axisymqq_nb3.cpp

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

  nodecoord (nxi,neta);
  
  for (ii=0;ii<nb;ii++){
    allocv (intordsm[ii][ii],gp);
    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 (gp.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++){
      xi=gp[i];
      for (j=0;j<intordsm[ii][ii];j++){
	eta=gp[j];
	
	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 (xi,eta,cncomp[jj],ncomp[jj],eps,stra);
	  if (Mp->strainaver==1)
	    appstrain (lcid,eid,xi,eta,cncomp[jj],ncomp[jj],eps);

	  /*
	  if (Mt->elements[eid].presctemp==1){
	    allocv (tncomp,epstt);
	    tempstrains (lcid,eid,ipp,xi,eta,epstt);
	    allocv (ncomp[jj],epst);
	    extract (epst,epstt,cncomp[jj],ncomp[jj]);
	    subv (eps,epst,eps);
	    destrv (epst);  destrv (epstt);
	  }
	  */

	  //dmatblock (ii,jj,d,dd);
	  //mxv (dd,eps,auxsig);

	  fprintf (Out,"\n element %6ld   int. point %6ld %6ld  %e %e %e %e",eid+1,ii,jj,eps[0],eps[1],eps[2],eps[3]);
	  printf ("\n element %6ld   int. point %6ld %6ld  %e %e %e %e",eid+1,i,j,eps[0],eps[1],eps[2],eps[3]);

	  mxv (d,eps,auxsig);
	  addv (auxsig,sig,sig);
	  destrm (dd);  destrv (eps);
	}

	natcoord[0]=xi;  natcoord[1]=eta;
	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 (gp);
  }
  
  delete [] lsm;
}


/**
   function computes stresses in arbitrary point on element
   
   @param lcid - load case id
   @param eid - element id
   @param xi, eta - natural coordinates of the point
   @param fi,li - first and last indices
   @param sig - array containing stresses
   
   11.5.2002
*/
void axisymqq::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 axisymqq::res_allip_stresses (long lcid,long eid)
{
  allip_stresses (lcid,eid,0,0);
}

/**
   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 axisymqq::allip_stresses (long lcid,long eid,long ri,long ci)
{
  res_mainip_stresses (lcid,eid);
}

void axisymqq::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);
    //mainip_stresses (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 load matrix of the axisymmetric quadrilateral
   finite element with bilinear approximation functions
   load vector is obtained after premultiplying load matrix
   by nodal load values
   
   @param eid - number of element
   @param lm - load matrix

   8.12.2001
*/
void axisymqq::load_matrix (long eid,matrix &lm)
{
  long i,j;
  double jac,xi,eta,r;
  ivector nodes(nne);
  vector x(nne),y(nne),w(intordmm),gp(intordmm);
  matrix n(napfun,ndofe);
  
  Mt->give_elemnodes (eid,nodes);
  Mt->give_node_coord2d (x,y,eid);
  gauss_points (gp.a,w.a,intordmm);
  
  fillm (0.0,lm);

  for (i=0;i<intordmm;i++){
    xi=gp[i];
    for (j=0;j<intordmm;j++){
      eta=gp[j];
      jac_2d (jac,x,y,xi,eta);
      bf_matrix (n,xi,eta);
      
      r = approx (xi,eta,x);
      jac*=r*w[i]*w[j];
      
      nnj (lm.a,n.a,jac,n.m,n.n);
    }
  }
  
}





void axisymqq::res_temp_forces (long lcid,long eid,vector &nfor)
{
  vector x(nne),y(nne);
  Mt->give_node_coord2d (x,y,eid);
  temp_forces (lcid,eid,0,0,nfor,x,y);
}

/**
   function computes nodal forces caused by temperature changes
   
   @param eid - element id
   @param ri,ci - row and column indices
   @param nfor - array containing nodal forces
   @param x,y - nodal coordinates
   
   22.11.2002, JK
*/
void axisymqq::temp_forces (long lcid,long eid,long ri,long ci,vector &nfor,vector &x,vector &y)
{
  long i,j,k,ii,ipp;
  double xi,eta,jac;
  vector eps,sig,contr(ndofe),epst(tncomp),gp,w;
  matrix d(tncomp,tncomp),dd,gm;
  
  fillv (0.0,nfor);

  for (ii=0;ii<nb;ii++){
    
    allocv (intordsm[ii][ii],w);
    allocv (intordsm[ii][ii],gp);
    
    allocm (ncomp[ii],ndofe,gm);
    allocm (ncomp[ii],ncomp[ii],dd);
    allocv (ncomp[ii],eps);
    allocv (ncomp[ii],sig);
    
    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];
	
	tempstrains (lcid,eid,ipp,xi,eta,epst);
	extract (eps,epst,cncomp[ii],ncomp[ii]);
	
	Mm->matstiff (d,ipp);
	ipp++;
	dmatblock (ii,ii,d,dd);
	mxv (dd,eps,sig);
	geom_matrix_block (gm,ii,x,y,xi,eta,jac);
	mtxv (gm,sig,contr);
	cmulv (jac*w[i]*w[j],contr);
	
	for (k=0;k<contr.n;k++){
	  nfor[k]+=contr[k];
	}
	
      }
    }
    destrv (sig);  destrv (eps);  destrv (gp);  destrv (w);
    destrm (dd);  destrm (gm);
  }
}

/**
   function computes strains caused by temperature changes
   
   @param lcid - load case id
   @param eid - element id
   @param ipp - integration point pointer
   @param xi,eta - natural coordinates
   @param eps - array containing strains
   
   22.12.2002, JK
*/
void axisymqq::tempstrains (long lcid,long eid,long ipp,double xi,double eta,vector &eps)
{
  double temp;
  ivector nodes(nne);
  vector dt(nne),tvect(tncomp);
  matrix d(tncomp,tncomp);

  Mt->give_elemnodes (eid,nodes);
  Mb->lc[lcid].tempchanges (dt.a,nodes);

  temp = approx (xi,eta,dt);
  fillv (temp,tvect);
  
  Mm->matdilat (d,ipp);
  mxv (d,tvect,eps);
  
  Mm->storeeigstrain (ipp,eps);
}







/**
   function computes internal forces

   @param lcid - number of load case
   @param eid - element id
   @param ri,ci - row and column indices
   @param ifor - vector of internal forces
   
   8.12.2001
*/
void axisymqq::internal_forces (long lcid,long eid,vector &ifor)
{
  long i,j,k,ii,ipp;
  double xi,eta,jac,rad;
  ivector nodes(nne),cn(ndofe);
  vector x(nne),y(nne),w,gp;
  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 (0,r.a,cn.a,ndofe);
  
  fillv (0.0,ifor);
  
  for (ii=0;ii<nb;ii++){
    if (intordsm[ii][ii]==0)  continue;
    
    allocv (intordsm[ii][ii],gp);
    allocv (intordsm[ii][ii],w);
    allocm (ncomp[ii],ndofe,gm);
    allocv (ncomp[ii],sig);
    
    gauss_points (gp.a,w.a,intordsm[ii][ii]);
    ipp=Mt->elements[eid].ipp[ii][ii];
    
    for (i=0;i<intordsm[ii][ii];i++){
      xi=gp[i];
      for (j=0;j<intordsm[ii][ii];j++){
	eta=gp[j];
	
	
	Mm->computenlstresses (ipp);
	
	Mm->givestress (lcid,ipp,cncomp[ii],ncomp[ii],sig);

	geom_matrix_block (gm,ii,x,y,xi,eta,jac);
	mtxv (gm,sig,contr);
	
	rad = approx (xi,eta,x);
	cmulv (rad*jac*w[i]*w[j],contr);
	
	for (k=0;k<contr.n;k++){
	  ifor[k]+=contr[k];
	}
	
	ipp++;
	
      }
    }
    destrv (sig);  destrm (gm);  destrv (w);  destrv (gp);
  }
}

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


void axisymqq::nodeforces (long eid,long *le,double *nv,vector &nf)
{
  long i;
  double ww,jac,xi,eta;
  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);
    eta = 1.0;
    for (i=0;i<intordb;i++){
      xi = gp[i];
      ww = w[i];
      
      bf_matrix (n,xi,eta);
      
      jac1d_2d (jac,x,y,xi,0);
      jac *= ww;

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

      bf_matrix (n,xi,eta);
      
      jac1d_2d (jac,x,y,eta,1);
      jac *= ww;
      
      nnj (am.a,n.a,jac,n.m,n.n);
    }
    fillv (0.0,av);
    av[2]=nv[4];  av[3]=nv[5];  av[4]=nv[6];  av[5]=nv[7];
    mxv (am,av,v);  addv (nf,v,nf);
  }
  if (le[2]==1){
    fillm (0.0,am);
    eta = -1.0;
    for (i=0;i<intordb;i++){
      xi = gp[i];
      ww = w[i];
      
      bf_matrix (n,xi,eta);
      
      jac1d_2d (jac,x,y,xi,2);
      jac *= ww;
      
      nnj (am.a,n.a,jac,n.m,n.n);
    }
    fillv (0.0,av);
    av[4]=nv[8];  av[5]=nv[9];  av[6]=nv[10];  av[7]=nv[11];
    mxv (am,av,v);  addv (nf,v,nf);
  }
  if (le[3]==1){
    fillm (0.0,am);
    xi = 1.0;
    for (i=0;i<intordb;i++){
      eta = gp[i];
      ww = w[i];
      
      bf_matrix (n,xi,eta);
      
      jac1d_2d (jac,x,y,eta,3);
      jac *= ww;

      nnj (am.a,n.a,jac,n.m,n.n);
    }
    fillv (0.0,av);
    av[6]=nv[12];  av[7]=nv[13];  av[0]=nv[14];  av[1]=nv[15];
    mxv (am,av,v);  addv (nf,v,nf);
  }
}


void axisymqq::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++)
      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++;
  }
}