif
                  ze=2.d0*(dlayer(ki)+(ze+1.d0)/2.d0*xlayer(ilayer,ki))/
     &                 tlayer(ki)-1.d0
                  weight=weight*xlayer(ilayer,ki)/tlayer(ki)
!
!                 material and orientation
!
                  imat=ielmat(ilayer,nelem)
                  amat=matname(imat)
                  if(norien.gt.0) then
                     iorien=ielorien(ilayer,nelem)
                  else
                     iorien=0
                  endif
!     
                  if(nelcon(1,imat).lt.0) then
                     ihyper=1
                  else
                     ihyper=0
                  endif
               endif
            elseif(lakonl(4:4).eq.'6') then
               xi=gauss3d7(1,kk)
               et=gauss3d7(2,kk)
               ze=gauss3d7(3,kk)
               weight=weight3d7(kk)
            endif
         else
            if((lakonl(4:4).eq.'8').or.(lakonl(4:4).eq.'2')) then
               xi=gauss3d3(1,kk)
               et=gauss3d3(2,kk)
               ze=gauss3d3(3,kk)
               weight=weight3d3(kk)
            elseif((lakonl(4:5).eq.'10').or.(lakonl(4:4).eq.'4')) then
               xi=gauss3d6(1,kk)
               et=gauss3d6(2,kk)
               ze=gauss3d6(3,kk)
               weight=weight3d6(kk)
            else
               xi=gauss3d8(1,kk)
               et=gauss3d8(2,kk)
               ze=gauss3d8(3,kk)
               weight=weight3d8(kk)
            endif
         endif
c         if(nelem.eq.1) then
c                  write(*,*) 'kk', kk
c                  write(*,*) 'coords',xi,et,ze
c                  write(*,*) 'weight',weight
c                  write(*,*) 'dlayer',dlayer(ki)
c         endif
!
!           calculation of the shape functions and their derivatives
!           in the gauss point
!
c     Bernhardi start
         if(lakonl(1:5).eq.'C3D8R') then
            call shape8hr(xl,xsj,shp,gs,a)
         elseif(lakonl(1:5).eq.'C3D8I') then
            call shape8hu(xi,et,ze,xl,xsj,shp,iflag)
         elseif(nope.eq.20) then
c     Bernhardi end
            if(lakonl(7:7).eq.'A') then
               call shape20h_ax(xi,et,ze,xl,xsj,shp,iflag)
            elseif((lakonl(7:7).eq.'E').or.(lakonl(7:7).eq.'S')) then
               call shape20h_pl(xi,et,ze,xl,xsj,shp,iflag)
            else
               call shape20h(xi,et,ze,xl,xsj,shp,iflag)
            endif
         elseif(nope.eq.8) then
            call shape8h(xi,et,ze,xl,xsj,shp,iflag)
         elseif(nope.eq.10) then
            call shape10tet(xi,et,ze,xl,xsj,shp,iflag)
         elseif(nope.eq.4) then
            call shape4tet(xi,et,ze,xl,xsj,shp,iflag)
         elseif(nope.eq.15) then
            call shape15w(xi,et,ze,xl,xsj,shp,iflag)
         else
            call shape6w(xi,et,ze,xl,xsj,shp,iflag)
         endif
!
!           check the jacobian determinant
!
         if(xsj.lt.1.d-20) then
            write(*,*) '*ERROR in e_c3d: nonpositive jacobian'
            write(*,*) '       determinant in element',nelem
            write(*,*)
            xsj=dabs(xsj)
            nmethod=0
         endif
!
c         if((iperturb(1).ne.0).and.stiffness.and.(.not.buckling))
         if(((iperturb(1).eq.1).or.(iperturb(2).eq.1)).and.
     &           (stiffness.eq.1).and.(buckling.eq.0))then
!
!              stresses for 2nd order static and modal theory
!
            s11=sti(1,kk,nelem)
            s22=sti(2,kk,nelem)
            s33=sti(3,kk,nelem)
            s12=sti(4,kk,nelem)
            s13=sti(5,kk,nelem)
            s23=sti(6,kk,nelem)
         endif
!
!           calculating the temperature in the integration
!           point
!
         t0l=0.d0
         t1l=0.d0
         if(ithermal.eq.1) then
            if(lakonl(4:5).eq.'8 ') then
               do i1=1,nope
                  t0l=t0l+t0(konl(i1))/8.d0
                  t1l=t1l+t1(konl(i1))/8.d0
               enddo
            elseif(lakonl(4:6).eq.'20 ')then
               nopered=20
               call lintemp(t0,t1,konl,nopered,kk,t0l,t1l)
            else
               do i1=1,nope
                  t0l=t0l+shp(4,i1)*t0(konl(i1))
                  t1l=t1l+shp(4,i1)*t1(konl(i1))
               enddo
            endif
         elseif(ithermal.ge.2) then
            if(lakonl(4:5).eq.'8 ') then
               do i1=1,nope
                  t0l=t0l+t0(konl(i1))/8.d0
                  t1l=t1l+vold(0,konl(i1))/8.d0
               enddo
            elseif(lakonl(4:6).eq.'20 ')then
               nopered=20
               call lintemp_th(t0,vold,konl,nopered,kk,t0l,t1l,mi)
            else
               do i1=1,nope
                  t0l=t0l+shp(4,i1)*t0(konl(i1))
                  t1l=t1l+shp(4,i1)*vold(0,konl(i1))
               enddo
            endif
         endif
         tt=t1l-t0l
!
!           calculating the coordinates of the integration point
!           for material orientation purposes (for cylindrical
!           coordinate systems)
!
         if(iorien.gt.0) then
            do j=1,3
               coords(j)=0.d0
               do i1=1,nope
                  coords(j)=coords(j)+shp(4,i1)*co(j,konl(i1))
               enddo
            enddo
         endif
!
!           for deformation plasticity: calculating the Jacobian
!           and the inverse of the deformation gradient
!           needed to convert the stiffness matrix in the spatial
!           frame of reference to the material frame
!
         kode=nelcon(1,imat)
!
!           material data and local stiffness matrix
!
         istiff=1
         call materialdata_me(elcon,nelcon,rhcon,nrhcon,alcon,nalcon,
     &        imat,amat,iorien,coords,orab,ntmat_,elas,rho,
     &        nelem,ithermal,alzero,mattyp,t0l,t1l,
     &        ihyper,istiff,elconloc,eth,kode,plicon,
     &        nplicon,plkcon,nplkcon,npmat_,
     &        plconloc,mi(1),dtime,nelem,kk,
     &        xstiff,ncmat_)
!
         if(mattyp.eq.1) then
c            write(*,*) 'elastic co', elas(1),elas(2)
            e=elas(1)
            un=elas(2)
            um=e/(1.d0+un)
            al=un*um/(1.d0-2.d0*un)
            um=um/2.d0
         elseif(mattyp.eq.2) then
c            call orthotropic(elas,anisox)
         else
            call anisotropic(elas,anisox)
         endif
!
!           initialisation for the body forces
!
         om=omx*rho
         if(rhsi.eq.1) then
            if(nbody.ne.0) then
               do ii=1,3
                  bodyf(ii)=bodyfx(ii)*rho
               enddo
            endif
         endif
!
         if(buckling.eq.1) then
!
!              buckling stresses
!
            s11b=stx(1,kk,nelem)
            s22b=stx(2,kk,nelem)
            s33b=stx(3,kk,nelem)
            s12b=stx(4,kk,nelem)
            s13b=stx(5,kk,nelem)
            s23b=stx(6,kk,nelem)
!
         endif
!
!           incorporating the jacobian determinant in the shape
!           functions
!
         xsjj=dsqrt(xsj)
         do i1=1,nope
            shpj(1,i1)=shp(1,i1)*xsjj
            shpj(2,i1)=shp(2,i1)*xsjj
            shpj(3,i1)=shp(3,i1)*xsjj
            shpj(4,i1)=shp(4,i1)*xsj
         enddo
!
!           determination of the stiffness, and/or mass and/or
!           buckling matrix
!
         if((stiffness.eq.1).or.(mass.eq.1).or.(buckling.eq.1).or.
     &      (coriolis.eq.1)) then
!
            if(((iperturb(1).ne.1).and.(iperturb(2).ne.1)).or.
     &          (buckling.eq.1)) then
!
!               calculating the total mass of the element for
!               lumping purposes: only for explicit
!               dynamic calculations
!
               if((mass.eq.1).and.(iexpl.gt.1)) then
                  summass=summass+rho*xsj
               endif
!
               jj1=1
               do jj=1,nope
!
                  ii1=1
                  do ii=1,jj
!
!                   all products of the shape functions for a given ii
!                   and jj
!
                     do i1=1,3
                        do j1=1,3
                           w(i1,j1)=shpj(i1,ii)*shpj(j1,jj)
                        enddo
                     enddo
!
!                   the following section calculates the static
!                   part of the stiffness matrix which, for buckling 
!                   calculations, is done in a preliminary static
!                   call
!
                     if(buckling.eq.0) then
!
                        if(mattyp.eq.1) then
!
                           s(ii1,jj1)=s(ii1,jj1)+(al*w(1,1)+
     &                          um*(2.d0*w(1,1)+w(2,2)+w(3,3)))*weight
!                          
                           s(ii1,jj1+1)=s(ii1,jj1+1)+(al*w(1,2)+
     &                          um*w(2,1))*weight
                           s(ii1,jj1+2)=s(ii1,jj1+2)+(al*w(1,3)+
     &                          um*w(3,1))*weight
                           s(ii1+1,jj1)=s(ii1+1,jj1)+(al*w(2,1)+
     &                          um*w(1,2))*weight
                           s(ii1+1,jj1+1)=s(ii1+1,jj1+1)+(al*w(2,2)+
     &                          um*(2.d0*w(2,2)+w(1,1)+w(3,3)))*weight
                           s(ii1+1,jj1+2)=s(ii1+1,jj1+2)+(al*w(2,3)+
     &                          um*w(3,2))*weight
                           s(ii1+2,jj1)=s(ii1+2,jj1)+(al*w(3,1)+
     &                          um*w(1,3))*weight
                           s(ii1+2,jj1+1)=s(ii1+2,jj1+1)+(al*w(3,2)+
     &                          um*w(2,3))*weight
                           s(ii1+2,jj1+2)=s(ii1+2,jj1+2)+(al*w(3,3)+
     &                          um*(2.d0*w(3,3)+w(2,2)+w(1,1)))*weight
!
                        elseif(mattyp.eq.2) then
!
                           s(ii1,jj1)=s(ii1,jj1)+(elas(1)*w(1,1)+
     &                          elas(7)*w(2,2)+elas(8)*w(3,3))*weight
                           s(ii1,jj1+1)=s(ii1,jj1+1)+(elas(2)*w(1,2)+
     &                          elas(7)*w(2,1))*weight
                           s(ii1,jj1+2)=s(ii1,jj1+2)+(elas(4)*w(1,3)+
     &                          elas(8)*w(3,1))*weight
                           s(ii1+1,jj1)=s(ii1+1,jj1)+(elas(7)*w(1,2)+
     &                          elas(2)*w(2,1))*weight
                           s(ii1+1,jj1+1)=s(ii1+1,jj1+1)+
     &                          (elas(7)*w(1,1)+
     &                          elas(3)*w(2,2)+elas(9)*w(3,3))*weight
                           s(ii1+1,jj1+2)=s(ii1+1,jj1+2)+
     &                          (elas(5)*w(2,3)+
     &                          elas(9)*w(3,2))*weight
                           s(ii1+2,jj1)=s(ii1+2,jj1)+
     &                          (elas(8)*w(1,3)+
     &                          elas(4)*w(3,1))*weight
                           s(ii1+2,jj1+1)=s(ii1+2,jj1+1)+
     &                          (elas(9)*w(2,3)+
     &                          elas(5)*w(3,2))*weight
                           s(ii1+2,jj1+2)=s(ii1+2,jj1+2)+
     &                          (elas(8)*w(1,1)+
     &                          elas(9)*w(2,2)+elas(6)*w(3,3))*weight
!
                        else
!
                           do i1=1,3
                              do j1=1,3
                                 do k1=1,3
                                    do l1=1,3
                                       s(ii1+i1-1,jj1+j1-1)=
     &                                      s(ii1+i1-1,jj1+j1-1)
     &                                      +anisox(i1,k1,j1,l1)
     &                                      *w(k1,l1)*weight
                                    enddo
                                 enddo
                              enddo
                           enddo
!
                        endif
!
!                     mass matrix
!
                        if(mass.eq.1) then
                           sm(ii1,jj1)=sm(ii1,jj1)
     &                          +rho*shpj(4,ii)*shp(4,jj)*weight
                           sm(ii1+1,jj1+1)=sm(ii1,jj1)
                           sm(ii1+2,jj1+2)=sm(ii1,jj1)
                        endif
!
!                     Coriolis matrix
!
                        if(coriolis.eq.1) then
                           dmass=2.d0*
     &                        rho*shpj(4,ii)*shp(4,jj)*weight*dsqrt(omx)
                           sm(ii1,jj1+1)=sm(ii1,jj1+1)-p2(3)*dmass
                           sm(ii1,jj1+2)=sm(ii1,jj1+2)+p2(2)*dmass
                           sm(ii1+1,jj1)=sm(ii1+1,jj1)+p2(3)*dmass
                           sm(ii1+1,jj1+2)=sm(ii1+1,jj1+2)-p2(1)*dmass
                           sm(ii1+2,jj1)=sm(ii1+2,jj1)-p2(2)*dmass
                           sm(ii1+2,jj1+1)=sm(ii1+2,jj1+1)+p2(1)*dmass
                        endif
!
                     else
!
!                     buckling matrix  
!
                        senergyb=
     &                       (s11b*w(1,1)+s12b*(w(1,2)+w(2,1))
     &                       +s13b*(w(1,3)+w(3,1))+s22b*w(2,2)
     &                       +s23b*(w(2,3)+w(3,2))+s33b*w(3,3))*weight
                        sm(ii1,jj1)=sm(ii1,jj1)-senergyb
                        sm(ii1+1,jj1+1)=sm(ii1+1,jj1+1)-senergyb
                        sm(ii1+2,jj1+2)=sm(ii1+2,jj1+2)-senergyb
!
                     endif
!
                     ii1=ii1+3
                  enddo
                  jj1=jj1+3
               enddo
            else
!
!               stiffness matrix for static and modal
!               2nd order calculations
!
!               large displacement stiffness
!               
               do i1=1,3
                  do j1=1,3
                     vo(i1,j1)=0.d0
                     do k1=1,nope
                        vo(i1,j1)=vo(i1,j1)+shp(j1,k1)*voldl(i1,k1)
                     enddo
                  enddo
               enddo
!
               if(mattyp.eq.1) then
                  call wcoef(v,vo,al,um)
               endif
!
!               calculating the total mass of the element for
!               lumping purposes: only for explicit
!               dynamic calculations
!
               if((mass.eq.1).and.(iexpl.gt.1)) then
                  summass=summass+rho*xsj
               endif
!
               jj1=1
               do jj=1,nope
!
                  ii1=1
                  do ii=1,jj
!
!                   all products of the shape functions for a given ii
!                   and jj
!
                     do i1=1,3
                        do j1=1,3
                           w(i1,j1)=shpj(i1,ii)*shpj(j1,jj)
                        enddo
                     enddo
!
                     if(mattyp.eq.1) then
!
                        do m1=1,3
                           do m2=1,3
                              do m3=1,3
                                 do m4=1,3
                                    s(ii1+m2-1,jj1+m1-1)=
     &                                   s(ii1+m2-1,jj1+m1-1)
     &                                   +v(m4,m3,m2,m1)*w(m4,m3)*weight
                                 enddo
                              enddo
                           enddo
                        enddo
!                      
                     elseif(mattyp.eq.2) then
!
                        call orthonl(w,vo,elas,s,ii1,jj1,weight)
!
                     else
!
                        call anisonl(w,vo,elas,s,ii1,jj1,weight)
!
                     endif
!
!                   stress stiffness
!
                     senergy=
     &                    (s11*w(1,1)+s12*(w(1,2)+w(2,1))
     &                    +s13*(w(1,3)+w(3,1))+s22*w(2,2)
     &                    +s23*(w(2,3)+w(3,2))+s33*w(3,3))*weight
                     s(ii1,jj1)=s(ii1,jj1)+senergy
                     s(ii1+1,jj1+1)=s(ii1+1,jj1+1)+senergy
                     s(ii1+2,jj1+2)=s(ii1+2,jj1+2)+senergy
!
!                    stiffness contribution of centrifugal forces
!
                     if((mass.eq.1).and.(om.gt.0.d0)) then
                        dmass=shpj(4,ii)*shp(4,jj)*weight*om
                        do m1=1,3
                           s(ii1+m1-1,jj1+m1-1)=s(ii1+m1-1,jj1+m1-1)-
     &                          dmass
                           do m2=1,3
                              s(ii1+m1-1,jj1+m2-1)=s(ii1+m1-1,jj1+m2-1)+
     &                             dmass*p2(m1)*p2(m2)
                           enddo
                        enddo
                     endif
!
!                   mass matrix
!
                     if(mass.eq.1) then
                        sm(ii1,jj1)=sm(ii1,jj1)
     &                       +rho*shpj(4,ii)*shp(4,jj)*weight
                        sm(ii1+1,jj1+1)=sm(ii1,jj1)
                        sm(ii1+2,jj1+2)=sm(ii1,jj1)
                     endif
!
!                     Coriolis matrix
!
                     if(coriolis.eq.1) then
                        dmass=2.d0*
     &                    rho*shpj(4,ii)*shp(4,jj)*weight*dsqrt(omx)
                        sm(ii1,jj1+1)=sm(ii1,jj1+1)-p2(3)*dmass
                        sm(ii1,jj1+2)=sm(ii1,jj1+2)+p2(2)*dmass
                        sm(ii1+1,jj1)=sm(ii1+1,jj1)+p2(3)*dmass
                        sm(ii1+1,jj1+2)=sm(ii1+1,jj1+2)-p2(1)*dmass
                        sm(ii1+2,jj1)=sm(ii1+2,jj1)-p2(2)*dmass
                        sm(ii1+2,jj1+1)=sm(ii1+2,jj1+1)+p2(1)*dmass
                     endif
!
                     ii1=ii1+3
                  enddo
                  jj1=jj1+3
               enddo
            endif
!
         endif
!
!        add hourglass control stiffnesses: C3D8R only. 
         if(lakonl(1:5).eq.'C3D8R') then 
            call hgstiffness(s,elas,a,gs)
         endif
!
!        computation of the right hand side
!
         if(rhsi.eq.1) then
!
!           distributed body flux
!
            if(nload.gt.0) then
               call nident2(nelemload,nelem,nload,id)
               do
                  if((id.eq.0).or.(nelemload(1,id).ne.nelem)) exit
                  if((sideload(id)(1:2).ne.'BX').and.
     &               (sideload(id)(1:2).ne.'BY').and.
     &               (sideload(id)(1:2).ne.'BZ')) then
                     id=id-1
                     cycle
                  endif
                  if(sideload(id)(3:4).eq.'NU') then
                     do j=1,3
                        coords(j)=0.d0
                        do i1=1,nope
                           coords(j)=coords(j)+
     &                          shp(4,i1)*xl(j,i1)
                        enddo
                     enddo
                     if(sideload(id)(1:2).eq.'BX') then
                        jltyp=1
                     elseif(sideload(id)(1:2).eq.'BY') then
                        jltyp=2
                     elseif(sideload(id)(1:2).eq.'BZ') then
                        jltyp=3
                     endif
                     iscale=1
                     call dload(xload(1,id),istep,iinc,tvar,nelem,i,
     &                  layer,kspt,coords,jltyp,sideload(id),vold,co,
     &                  lakonl,konl,ipompc,nodempc,coefmpc,nmpc,ikmpc,
     &                  ilmpc,iscale,veold,rho,amat,mi)
                     if((nmethod.eq.1).and.(iscale.ne.0))
     &                    xload(1,id)=xloadold(1,id)+
     &                   (xload(1,id)-xloadold(1,id))*reltime
                  endif
                  jj1=1
                  do jj=1,nope
                     if(sideload(id)(1:2).eq.'BX')
     &                    ff(jj1)=ff(jj1)+xload(1,id)*shpj(4,jj)*weight
                     if(sideload(id)(1:2).eq.'BY')
     &                 ff(jj1+1)=ff(jj1+1)+xload(1,id)*shpj(4,jj)*weight
                     if(sideload(id)(1:2).eq.'BZ')
     &                 ff(jj1+2)=ff(jj1+2)+xload(1,id)*shpj(4,jj)*weight
                     jj1=jj1+3
                  enddo
                  id=id-1
               enddo
            endif
!
!           body forces
!
            if(nbody.ne.0) then
               if(om.gt.0.d0) then
                  do i1=1,3
!
!                   computation of the global coordinates of the gauss
!                   point
!
                     q(i1)=0.d0
c                     if(iperturb(1).eq.0) then
                     if((iperturb(1).ne.1).and.(iperturb(2).ne.1)) then
                        do j1=1,nope
                           q(i1)=q(i1)+shp(4,j1)*xl(i1,j1)
                        enddo
                     else
                        do j1=1,nope
                           q(i1)=q(i1)+shp(4,j1)*
     &                          (xl(i1,j1)+voldl(i1,j1))
                        enddo
                     endif
!                       
                     q(i1)=q(i1)-p1(i1)
                  enddo
                  const=q(1)*p2(1)+q(2)*p2(2)+q(3)*p2(3)
!
!                 inclusion of the centrifugal force into the body force
!
                  do i1=1,3
                     bf(i1)=bodyf(i1)+(q(i1)-const*p2(i1))*om
                  enddo
               else
                  do i1=1,3
                     bf(i1)=bodyf(i1)
                  enddo
               endif
               jj1=1
               do jj=1,nope
                  ff(jj1)=ff(jj1)+bf(1)*shpj(4,jj)*weight
                  ff(jj1+1)=ff(jj1+1)+bf(2)*shpj(4,jj)*weight
                  ff(jj1+2)=ff(jj1+2)+bf(3)*shpj(4,jj)*weight
                  jj1=jj1+3
               enddo
            endif
!
         endif
!
      enddo
!
c      write(*,*) nelem
c      write(*,'(6(1x,e11.4))') ((s(i1,j1),i1=1,j1),j1=1,60)
c      write(*,*)
c
      if((buckling.eq.0).and.(nload.ne.0)) then
!
!       distributed loads
!
         call nident2(nelemload,nelem,nload,id)
         do
            if((id.eq.0).or.(nelemload(1,id).ne.nelem)) exit
            if(sideload(id)(1:1).ne.'P') then
               id=id-1
               cycle
            endif
c            read(sideload(id)(2:2),'(i1)') ig
            ig=ichar(sideload(id)(2:2))-48
!
!
!         treatment of wedge faces
!
            if(lakonl(4:4).eq.'6') then
               mint2d=1
               if(ig.le.2) then
                  nopes=3
               else
                  nopes=4
               endif
            endif
          if(lakonl(4:5).eq.'15') then
             if(ig.le.2) then
                mint2d=3
                nopes=6
             else
                mint2d=4
                nopes=8
             endif
          endif
!
c     Bernhardi start
          if((nope.eq.20).or.(nope.eq.8).or.
     &       (nope.eq.11)) then
c     Bernhardi end
c             if(iperturb(1).eq.0) then
             if((iperturb(1).ne.1).and.(iperturb(2).ne.1)) then
                do i=1,nopes
                   do j=1,3
                      xl2(j,i)=co(j,konl(ifaceq(i,ig)))
                   enddo
                enddo
             else
                if(mass.eq.1) then
                   do i=1,nopes
                      do j=1,3
                         xl1(j,i)=co(j,konl(ifaceq(i,ig)))
                      enddo
                   enddo
                endif
                do i=1,nopes
                   do j=1,3
                      xl2(j,i)=co(j,konl(ifaceq(i,ig)))+
     &                     vold(j,konl(ifaceq(i,ig)))
                   enddo
                enddo
             endif
          elseif((nope.eq.10).or.(nope.eq.4)) then
c             if(iperturb(1).eq.0) then
             if((iperturb(1).ne.1).and.(iperturb(2).ne.1)) then
                do i=1,nopes
                   do j=1,3
                      xl2(j,i)=co(j,konl(ifacet(i,ig)))
                   enddo
                enddo
             else
                if(mass.eq.1) then
                   do i=1,nopes
                      do j=1,3
                         xl1(j,i)=co(j,konl(ifacet(i,ig)))
                      enddo
                   enddo
                endif
                do i=1,nopes
                   do j=1,3
                      xl2(j,i)=co(j,konl(ifacet(i,ig)))+
     &                     vold(j,konl(ifacet(i,ig)))
                   enddo
                enddo
             endif
          else
c             if(iperturb(1).eq.0) then
             if((iperturb(1).ne.1).and.(iperturb(2).ne.1)) then
                do i=1,nopes
                   do j=1,3
                      xl2(j,i)=co(j,konl(ifacew(i,ig)))
                   enddo
                enddo
             else
                if(mass.eq.1) then
                   do i=1,nopes
                      do j=1,3
                         xl1(j,i)=co(j,konl(ifacew(i,ig)))
                      enddo
                   enddo
                endif
                do i=1,nopes
                   do j=1,3
                      xl2(j,i)=co(j,konl(ifacew(i,ig)))+
     &                     vold(j,konl(ifacew(i,ig)))
                   enddo
                enddo
             endif
          endif
!
          do i=1,mint2d
             if((lakonl(4:5).eq.'8R').or.
     &            ((lakonl(4:4).eq.'6').and.(nopes.eq.4))) then
                xi=gauss2d1(1,i)
                et=gauss2d1(2,i)
                weight=weight2d1(i)
             elseif((lakonl(4:4).eq.'8').or.
     &              (lakonl(4:6).eq.'20R').or.
     &              ((lakonl(4:5).eq.'15').and.(nopes.eq.8))) then
                xi=gauss2d2(1,i)
                et=gauss2d2(2,i)
                weight=weight2d2(i)
             elseif(lakonl(4:4).eq.'2') then
                xi=gauss2d3(1,i)
                et=gauss2d3(2,i)
                weight=weight2d3(i)
             elseif((lakonl(4:5).eq.'10').or.
     &               ((lakonl(4:5).eq.'15').and.(nopes.eq.6))) then
                xi=gauss2d5(1,i)
                et=gauss2d5(2,i)
                weight=weight2d5(i)
             elseif((lakonl(4:4).eq.'4').or.
     &               ((lakonl(4:4).eq.'6').and.(nopes.eq.3))) then
                xi=gauss2d4(1,i)
                et=gauss2d4(2,i)
                weight=weight2d4(i)
             endif
!
             if(rhsi.eq.1) then
                if(nopes.eq.9) then
                   call shape9q(xi,et,xl2,xsj2,xs2,shp2,iflag)
                elseif(nopes.eq.8) then
                   call shape8q(xi,et,xl2,xsj2,xs2,shp2,iflag)
                elseif(nopes.eq.4) then
                   call shape4q(xi,et,xl2,xsj2,xs2,shp2,iflag)
                elseif(nopes.eq.6) then
                   call shape6tri(xi,et,xl2,xsj2,xs2,shp2,iflag)
                elseif(nopes.eq.7) then
                   call shape7tri(xi,et,xl2,xsj2,xs2,shp2,iflag)
                else
                   call shape3tri(xi,et,xl2,xsj2,xs2,shp2,iflag)
                endif
!
!            for nonuniform load: determine the coordinates of the
!            point (transferred into the user subroutine)
!
                if(sideload(id)(3:4).eq.'NU') then
                   do k=1,3
                      coords(k)=0.d0
                      do j=1,nopes
                         coords(k)=coords(k)+xl2(k,j)*shp2(4,j)
                      enddo
                   enddo
c                   read(sideload(id)(2:2),'(i1)') jltyp
                   jltyp=ichar(sideload(id)(2:2))-48
                   jltyp=jltyp+20
                   iscale=1
                   call dload(xload(1,id),istep,iinc,tvar,nelem,i,layer,
     &                  kspt,coords,jltyp,sideload(id),vold,co,lakonl,
     &                  konl,ipompc,nodempc,coefmpc,nmpc,ikmpc,ilmpc,
     &                  iscale,veold,rho,amat,mi)
                   if((nmethod.eq.1).and.(iscale.ne.0))
     &                   xload(1,id)=xloadold(1,id)+
     &                  (xload(1,id)-xloadold(1,id))*reltime
                elseif(sideload(id)(3:4).eq.'SM') then
!
!                  submodel boundary: interpolation from the
!                  global model
!
                   do k=1,3
                      coords(k)=0.d0
                      do j=1,nopes
                         coords(k)=coords(k)+xl2(k,j)*shp2(4,j)
                      enddo
                   enddo
c                   read(sideload(id)(2:2),'(i1)') jltyp
                   jltyp=ichar(sideload(id)(2:2))-48
!
                   entity='T'
                   six=6
                   do k=1,6
                      iselect(k)=k+4
                   enddo
                   iface=10*nelem+jltyp
                   call interpolsubmodel(integerglob,doubleglob,stress,
     &                  coords,iselect,six,iface,tieset,istartset,
     &                  iendset,ialset,ntie,entity)
c                   write(*,*) 'e_c3d ',(stress(k),k=1,6)
!
!                  cave: stress order of cgx: xx,yy,zz,xy,yz,xz
!
                   t(1)=stress(1)*xsj2(1)+stress(4)*xsj2(2)+
     &                  stress(6)*xsj2(3)
                   t(2)=stress(4)*xsj2(1)+stress(2)*xsj2(2)+
     &                  stress(5)*xsj2(3)
                   t(3)=stress(6)*xsj2(1)+stress(5)*xsj2(2)+
     &                  stress(3)*xsj2(3)
!
                   xload(1,id)=-1.d0
                   do k=1,3
                      xsj2(k)=t(k)
                   enddo
                endif
!
                do k=1,nopes
c    Bernhardi start
                   if((nope.eq.20).or.(nope.eq.8).or.
     &                (nope.eq.11)) then
c    Bernhardi end
                      ipointer=(ifaceq(k,ig)-1)*3
                   elseif((nope.eq.10).or.(nope.eq.4)) then
                      ipointer=(ifacet(k,ig)-1)*3
                   else
                      ipointer=(ifacew(k,ig)-1)*3
                   endif
                   ff(ipointer+1)=ff(ipointer+1)-shp2(4,k)*xload(1,id)
     &                  *xsj2(1)*weight
                   ff(ipointer+2)=ff(ipointer+2)-shp2(4,k)*xload(1,id)
     &                  *xsj2(2)*weight
                   ff(ipointer+3)=ff(ipointer+3)-shp2(4,k)*xload(1,id)
     &                  *xsj2(3)*weight
                enddo
!
!            stiffness< contribution of the distributed load 
!            reference: Dhondt G., The Finite Element Method for
!            three-dimensional thermomechanical Applications,
!            Wiley, 2004, p 153, eqn. (3.54).
!
c             elseif((mass.eq.1).and.(iperturb(1).ne.0)) then
             elseif((mass.eq.1).and.
     &            ((iperturb(1).eq.1).or.(iperturb(2).eq.1))) then
                if(nopes.eq.9) then
                   call shape9q(xi,et,xl1,xsj2,xs2,shp2,iflag)
                elseif(nopes.eq.8) then
                   call shape8q(xi,et,xl1,xsj2,xs2,shp2,iflag)
                elseif(nopes.eq.4) then
                   call shape4q(xi,et,xl1,xsj2,xs2,shp2,iflag)
                elseif(nopes.eq.6) then
                   call shape6tri(xi,et,xl1,xsj2,xs2,shp2,iflag)
                elseif(nopes.eq.7) then
                   call shape7tri(xi,et,xl1,xsj2,xs2,shp2,iflag)
                else
                   call shape3tri(xi,et,xl1,xsj2,xs2,shp2,iflag)
                endif
!
!            for nonuniform load: determine the coordinates of the
!            point (transferred into the user subroutine)
!
                if(sideload(id)(3:4).eq.'NU') then
                   do k=1,3
                      coords(k)=0.d0
                      do j=1,nopes
                         coords(k)=coords(k)+xl1(k,j)*shp2(4,j)
                      enddo
                   enddo
c                   read(sideload(id)(2:2),'(i1)') jltyp
                   jltyp=ichar(sideload(id)(2:2))-48
                   jltyp=jltyp+20
                   iscale=1
                   call dload(xload(1,id),istep,iinc,tvar,nelem,i,layer,
     &                  kspt,coords,jltyp,sideload(id),vold,co,lakonl,
     &                  konl,ipompc,nodempc,coefmpc,nmpc,ikmpc,ilmpc,
     &                  iscale,veold,rho,amat,mi)
                   if((nmethod.eq.1).and.(iscale.ne.0))
     &                   xload(1,id)=xloadold(1,id)+
     &                  (xload(1,id)-xloadold(1,id))*reltime
                elseif(sideload(id)(3:4).eq.'SM') then
!
!                  submodel boundary: interpolation from the
!                  global model
!
                   do k=1,3
                      coords(k)=0.d0
                      do j=1,nopes
                         coords(k)=coords(k)+xl2(k,j)*shp2(4,j)
                      enddo
                   enddo
c                   read(sideload(id)(2:2),'(i1)') jltyp
                   jltyp=ichar(sideload(id)(2:2))-48
!
                   entity='T'
                   six=6
                   do k=1,6
                      iselect(k)=k+4
                   enddo
                   iface=10*nelem+jltyp
                   call interpolsubmodel(integerglob,doubleglob,stress,
     &                  coords,iselect,six,iface,tieset,istartset,
     &                  iendset,ialset,ntie,entity)
c                   write(*,*) 'e_c3d ',(stress(k),k=1,6)
!
                   stre(1,1)=stress(1)
                   stre(1,2)=stress(4)
                   stre(1,3)=stress(6)
                   stre(2,1)=stress(4)
                   stre(2,2)=stress(2)
                   stre(2,3)=stress(5)
                   stre(3,1)=stress(6)
                   stre(3,2)=stress(5)
                   stre(3,3)=stress(3)
                endif
!
!               calculation of the deformation gradient
!
                do k=1,3
                   do l=1,3
                      xkl(k,l)=0.d0
                      do ii=1,nopes
                         xkl(k,l)=xkl(k,l)+shp2(l,ii)*xl2(k,ii)
                      enddo
                   enddo
                enddo
!
                do ii=1,nopes
c     Bernhardi start
                   if((nope.eq.20).or.(nope.eq.8).or.
     &                (nope.eq.11)) then
c     Bernhardi end
                      ipointeri=(ifaceq(ii,ig)-1)*3
                   elseif((nope.eq.10).or.(nope.eq.4))then
                     ipointeri=(ifacet(ii,ig)-1)*3
                   else
                      ipointeri=(ifacew(ii,ig)-1)*3
                   endif
                   do jj=1,nopes
c     Bernhardi start
                      if((nope.eq.20).or.(nope.eq.8)
     &                 .or.(nope.eq.11)) then
c     Bernhardi end
                         ipointerj=(ifaceq(jj,ig)-1)*3
                      elseif((nope.eq.10).or.(nope.eq.4)) then
                         ipointerj=(ifacet(jj,ig)-1)*3
                      else
                         ipointerj=(ifacew(jj,ig)-1)*3
                      endif
!
!                     if no submodel: only pressure
!                     else: complete stress vector
!
                      if(sideload(id)(3:4).ne.'SM') then
                         do k=1,3
                            do l=1,3
                               if(k.eq.l) cycle
                               eknlsign=1.d0
                               if(k*l.eq.2) then
                                  n=3
                                  if(k.lt.l) eknlsign=-1.d0
                               elseif(k*l.eq.3) then
                                  n=2
                                  if(k.gt.l) eknlsign=-1.d0
                               else
                                  n=1
                                  if(k.lt.l) eknlsign=-1.d0
                               endif
                               term=weight*xload(1,id)*shp2(4,ii)*
     &                              eknlsign*(xsj2(1)*
     &                              (xkl(n,2)*shp2(3,jj)-xkl(n,3)*
     &                              shp2(2,jj))+xsj2(2)*
     &                              (xkl(n,3)*shp2(1,jj)-xkl(n,1)*
     &                              shp2(3,jj))+xsj2(3)*
     &                              (xkl(n,1)*shp2(2,jj)-xkl(n,2)*
     &                              shp2(1,jj)))
                               s(ipointeri+k,ipointerj+l)=
     &                              s(ipointeri+k,ipointerj+l)+term/2.d0
                               s(ipointerj+l,ipointeri+k)=
     &                              s(ipointerj+l,ipointeri+k)+term/2.d0
                            enddo
                         enddo
                      else
                         do kk=1,3
                            do k=1,3
                               do l=1,3
                                  if(k.eq.l) cycle
                                  eknlsign=1.d0
                                  if(k*l.eq.2) then
                                     n=3
                                     if(k.lt.l) eknlsign=-1.d0
                                  elseif(k*l.eq.3) then
                                     n=2
                                     if(k.gt.l) eknlsign=-1.d0
                                  else
                                     n=1
                                     if(k.lt.l) eknlsign=-1.d0
                                  endif
                                  term=-weight*stre(kk,k)*shp2(4,ii)*
     &                                 eknlsign*(xsj2(1)*
     &                                 (xkl(n,2)*shp2(3,jj)-xkl(n,3)*
     &                                 shp2(2,jj))+xsj2(2)*
     &                                 (xkl(n,3)*shp2(1,jj)-xkl(n,1)*
     &                                 shp2(3,jj))+xsj2(3)*
     &                                 (xkl(n,1)*shp2(2,jj)-xkl(n,2)*
     &                                 shp2(1,jj)))
                                  s(ipointeri+kk,ipointerj+l)=
     &                             s(ipointeri+kk,ipointerj+l)+term/2.d0
                                  s(ipointerj+l,ipointeri+kk)=
     &                             s(ipointerj+l,ipointeri+kk)+term/2.d0
                               enddo
                            enddo
                         enddo
                      endif
                   enddo
                enddo
!
             endif
          enddo
!
          id=id-1
       enddo
      endif
!
!     for axially symmetric and plane stress/strain elements: 
!     complete s and sm
!
      if(((lakonl(4:5).eq.'8 ').or.
     &    ((lakonl(4:6).eq.'20R').and.(lakonl(7:8).ne.'BR'))).and.
     &   ((lakonl(7:7).eq.'A').or.(lakonl(7:7).eq.'S').or.
     &    (lakonl(7:7).eq.'E'))) then
         do i=1,60
            do j=i,60
               k=abs(iperm(i))
               l=abs(iperm(j))
               if(k.gt.l) then
                  m=k
                  k=l
                  l=m
               endif
               sax(i,j)=s(k,l)*iperm(i)*iperm(j)/(k*l)
            enddo
         enddo
         do i=1,60
            do j=i,60
               s(i,j)=s(i,j)+sax(i,j)
            enddo
         enddo
!
         if((nload.ne.0).or.(nbody.ne.0)) then
            do i=1,60
               k=abs(iperm(i))
               ffax(i)=ff(k)*iperm(i)/k
            enddo
            do i=1,60
               ff(i)=ff(i)+ffax(i)
            enddo
         endif
!
         if(mass.eq.1) then
            summass=2.d0*summass
            do i=1,60
               do j=i,60
                  k=abs(iperm(i))
                  l=abs(iperm(j))
                  if(k.gt.l) then
                     m=k
                     k=l
                     l=m
                  endif
                  sax(i,j)=sm(k,l)*iperm(i)*iperm(j)/(k*l)
               enddo
            enddo
            do i=1,60
               do j=i,60
                  sm(i,j)=sm(i,j)+sax(i,j)
               enddo
            enddo
         endif
      endif
!
      if((mass.eq.1).and.(iexpl.gt.1)) then
!
!        scaling the diagonal terms of the mass matrix such that the total mass
!        is right (LUMPING; for explicit dynamic calculations)
!
         sume=0.d0
         summ=0.d0
         do i=1,3*nopev,3
            sume=sume+sm(i,i)
         enddo
         do i=3*nopev+1,3*nope,3
            summ=summ+sm(i,i)
         enddo
!
         if(nope.eq.20) then
c            alp=.2215d0
            alp=.2917d0
!              maybe alp=.2917d0 is better??
         elseif(nope.eq.10) then
            alp=0.1203d0
         elseif(nope.eq.15) then
            alp=0.2141d0
         endif
!
         if((nope.eq.20).or.(nope.eq.10).or.
     &      (nope.eq.15)) then
            factore=summass*alp/(1.d0+alp)/sume
            factorm=summass/(1.d0+alp)/summ
         else
            factore=summass/sume
         endif
!
         do i=1,3*nopev,3
            sm(i,i)=sm(i,i)*factore
            sm(i+1,i+1)=sm(i,i)
            sm(i+2,i+2)=sm(i,i)
         enddo
         do i=3*nopev+1,3*nope,3
            sm(i,i)=sm(i,i)*factorm
            sm(i+1,i+1)=sm(i,i)
            sm(i+2,i+2)=sm(i,i)
         enddo
!
      endif
!
c      if(nelem.eq.1) then
c         open(30,file='nelem1.dat',status='unknown')
c         write(30,'(8(1x,e11.4))') ((s(i,j),i=1,60),j=1,60)
c         close(30)
c      elseif(nelem.eq.2) then
c         open(31,file='nelem2.dat',status='unknown')
c         write(31,'(8(1x,e11.4))') ((s(i,j),i=1,60),j=1,60)
c         close(31)
c      elseif(nelem.eq.3) then
c         open(32,file='nelem3.dat',status='unknown')
c         write(32,'(8(1x,e11.4))') ((s(i,j),i=1,60),j=1,60)
c         close(32)
c      else
c         open(33,file='nelem4.dat',status='unknown')
c         write(33,'(8(1x,e11.4))') ((s(i,j),i=1,60),j=1,60)
c         close(33)
c      endif
      return
      end

