q4plate.cpp

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

  atd_matrix (atd,x,y,eid);


  fillm (0.0,lm);

  for (i=0;i<intordmm;i++){
    xi=gp[i];  w1=w[i];
    for (j=0;j<intordmm;j++){
      eta=gp[j];  w2=w[j];
      
      bf_matrix (n,atd,x,y,gp);
      
      thick = approx (xi,eta,t);
      
      jac=(a+a0*l[0]+a1*l[1])/8.*w[i]*w[j];

      jac*=thick;
      
      nnj (lm.a,n.a,jac,n.m,n.n);
    }
  }
  
}

void q4plate::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 strains Q4
   
   @param lcid - load case id
   @param eid - element id
*/
void q4plate::res_ip_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
  //  (in the case of nodal coordinate systems)
  long transf = Mt->locsystems (nodes);
  if (transf>0){
    allocv (ndofe,aux);
    allocm (ndofe,ndofe,tmat);
    transfmat (nodes,tmat);
    //locglobtransf (aux,r,tmat);
    lgvectortransf (aux,r,tmat);
    copyv (aux,r);
    destrv (aux);
    destrm (tmat);
  }

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

/**
   function computes strains at integration points of element
   
   @param lcid - load case id
   @param eid - element id
   @param ri - row index
   @param ci - column index
   @param x,y - %vectors of nodal coordinates
   @param r - %vector of nodal displacements
   
*/
void q4plate::ip_strains (long lcid,long eid,long ri,long ci,vector &x,vector &y,vector &r)
{
  long i,j,ii,ipp;
  double a;
  vector gp,w,eps,aux,natcoord(2),l(3);
  matrix gm,tmat,atd(16,12);
  
  // translation to center it is necesary for w which in local coord. and no in relation
  a=(x[0]+x[1]+x[2]+x[3])/4.;
  x[0]=x[0]-a;
  x[1]=x[1]-a;
  x[2]=x[2]-a;
  x[3]=x[3]-a;
  a=(y[0]+y[1]+y[2]+y[3])/4.;
  y[0]=y[0]-a;
  y[1]=y[1]-a;
  y[2]=y[2]-a;
  y[3]=y[3]-a;
  atd_matrix (atd,x,y,eid);
  
  //  fprintf (Out,"\n\n eps,Mainip prvek cislo %ld\n",eid);
  for (ii=0;ii<nb;ii++){
    if (intordsm[ii][ii]==0)  continue;
    allocv (intordsm[ii][ii],w); allocv (intordsm[ii][ii],gp);
    allocm (ncomp[ii],ndofe,gm); allocv (ncomp[ii],eps);
    ipp=Mt->elements[eid].ipp[ri+ii][ci+ii];     
    gauss_points (gp.a,w.a,intordsm[ii][ii]);
    
    for (i=0;i<intordsm[ii][ii];i++){
      l[0]=gp[i];
      for (j=0;j<intordsm[ii][ii];j++){
	l[1]=gp[j];
	if(ii==0) geom_matrix_bending (gm,atd,x,y,l);
	else if(ii==1) geom_matrix_shear (gm,atd,x,y,l);
	mxv (gm,r,eps);
	Mm->storestrain (lcid,ipp,cncomp[ii],eps);
	ipp++;
	
	//          fprintf (Out,"\n");
	//		  for (ij=0;ij<ncomp[ii];ij++){
	//		    fprintf (Out,"%20.10e",eps[ij]);
	//			}
      }
    }
    destrm (gm);  destrv (eps);  destrv (gp);
  }
  
}


/**
   function assembles strains at nodes of element
   strains are obtained from the nearest integration points

   @param lcid - load case id
   @param eid - element id
   @param ri,ci - row and column indices (default value is 0, nonzero values are used in shell elements)

   10.5.2002
*/
void q4plate::nod_strains_ip (long lcid,long eid,long ri,long ci)
{
  long i,j,ipp;
  ivector ipnum(nne),nod(nne);
  vector eps(tncomp);
  
  //  numbers of integration points closest to nodes
  //  (function is from the file GEFEL/ordering.cpp)
  ipp=Mt->elements[eid].ipp[ri][ci];
  nodip_planelq (ipp,intordsm[0][0],ipnum);
  
  //  node numbers of the element
  Mt->give_elemnodes (eid,nod);
  
  for (i=0;i<nne;i++){
    //  strains at the closest integration point
    Mm->givestrain (lcid,ipnum[i],eps);
    
    //  storage of strains to the node
    j=nod[i];
    Mt->nodes[j].storestrain (lcid,0,eps);
  }
  
}


void q4plate::strains (long lcid,long eid,long ri,long ci)
{
  long i,naep,ncp,sid;
  double **stra;
  vector coord,eps;
  
  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 dstelem::strains (%s, line %d).\n",__FILE__,__LINE__);
  }
  }
  if (Mp->strainaver==0){
    for (i=0;i<nne;i++){
      delete [] stra[i];
    }
    delete [] stra;
  }

}



void q4plate::res_ip_stresses (long lcid,long eid)
{
  ip_stresses (lcid,eid,0,0);
}

void q4plate::ip_stresses (long lcid,long eid,long ri,long ci)
{
  long i,j,ii,ipp;
  double xi,eta,thick;
  vector gp,w,eps,sig,natcoord(2),t(nne);
  ivector nodes(nne);
  matrix d(tncomp,tncomp),dd;
  
  Mt->give_elemnodes (eid,nodes);
  Mc->give_thickness (eid,nodes,t);
  
  //  fprintf (Out,"\n\n sigma Mainip prvek cislo %ld",eid);
  
  for (ii=0;ii<nb;ii++){   
    allocv (ncomp[ii],eps);  allocv (ncomp[ii],sig);
    allocv (intordsm[ii][ii],gp);    allocv (intordsm[ii][ii],w);
    allocm (ncomp[ii],ncomp[ii],dd);
    gauss_points (gp.a,w.a,intordsm[ii][ii]);
    
    ipp=Mt->elements[eid].ipp[ri+ii][ci+ii];
    
    for (i=0;i<intordsm[ii][ii];i++){
      xi=gp[i];
      for (j=0;j<intordsm[ii][ii];j++){
	eta=gp[j];
	Mm->matstiff (d,ipp);
	//			if (Mp->strainaver==0)
	Mm->givestrain (lcid,ipp,cncomp[ii],eps);
	//			if (Mp->strainaver==1)
	//				appstrain (lcid,eid,xi,eta,cncomp[ii],ncomp[ii],eps);
	thick=approx (xi,eta,t);
	dmatblock (dd, d,ii,ii,thick);
	mxv (dd,eps,sig);
	Mm->storestress (lcid,ipp,cncomp[ii],sig);      
	ipp++;    
	
      }
    }
    
    destrv (eps);  destrv (sig);  destrv (w);  destrv (gp);
    destrm (dd);
  }
  
}

void q4plate::nod_stresses_ip (long lcid,long eid,long ri,long ci)
{
  long i,j,ipp;
  ivector ipnum(nne),nod(nne);
  vector sig(tncomp);
  
  //  numbers of integration points closest to nodes
  //  (function is from the file GEFEL/ordering.cpp)
  ipp=Mt->elements[eid].ipp[ri][ci];
  nodip_planelq (ipp,intordsm[0][0],ipnum);
  
  //  node numbers of the element
  Mt->give_elemnodes (eid,nod);
  
  for (i=0;i<nne;i++){
    //  stresses at the closest integration point
    Mm->givestress (lcid,ipnum[i],sig);
    
    //  storage of stresses to the node
    j=nod[i];
    Mt->nodes[j].storestress (lcid,0,sig);
  }
}

void q4plate::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 planeelemrotlq::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;
  }

}


void q4plate::res_internal_forces (long lcid,long eid,vector &ifor)
{
//  long transf;
  ivector nodes(nne);
  vector x(nne),y(nne);
  Mt->give_node_coord2d (x,y,eid);
  Mt->give_elemnodes (eid,nodes);
  
  internal_forces (lcid,eid,0,0,ifor,x,y);
//  glvectortransf3dblock (ifor,tran); From LCS To GCS in shell
/*
//  transformation of Forces
  transf = Mt->locsystems (nodes);
  if (transf>0){
    matrix tmat (ndofe,ndofe);
    transfmat (nodes,tmat);
    locglobtransf (ifor,rl,tmat);
  }
*/
}

void q4plate::internal_forces (long lcid,long eid,long ri,long ci,vector &ifor,vector &x,vector &y)
{
  long i,j,k,ii,jj,ipp;
  double jac,a,a0,a1,thick;
  ivector nodes(nne);
  vector w,gp,l(2),t(nne),sig,f(ndofe);
  matrix gm,atd(16,12);
  
  // translation to center it is necesary for w which in local coord. and no in relation
  a=(x[0]+x[1]+x[2]+x[3])/4.;
  x[0]=x[0]-a;
  x[1]=x[1]-a;
  x[2]=x[2]-a;
  x[3]=x[3]-a;
  a=(y[0]+y[1]+y[2]+y[3])/4.;
  y[0]=y[0]-a;
  y[1]=y[1]-a;
  y[2]=y[2]-a;
  y[3]=y[3]-a;
  //     jakobian
  a = (x[2]-x[0])*(y[3]-y[1])-(y[2]-y[0])*(x[3]-x[1]);
  a0=-(x[3]-x[2])*(y[1]-y[0])+(y[3]-y[2])*(x[1]-x[0]);
  a1=-(x[2]-x[1])*(y[3]-y[0])+(y[2]-y[1])*(x[3]-x[0]);
  
  atd_matrix (atd,x,y,eid);
  
  Mt->give_elemnodes (eid,nodes);
  Mc->give_thickness (eid,nodes,t);
  
  fillv (0.0,ifor);
  
  //  fprintf (Out,"\n\n eps,Sig prvek cislo %ld\n",eid);
  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],gp);
      allocm (ncomp[jj],ndofe,gm); allocv (ncomp[jj],sig);
      
      gauss_points (gp.a,w.a,intordsm[ii][jj]);
      ipp=Mt->elements[eid].ipp[ri+ii][ci+jj];
      
      for (i=0;i<intordsm[ii][jj];i++){
	l[0]=gp[i];
	for (j=0;j<intordsm[ii][jj];j++){
	  l[1]=gp[j];
	  
	  thick=approx (l[0],l[1],t);
	  if(ii==0) {
	    geom_matrix_bending (gm,atd,x,y,l);
	    jac=(a+a0*l[0]+a1*l[1])/8.*w[i]*w[j]*thick*thick*thick;
	  }
	  else if(ii==1) {
	    geom_matrix_shear (gm,atd,x,y,l);
	    jac=(a+a0*l[0]+a1*l[1])/8.*w[i]*w[j]*thick*5.0/6.0;
	  }
	  
	  Mm->computenlstresses (ipp);
	  Mm->givestress (lcid,ipp,cncomp[ii],sig);
	  
	  mtxv (gm,sig,f);
	  for (k=0;k<f.n;k++){
	    ifor[k]+=f[k]*jac;
	    ifor[k]=0.0;                     //nekonsoliduje 
	  }	
	  ipp++;
	}
      }
      destrm (gm);  destrv (w);  destrv (gp);
    }
    destrv (sig);  
  }
  
  //  fprintf (Out,"\n\n Fint prvek cislo %ld\n",eid);
  // for (k=0;k<ndofe;k++){fprintf (Out," %15.5e",ifor[k]);}
  
}




/**
  function computes load vector from area forces fz of the Q4plate
  20.3.2002
*/
void q4plate::areaforces (long eid,double *nv,vector &lm)
{
  long i,j;
  double jac,a,a0,a1,w1,w2;
  ivector nodes(nne);
  vector x(nne),y(nne),l(2),gp(intordmm),w(intordmm);
  matrix atd(16,12),n(1,ndofe),mm(ndofe,ndofe);

  Mt->give_elemnodes (eid,nodes);
  Mt->give_node_coord2d (x,y,eid);
// translation to center it is necesary for w which in local coord. and no in relation
  a=(x[0]+x[1]+x[2]+x[3])/4.;
  x[0]=x[0]-a;
  x[1]=x[1]-a;
  x[2]=x[2]-a;
  x[3]=x[3]-a;
  a=(y[0]+y[1]+y[2]+y[3])/4.;
  y[0]=y[0]-a;
  y[1]=y[1]-a;
  y[2]=y[2]-a;
  y[3]=y[3]-a;
  
  //     jakobian
  a = (x[2]-x[0])*(y[3]-y[1])-(y[2]-y[0])*(x[3]-x[1]);
  a0=-(x[3]-x[2])*(y[1]-y[0])+(y[3]-y[2])*(x[1]-x[0]);
  a1=-(x[2]-x[1])*(y[3]-y[0])+(y[2]-y[1])*(x[3]-x[0]);
  
  gauss_points (gp.a,w.a,intordmm);
  atd_matrix (atd,x,y,eid);
  
  fillv (0.0,lm);
  
  for (i=0;i<intordmm;i++){
    for (j=0;j<intordmm;j++){
      l[0]=gp[i];  l[1]=gp[j];  w1=w[i];  w2=w[j];
      jac=(a+a0*l[0]+a1*l[1])*w1*w2;
      
      bf_matrix (n,atd,x,y,l);
      
      nnj (mm.a,n.a,jac,n.m,n.n);
      
    }
  }
}




void q4plate::inicipval(long eid, long ri, long ci, matrix &nodval, inictype *ictn)
{
  long i, j, k, l, ipp;
  long ii, jj, nv = nodval.n;
  long nstra;
  double xi, eta, ipval;
  vector w, gp, 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],gp);
        allocv (intordsm[ii][jj],w);
        gauss_points (gp.a,w.a,intordsm[ii][jj]);
        for (k = 0; k < intordsm[ii][jj]; k++)
        {
          xi=gp[k];
          for (l = 0; l < intordsm[ii][jj]; l++)
          {
            eta=gp[l];
            //  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 (gp);  destrv (w);
      }
    }
    if (ictn[i] & inistrain) nstra++;
  }
}