dst.cpp

Finite element program for mechanical problem. It can solve various problem in solid problem

void dstelem::stiffness_matrix (long eid,long ri,long ci, matrix &sm,vector &x, vector &y)
{
  long i,ii,jj,ipp;
  double jac,det,thick;
  ivector nodes(nne);
  vector w,gp1,gp2,l(3),t(nne);
  matrix gmc,dd,a(3,9),ct(3,2),d(tncomp,tncomp);

  Mt->give_elemnodes (eid,nodes);
  Mc->give_thickness (eid,nodes,t);
  tran_matrix (a,ct,eid);

  //  det is equal to double area of the element
  det = (x[1]-x[0])*(y[2]-y[0])-(x[2]-x[0])*(y[1]-y[0]);

  fillm (0.0,sm);

  for (ii=0;ii<nb;ii++){
    for (jj=0;jj<nb;jj++){
      if (intordsm[ii][jj]==0)  continue;

      allocv (intordsm[ii][jj],w);
      allocv (intordsm[ii][jj],gp1); allocv (intordsm[ii][jj],gp2);
      allocm (ncomp[ii],ndofe,gmc);
      allocm (ncomp[ii],ncomp[jj],dd);

      gauss_points_tr (gp1.a,gp2.a,w.a,intordsm[ii][jj]);

      ipp=Mt->elements[eid].ipp[ri+ii][ci+jj];

      for (i=0;i<intordsm[ii][jj];i++){
       fillm (0.0,gmc);
 	   l[0]=gp1[i];  l[1]=gp2[i];  l[2]=1.0-l[0]-l[1];
//	l[0]=0.5;  l[1]=0.5;  l[2]=1.0-l[0]-l[1];
	   if (ii==0){  fillm (0.0,gmc);   geom_matrix_bconst (gmc,x,y);  }
	   else	if(ii==1)geom_matrix_b (gmc,a,ct,x,y,l);
	   else if(ii==2)geom_matrix_shear (gmc,a,ct,eid);

	   Mm->matstiff (d,ipp);
	   ipp++;
	   thick = t[0]*l[0]+t[1]*l[1]+t[2]*l[2];
//  thick=0.7;
	   dmatblock (dd, d,ii,jj,thick);
	   jac=det*w[i];
	   bdbjac (sm,gmc,dd,gmc,jac);

//	   fprintf (Out,"\n %ld   %lf",ipp,sm[0][0]);

      }
      destrm (dd);  destrm (gmc);  destrv (gp1);  destrv (gp2);  destrv (w);
    }
  }

}

void dstelem::res_stiffness_matrix (long eid,matrix &sm)
{
  long transf;
  ivector nodes(nne);
  vector x(nne),y(nne);
  Mt->give_node_coord2d (x,y,eid);
  Mt->give_elemnodes (eid,nodes);

  stiffness_matrix (eid,0,0,sm,x,y);

  //  transformation of stiffness matrix
  transf = Mt->locsystems (nodes);
  if (transf>0){
    matrix tmat (ndofe,ndofe);
    transf_matrix (nodes,tmat);
    glmatrixtransf (sm,tmat);
  }
}
void dstelem::nodecoord (vector &xi,vector &eta)
{
  xi[0] = 0.0;  eta[0] = 0.0;
  xi[1] = 1.0;  eta[1] = 0.0;
  xi[2] = 0.0;  eta[2] = 1.0;
}

/**
   function computes strains DST
*/
void dstelem::appval (vector &l, long fi,long nc,vector &eps,double **val)
{
  long i,j,k;
  vector nodval;
  
  k=0;
  allocv (nne,nodval);
  for (i=fi;i<fi+nc;i++){
    for (j=0;j<nne;j++){
      nodval[j]=val[j][i];
    }
    eps[k] = nodval[0]*l[0]+nodval[1]*l[1]+nodval[2]*l[2];
    k++;
  }
  
  destrv (nodval);
}
void dstelem::res_mainip_strains (long lcid,long eid)
{
  vector aux,x(nne),y(nne),r(ndofe);
  ivector cn(ndofe),nodes(nne);
  matrix tmat;

  Mt->give_node_coord2d (x,y,eid);
  Mt->give_elemnodes (eid,nodes);
  Mt->give_code_numbers (eid,cn.a);
  eldispl (lcid,eid,r.a,cn.a,ndofe);
  
  //  transformation of displacement vector
  long transf = Mt->locsystems (nodes);
  if (transf>0){
    allocv (ndofe,aux);
    allocm (ndofe,ndofe,tmat);
    transf_matrix (nodes,tmat);
    //locglobtransf (aux,r,tmat);
    lgvectortransf (aux,r,tmat);
    copyv (aux,r);
    destrv (aux);
    destrm (tmat);
  }

  mainip_strains (lcid,eid,0,0,x,y,r);
}


void dstelem::mainip_strains (long lcid,long eid,long ri,long ci,vector &x,vector &y,vector &r)
{
  long ii,i,ipp;
  vector eps,w,gp1,gp2,l(3);
  matrix gm,a(3,9),ct(3,2);

  tran_matrix (a,ct,eid);
  
  for (ii=0;ii<nb;ii++){
    ipp=Mt->elements[eid].ipp[ii+ri][ii+ci];
    allocm (ncomp[ii],ndofe,gm);
    allocv (ncomp[ii],eps);allocv (intordsm[ii][ii],w);
    allocv (intordsm[ii][ii],gp1);allocv (intordsm[ii][ii],gp2);
    gauss_points_tr (gp1.a,gp2.a,w.a,intordsm[ii][ii]);
    
    for (i=0;i<intordsm[ii][ii];i++){
      l[0]=gp1[i];  l[1]=gp2[i];  l[2]=1.0-l[0]-l[1];
      
      if(ii==2) geom_matrix_shear (gm,a,ct,eid);
      else{
	   geom_matrix_b (gm,a,ct,x,y,l);
	   geom_matrix_bconst (gm,x,y);
      }
      
      mxv (gm,r,eps);
      Mm->storestrain (lcid,ipp,cncomp[ii],ncomp[ii],eps);
      ipp++;
    }
    destrv (eps);  destrv (w);  destrv (gp1);  destrv (gp2);
    destrm (gm);
  }
}

void dstelem::nod_strains (long lcid,long eid,long ri,long ci)
{
  long i,ii,ipp;
  double *lsm,*lhs,*rhs;
  vector eps,w,gp1,gp2,nxi(nne),neta(nne),natcoord(2),l(3);
  ivector nodes(nne);

  lsm = new double [9];

  nodecoord (nxi,neta);
  Mt->give_elemnodes (eid,nodes);
  
  for (ii=0;ii<nb;ii++){
    ipp=Mt->elements[eid].ipp[ii+ri][ii+ci];
    lhs = new double [ncomp[ii]*3];
    rhs = new double [ncomp[ii]*3];
    allocv (ncomp[ii],eps);allocv (intordsm[ii][ii],w);
    allocv (intordsm[ii][ii],gp1);allocv (intordsm[ii][ii],gp2);
    gauss_points_tr (gp1.a,gp2.a,w.a,intordsm[ii][ii]);
  
    nullv (lsm,9);
    nullv (rhs,ncomp[ii]*3);

    for (i=0;i<intordsm[ii][ii];i++){
      l[0]=gp1[i];  l[1]=gp2[i];  l[2]=1.0-l[0]-l[1];
    
	  Mm->givestrain (lcid,ipp,cncomp[ii],ncomp[ii],eps);
      
      natcoord[0]=l[0];  natcoord[1]=l[1];
      matassem_lsm (lsm,natcoord);
      rhsassem_lsm (rhs,natcoord,eps);
      ipp++;
	}
    solve_lsm (lsm,lhs,rhs,Mp->zero,3,ncomp[ii]);
    Mt->strain_nodal_values (nodes,nxi,neta,nxi,lhs,2,cncomp[ii],ncomp[ii],lcid);

    delete [] lhs;  delete [] rhs;
    destrv (eps);  destrv (w);  destrv (gp1);  destrv (gp2);
  }
  
  delete [] lsm;
}

void dstelem::elem_strains (double **stra,long lcid,long eid,long ri,long ci)
{
  long ii,i,ipp;
  double *lsm,*lhs,*rhs;
  vector eps,w,gp1,gp2,nxi(nne),neta(nne),natcoord(2),l(3);
  ivector nodes(nne);

  nodecoord (nxi,neta);
  lsm = new double [9];

  Mt->give_elemnodes (eid,nodes);
  nodecoord (nxi,neta);
  
  for (ii=0;ii<nb;ii++){
    ipp=Mt->elements[eid].ipp[ii+ri][ii+ci];
    lhs = new double [ncomp[ii]*3];
    rhs = new double [ncomp[ii]*3];
    allocv (ncomp[ii],eps);allocv (intordsm[ii][ii],w);
    allocv (intordsm[ii][ii],gp1);allocv (intordsm[ii][ii],gp2);
    gauss_points_tr (gp1.a,gp2.a,w.a,intordsm[ii][ii]);
  
    nullv (lsm,9);
    nullv (rhs,ncomp[ii]*3);

    for (i=0;i<intordsm[ii][ii];i++){
      l[0]=gp1[i];  l[1]=gp2[i];  l[2]=1.0-l[0]-l[1];
    
	  Mm->givestrain (lcid,ipp,cncomp[ii],ncomp[ii],eps);
      
      natcoord[0]=l[0];  natcoord[1]=l[1];
      matassem_lsm (lsm,natcoord);
      rhsassem_lsm (rhs,natcoord,eps);
      ipp++;
	}
    solve_lsm (lsm,lhs,rhs,Mp->zero,3,ncomp[ii]);
    nodal_values (stra,nxi,neta,nxi,lhs,2,cncomp[ii],ncomp[ii]);

    delete [] lhs;  delete [] rhs;
    destrv (eps);  destrv (w);  destrv (gp1);  destrv (gp2);
  }
    
      
  delete [] lsm;
}

void dstelem::appstrain (long lcid,long eid,vector &l,long fi,long ncomp,vector &eps)
{
  long i,j,k;
  ivector nodes;
  vector nodval;
  if (ncomp != eps.n){
    fprintf (stderr,"\n\n wrong interval of indices in function strain (%s, line %d).\n",__FILE__,__LINE__);
    abort ();
  }

  allocv (nne,nodes);
  allocv (nne,nodval);
  Mt->give_elemnodes (eid,nodes);
  k=0;
  for (i=fi;i<fi+ncomp;i++){
    for (j=0;j<nne;j++){
      nodval[j]=Mt->nodes[nodes[j]].strain[lcid*tncomp+i];
    }
    eps[k] = nodval[0]*l[0]+nodval[1]*l[1]+nodval[2]*l[2];
//    eps[k]=approx (areacoord,nodval);
    k++;
  }
  
  destrv (nodes);  destrv (nodval);
}

void dstelem::allip_strains (double **stra,long lcid,long eid,long ri,long ci)
{
  long i,ii,ipp;
  vector eps,gp1,gp2,w,l(3);
  
  allocv (tncomp,eps);

  for (ii=0;ii<nb;ii++){
      allocv (intordsm[ii][ii],w);allocv (intordsm[ii][ii],gp1); allocv (intordsm[ii][ii],gp2);      
      gauss_points_tr (gp1.a,gp2.a,w.a,intordsm[ii][ii]);
      ipp=Mt->elements[eid].ipp[ri+ii][ci+ii];
      
      for (i=0;i<intordsm[ii][ii];i++){
        l[0]=gp1[i];  l[1]=gp2[i];  l[2]=1.0-l[0]-l[1];   
    	if (Mp->strainaver==0)
		  appval (l,0,tncomp,eps,stra);
	    if (Mp->strainaver==1)
	      appstrain (lcid,eid,l,0,tncomp,eps);
	    Mm->storestrain (lcid,ipp,eps);
	    ipp++;
      }
      destrv (w);  destrv (gp2);  destrv (gp1);
  }
  destrv (eps);
}

void dstelem::strains (long lcid,long eid,long ri,long ci)
{
  long i,naep,ncp,sid;
  double **stra;
  vector coord,eps,l(3);
  
  if (Mp->strainaver==0){
    stra = new double* [nne];
    for (i=0;i<nne;i++){
      stra[i] = new double [tncomp];
    }
    elem_strains (stra,lcid,eid,ri,ci);
  }
  
  switch (Mm->stra.tape[eid]){
  case nowhere:{
    break;
  }
  case intpts:{
    allip_strains (stra,lcid,eid,ri,ci);
    break;
  }
  case enodes:{
    break;
  }
  case userdefined:{
    //  number of auxiliary element points
    naep = Mm->stra.give_naep (eid);
    ncp = Mm->stra.give_ncomp (eid);
    sid = Mm->stra.give_sid (eid);
    allocv (ncp,eps);   allocv (2,coord);
    for (i=0;i<naep;i++){
      Mm->stra.give_aepcoord (sid,i,coord);
      l[0]=coord[0];l[1]=coord[1];l[2]=1-coord[1]-coord[2];
      if (Mp->strainaver==0)
	appval (l,0,ncp,eps,stra);
      if (Mp->strainaver==1)
        appstrain (lcid,eid,l,0,ncp,eps);
      Mm->stra.storevalues(lcid,eid,i,eps);
    }
    destrv (eps);    destrv (coord);
    break;
  }
  default:{
    fprintf (stderr,"\n\n unknown strain point is required in function dstelem::strains (%s, line %d).\n",__FILE__,__LINE__);
  }
  }
  if (Mp->strainaver==0){
    for (i=0;i<nne;i++){
      delete [] stra[i];
    }
    delete [] stra;
  }
  
}


/**
   function computes stresses DST
*/
void dstelem::res_allip_stresses (long lcid,long eid)
{
  //  blocks of stress components at integration points
  mainip_stresses (lcid,eid,0,0);
}

void dstelem::mainip_stresses (long lcid,long eid,long ri,long ci)
{
  long ii,i,ipp,ij;
  double thick;
  ivector nodes(nne);
  vector eps,sig,auxsig,w,gp1,gp2,l(3),t(nne);
  matrix d(5,5),dd;
    
  fprintf (Out,"\n\n stress");
  fprintf (Out,"\n\n prvek cislo %ld",eid);
  
  Mt->give_elemnodes (eid,nodes);
  Mc->give_thickness (eid,nodes,t);
  
  for (ii=0;ii<nb;ii++){
    allocv (ncomp[ii],eps);allocv (ncomp[ii],sig);allocv (ncomp[ii],auxsig);
    allocv (intordsm[ii][ii],w);allocv (intordsm[ii][ii],gp1);allocv (intordsm[ii][ii],gp2);
    gauss_points_tr (gp1.a,gp2.a,w.a,intordsm[ii][ii]);
    allocm (ncomp[ii],ncomp[ii],dd);
    
    ipp=Mt->elements[eid].ipp[ii+ri][ii+ci];
    
    for (i=0;i<intordsm[ii][ii];i++){      
      Mm->matstiff (d,ipp);
      fillv (0.0,sig);
      l[0]=gp1[i]; l[1]=gp2[i];l[2]=1.0-l[0]-l[1];
      fillv (0.0,sig);
//	  if (Mp->strainaver==0)