plelemsubqt.cpp

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

  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);
      
      if (Mp->strainaver==0)
	appval (coord[0],coord[1],0,ncp,eps,stra);
      if (Mp->strainaver==1)
	appstrain (lcid,eid,coord[0],coord[1],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 planeelemlt::strains (%s, line %d).\n",__FILE__,__LINE__);
  }
  }

  if (Mp->strainaver==0){
    for (i=0;i<nne;i++){
      delete [] stra[i];
    }
    delete [] stra;
  }
}

/**
   function assembles natural coordinates of nodes of element
   
   @param xi - array containing natural coordinates xi
   @param eta - array containing natrual coordinates eta
   
   10.5.2002
*/
void planeelemsubqt::nodecoord (vector &xi,vector &eta)
{
  xi[0] = 1.0;  eta[0] = 0.0;
  xi[1] = 0.0;  eta[1] = 1.0;
  xi[2] = 0.0;  eta[2] = 0.0;
  xi[3] = 0.5;  eta[3] = 0.5;
  xi[4] = 0.0;  eta[4] = 0.5;
  xi[5] = 0.5;  eta[5] = 0.0;
}


/**
   function computes strains in arbitrary point on element
   
   @param xi, eta - natural coordinates of the point
   @param eps - array containing strains
   @param val - array containing values on element
   
   11.5.2002
*/
void planeelemsubqt::appval (double xi,double eta,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]=approx (xi,eta,nodval);
    k++;
  }
  
  destrv (nodval);
}

/**
   function computes stresses in main integration points of element
   
   @param lcid - load case id
   @param eid - element id
   @param ri - row index
   @param ci - column index
   
   10.5.2002
*/
void planeelemsubqt::mainip_stresses (long lcid,long eid,long ri,long ci)
{
  long i,ii,jj,ipp;
  vector gp1,gp2,w,eps,sig,auxsig;
  matrix d(tncomp,tncomp),dd;

  for (ii=0;ii<nb;ii++){
    allocv (ncomp[ii],sig);
    allocv (ncomp[ii],auxsig);
    allocv (intordsm[ii][ii],gp1);
    allocv (intordsm[ii][ii],gp2);
    allocv (intordsm[ii][ii],w);
    
    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++){
      Mm->matstiff (d,ipp);
      
      fillv (0.0,sig);
      for (jj=0;jj<nb;jj++){
	allocv (ncomp[jj],eps);
	allocm (ncomp[ii],ncomp[jj],dd);
	
	if (Mp->strainaver==0)
	  Mm->givestrain (lcid,ipp,cncomp[jj],ncomp[jj],eps);
	if (Mp->strainaver==1)
	  appstrain (lcid,eid,gp1[i],gp2[i],cncomp[jj],ncomp[jj],eps);
	
	dmatblock (ii,jj,d,dd);
	mxv (dd,eps,auxsig);
	addv (auxsig,sig,sig);
	destrm (dd);  destrv (eps);
      }
      
      Mm->storestress (lcid,ipp,sig);
      
      ipp++;
    }
    destrv (w);  destrv (gp2);  destrv (gp1);  destrv (auxsig);  destrv (sig);
  }
}

/**
   function computes stresses in nodes
   
   @param lcid - load case id
   @param eid - element id
   @param ri,ci - row and column indices
   
   10.5.2002
*/
void planeelemsubqt::nod_stresses (long lcid,long eid,long ri,long ci)
{
  long i,ii,jj,ipp;
  double *lsm,*lhs,*rhs;
  vector nxi(nne),neta(nne),gp1,gp2,w,eps,sig,auxsig,natcoord(2);
  ivector nodes(nne);
  matrix d(tncomp,tncomp),dd;
  
  lsm = new double [9];

  Mt->give_elemnodes (eid,nodes);
  
  nodecoord (nxi,neta);

  for (ii=0;ii<nb;ii++){
    allocv (intordsm[ii][ii],gp1);
    allocv (intordsm[ii][ii],gp2);
    allocv (intordsm[ii][ii],w);
    allocv (ncomp[ii],sig);
    allocv (ncomp[ii],auxsig);
    lhs = new double [ncomp[ii]*3];
    rhs = new double [ncomp[ii]*3];
    gauss_points_tr (gp1.a,gp2.a,w.a,intordsm[ii][ii]);
    
    nullv (lsm,9);
    nullv (rhs,ncomp[ii]*3);
    
    ipp=Mt->elements[eid].ipp[ri+ii][ci+ii];
    
    for (i=0;i<intordsm[ii][ii];i++){
      
      Mm->matstiff (d,ipp);
      ipp++;
      
      fillv (0.0,sig);
      for (jj=0;jj<nb;jj++){
	allocv (ncomp[jj],eps);
	allocm (ncomp[ii],ncomp[jj],dd);
	
	if (Mp->strainaver==0)
	  Mm->givestrain (lcid,ipp,cncomp[jj],ncomp[jj],eps);
	if (Mp->strainaver==1)
	  appstrain (lcid,eid,gp1[i],gp2[i],cncomp[jj],ncomp[jj],eps);
	
	dmatblock (ii,jj,d,dd);
	mxv (dd,eps,auxsig);
	addv (auxsig,sig,sig);
	destrm (dd);  destrv (eps);
      }
      
      natcoord[0]=gp1[i];  natcoord[1]=gp2[i];
      matassem_lsm (lsm,natcoord);
      rhsassem_lsm (rhs,natcoord,sig);
      
    }
    
    solve_lsm (lsm,lhs,rhs,Mp->zero,3,ncomp[ii]);
    Mt->stress_nodal_values (nodes,nxi,neta,nxi,lhs,2,cncomp[ii],ncomp[ii],lcid);
    
    
    delete [] lhs;  delete [] rhs;
    destrv (auxsig);  destrv (sig);  destrv (eps);  destrv (w);  destrv (gp2);  destrv (gp1);
  }
  
  delete [] lsm;
}


void planeelemsubqt::elem_stresses (double **stra,double **stre,long lcid,long eid,long ri,long ci)
{
  long i,ii,jj,ipp;
  double *lsm,*lhs,*rhs;
  vector nxi(nne),neta(nne),gp1,gp2,w,eps,sig,auxsig,natcoord(2);
  ivector nodes(nne);
  matrix d(tncomp,tncomp),dd;
  
  lsm = new double [9];

  Mt->give_elemnodes (eid,nodes);
  
  nodecoord (nxi,neta);

  for (ii=0;ii<nb;ii++){
    allocv (intordsm[ii][ii],gp1);
    allocv (intordsm[ii][ii],gp2);
    allocv (intordsm[ii][ii],w);
    allocv (ncomp[ii],sig);
    allocv (ncomp[ii],auxsig);
    lhs = new double [ncomp[ii]*3];
    rhs = new double [ncomp[ii]*3];
    gauss_points_tr (gp1.a,gp2.a,w.a,intordsm[ii][ii]);
    
    nullv (lsm,9);
    nullv (rhs,ncomp[ii]*3);
    
    ipp=Mt->elements[eid].ipp[ri+ii][ci+ii];
    
    for (i=0;i<intordsm[ii][ii];i++){
      
      Mm->matstiff (d,ipp);
      ipp++;
      
      fillv (0.0,sig);
      for (jj=0;jj<nb;jj++){
	allocv (ncomp[jj],eps);
	allocm (ncomp[ii],ncomp[jj],dd);

	if (Mp->strainaver==0)
	  appval (gp1[i],gp2[i],cncomp[jj],ncomp[jj],eps,stra);
	if (Mp->strainaver==1)
	  appstrain (lcid,eid,gp1[i],gp2[i],cncomp[jj],ncomp[jj],eps);
	
	dmatblock (ii,jj,d,dd);
	mxv (dd,eps,auxsig);
	addv (auxsig,sig,sig);
	destrm (dd);  destrv (eps);
      }
      
      natcoord[0]=gp1[i];  natcoord[1]=gp2[i];
      matassem_lsm (lsm,natcoord);
      rhsassem_lsm (rhs,natcoord,sig);
      
    }
    
    solve_lsm (lsm,lhs,rhs,Mp->zero,3,ncomp[ii]);
    nodal_values (stre,nxi,neta,nxi,lhs,2,cncomp[ii],ncomp[ii]);
    
    delete [] lhs;  delete [] rhs;
    destrv (auxsig);  destrv (sig);  destrv (eps);  destrv (w);  destrv (gp2);  destrv (gp1);
  }
  
  delete [] lsm;
}


/**
   function computes stresses in arbitrary point on element
   
   @param lcid - load case id
   @param eid - element id
   @param xi,eta - natural coordinates
   @param fi,li - first and last indices
   @param sig - array containing stresses
   
   11.5.2002
*/
void planeelemsubqt::appstress (long lcid,long eid,double xi,double eta,long fi,long ncomp,vector &sig)
{
  long i,j,k;
  ivector nodes;
  vector nodval;
  
  if (ncomp != sig.n){
    fprintf (stderr,"\n\n wrong interval of indices in function stress (%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]].stress[lcid*tncomp+i];
    }
    sig[k]=approx (xi,eta,nodval);
    k++;
  }
  
  destrv (nodes);  destrv (nodval);
}

/**
   function computes stresses in all integration points
   
   @param lcid - load case id
   @param eid - element id
   @param ri,ci - row and column indices
   
   10.5.2002
*/
void planeelemsubqt::allip_stresses (double **stre,long lcid,long eid,long ri,long ci)
{
  long i,ii,jj,ipp;
  vector sig,gp1,gp2,w;
  
  allocv (tncomp,sig);

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

      allocv (intordsm[ii][jj],gp1);
      allocv (intordsm[ii][jj],gp2);
      allocv (intordsm[ii][jj],w);
      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++){
	appstress (lcid,eid,gp1[i],gp2[i],0,tncomp,sig);
	Mm->storestress (lcid,ipp,sig);
	ipp++;
      }
      destrv (w);  destrv (gp2);  destrv (gp1);
    }
  }
  destrv (sig);
}

void planeelemsubqt::stresses (long lcid,long eid,long ri,long ci)
{
  long i,naep,ncp,sid;
  double **stra,**stre;
  vector coord,sig;
  
  if (Mp->stressaver==0){
    stra = new double* [nne];
    stre = new double* [nne];
    for (i=0;i<nne;i++){
      stra[i] = new double [tncomp];
      stre[i] = new double [tncomp];
    }
    elem_strains (stra,lcid,eid,ri,ci);
    elem_stresses (stra,stre,lcid,eid,ri,ci);
  }

  switch (Mm->stre.tape[eid]){
  case nowhere:{
    break;
  }
  case intpts:{
    allip_stresses (stre,lcid,eid,ri,ci);
    break;
  }
  case enodes:{
    break;
  }
  case userdefined:{
    //  number of auxiliary element points
    naep = Mm->stre.give_naep (eid);
    ncp = Mm->stre.give_ncomp (eid);
    sid = Mm->stre.give_sid (eid);
    allocv (ncp,sig);
    allocv (2,coord);
    for (i=0;i<naep;i++){
      Mm->stre.give_aepcoord (sid,i,coord);
      
      if (Mp->stressaver==0)
	appval (coord[0],coord[1],0,ncp,sig,stre);
      if (Mp->stressaver==1)
	appstress (lcid,eid,coord[0],coord[1],0,ncp,sig);
      
      Mm->stre.storevalues(lcid,eid,i,sig);
    }
    destrv (sig);
    destrv (coord);
    break;
  }
  default:{
    fprintf (stderr,"\n\n unknown stress point is required in function planeelemlq::stresses (%s, line %d).\n",__FILE__,__LINE__);
  }
  }

  if (Mp->stressaver==0){
    for (i=0;i<nne;i++){
      delete [] stra[i];
      delete [] stre[i];
    }
    delete [] stra;
    delete [] stre;
  }
}










/**
   function computes internal forces

   @param lcid - load case id
   @param eid - element id
   @param ifor - vector of internal forces

   25.8.2001
*/
void planeelemsubqt::internal_forces (long lcid,long eid,long ri,long ci,vector &ifor)
{
  long i,k,ii,ipp;
  double jac;
  ivector nodes(nne),cn(ndofe);
  vector x(nne),y(nne),w,gp1,gp2;
  vector r(ndofe),eps(tncomp),sig,contr(ndofe),auxcontr(ndofe);
  matrix gm;
  
  Mt->give_elemnodes (eid,nodes);
  Mt->give_node_coord2d (x,y,eid);
  Mt->give_code_numbers (eid,cn.a);
  eldispl (lcid,eid,r.a,cn.a,ndofe);
  
  //  det is equal to double area of the element
  jac = (x[1]-x[0])*(y[2]-y[0])-(x[2]-x[0])*(y[1]-y[0]);

  fillv (0.0,ifor);
  
  for (ii=0;ii<nb;ii++){
    allocv (intordsm[ii][ii],gp1);
    allocv (intordsm[ii][ii],gp2);
    allocv (intordsm[ii][ii],w);
    
    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++){
      appstrain (lcid,eid,gp1[i],gp2[i],0,tncomp,eps);
      Mm->storestrain (lcid,ipp,eps);
      
      Mm->computenlstresses (ipp);
      
      Mm->givestress (lcid,ipp,cncomp[ii],ncomp[ii],sig);
      
      geom_matrix_block (gm,ii,x,y,gp1[i],gp2[i]);
      mtxv (gm,sig,contr);

      cmulv (jac*w[i],contr);
      
      for (k=0;k<contr.n;k++){
	ifor[k]+=contr[k];
      }
      
      ipp++;
      
    }
    destrv (w);  destrv (gp2);  destrv (gp1);
  }
}



void planeelemsubqt::res_internal_forces (long lcid,long eid,vector &ifor)
{
  internal_forces (lcid,eid,0,0,ifor);
}





void planeelemsubqt::ipcoord (long eid,long ipp,vector &coord)
  //  function returns coordinates of integration points
  //  eid - element id
  //  ipp - integration point pointer
  //  coord - vector of coordinates
  //  19.1.2002
{
  /*
  long i,ii;
  vector x(nne),y(nne),areacoord(3),w(intordsm),gp1(intordsm),gp2(intordsm);
  
  gauss_points_tr (gp1.a,gp2.a,w.a,intordsm);
  Mt->give_node_coord2d (x,y,eid);
  ii=Mt->elements[eid].ipp[0];
  
  for (i=0;i<intordsm;i++){
    areacoord[0]=gp1[i];
    areacoord[1]=gp2[i];
    areacoord[2]=1.0-areacoord[0]-areacoord[1];
    
    if (ii==ipp){
      coord[0]=approx (areacoord,x);
      coord[1]=approx (areacoord,y);
      coord[2]=0.0;
    }
    ii++;
  }
  */
}



void planeelemsubqt::nodeforces (long eid,long *le,double *nv,vector &nf)
{
  long i;
  double xi,eta,jac;
  vector x(nne),y(nne),gp(intordb),w(intordb),av(ndofe),v(ndofe);
  matrix n(napfun,ndofe),am(ndofe,ndofe);

  Mt->give_node_coord2d (x,y,eid);
  gauss_points (gp.a,w.a,intordb);

  if (le[0]==1){
    fillm (0.0,am);
    for (i=0;i<intordb;i++){
      xi=(1.0-gp[i])/2.0;  eta=(1.0+gp[i])/2.0;
      bf_matrix (n,xi,eta);

      jac1d_2d (jac,x,y,gp[i],0);
      jac*=w[i];

      nnj (am.a,n.a,jac,n.m,n.n);
    }
    fillv (0.0,av);
    av[0]=nv[0]; av[1]=nv[1]; av[6]=nv[2]; av[7]=nv[3]; av[2]=nv[4]; av[3]=nv[5];
    mxv (am,av,v);  addv (nf,v,nf);
  }
  if (le[1]==1){
    fillm (0.0,am);
    for (i=0;i<intordb;i++){
      xi=0.0;  eta=(1.0-gp[i])/2.0;
      bf_matrix (n,xi,eta);

      jac1d_2d (jac,x,y,gp[i],1);
      jac*=w[i];

      nnj (am.a,n.a,jac,n.m,n.n);
    }
    fillv (0.0,av);
    av[2]=nv[6]; av[3]=nv[7]; av[8]=nv[8]; av[9]=nv[9]; av[4]=nv[10]; av[5]=nv[11];
    mxv (am,av,v);  addv (nf,v,nf);
  }
  if (le[2]==1){
    fillm (0.0,am);
    for (i=0;i<intordb;i++){
      xi=(1.0+gp[i])/2.0;  eta=0.0;
      bf_matrix (n,xi,eta);

      jac1d_2d (jac,x,y,gp[i],2);
      jac*=w[i];

      nnj (am.a,n.a,jac,n.m,n.n);
    }
    fillv (0.0,av);
    av[4]=nv[12]; av[5]=nv[13]; av[10]=nv[14]; av[11]=nv[15]; av[0]=nv[16]; av[1]=nv[17];
    mxv (am,av,v);  addv (nf,v,nf);
  }
}



void planeelemsubqt::inicipval(long eid, long ri, long ci, matrix &nodval, inictype *ictn)
{
  long i, j, k, ipp;
  long ii, jj, nv = nodval.n;
  long nstra;
  double xi, eta, ipval;
  vector w, gp1, gp2, anv(nne);

  nstra = 0;
  for (j = 0; j < nv; j++) // for all initial values
  {
    for(i = 0; i < nne; i++) // for all nodes on element
      anv[i] = nodval[i][j];
    for (ii = 0; ii < nb; ii++)
    {
      for (jj = 0; jj < nb; jj++)
      {
        ipp=Mt->elements[eid].ipp[ri+ii][ci+jj];
        if (intordsm[ii][jj] == 0)
          continue;
        allocv (intordsm[ii][jj],gp1);
        allocv (intordsm[ii][jj],gp2);
        allocv (intordsm[ii][jj],w);
        gauss_points_tr (gp1.a, gp2.a, w.a, intordsm[ii][jj]);
        for (k = 0; k < intordsm[ii][jj]; k++)
        {
          xi=gp1[k];
          eta=gp2[k];
          //  value in integration point
          ipval = approx (xi,eta,anv);
          if ((ictn[i] & inistrain) && (j < Mm->ip[ipp].ncompstr))
          {
            Mm->ip[ipp].strain[j] += ipval;
            ipp++;
            continue;
          }
          if ((ictn[i] & inistress) && (j < nstra + Mm->ip[ipp].ncompstr))
          {
            Mm->ip[ipp].stress[j] += ipval;
            ipp++;
            continue;
          }
          if ((ictn[i] & iniother) && (j < nv))
          {
            Mm->ip[ipp].other[j] += ipval;
            ipp++;
            continue;
          }
          ipp++;
        }
        destrv(gp1);  destrv (gp2);  destrv (w);
      }
    }
    if (ictn[i] & inistrain) nstra++;
  }
}