plelemrotlt.cpp

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

  long i;
  double jac,area,thick;
  ivector nodes(nne);
  vector x(nne),y(nne),w(intordmm),gp1(intordmm),gp2(intordmm),b(3),c(3),areacoord(3),t(nne);
  matrix n(napfun,ndofe);
  
  Mt->give_elemnodes (eid,nodes);
  Mt->give_node_coord2d (x,y,eid);
  Mc->give_thickness (eid,nodes,t);

  gauss_points_tr (gp1.a,gp2.a,w.a,intordmm);

  area = ((x[1]-x[0])*(y[2]-y[0])-(x[2]-x[0])*(y[1]-y[0]))/2.0;
  b_coeff (b.a,y.a);
  c_coeff (c.a,x.a);

  fillm (0.0,lm);
  
  for (i=0;i<intordmm;i++){
    areacoord[0]=gp1[i];
    areacoord[1]=gp2[i];
    areacoord[2]=1.0-gp1[i]-gp2[i];
    
    bf_matrix (n,areacoord,b,c);
    
    thick = approx (areacoord,t);
    
    //  zkontrolovat deleni dvema
    jac=w[i]*thick*area*2.0;
    
    nnj (lm.a,n.a,jac,n.m,n.n);
  }
  
}



void planeelemrotlt::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);
}


/**
   function computes strains in 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 planeelemrotlt::mainip_strains (long lcid,long eid,long ri,long ci,vector &x,vector &y,vector &r)
{
  long i,ii,ipp;
  vector gp1,gp2,w,eps,areacoord(3);
  matrix gm;

  for (ii=0;ii<nb;ii++){
    allocv (intordsm[ii][ii],gp1);
    allocv (intordsm[ii][ii],gp2);
    allocv (intordsm[ii][ii],w);
    allocv (ncomp[ii],eps);
    allocm (ncomp[ii],ndofe,gm);

    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++){
      areacoord[0]=gp1[i];
      areacoord[1]=gp2[i];
      areacoord[2]=1.0-gp1[i]-gp2[i];
      
      geom_matrix_block (gm,ii,x,y,areacoord);
      mxv (gm,r,eps);
      
      Mm->storestrain (lcid,ipp,cncomp[ii],ncomp[ii],eps);
      ipp++;
    }
    
    destrm (gm);  destrv (eps);  destrv (w);  destrv (gp1);  destrv (gp2);
  }
}

/**
   function computes strains in nodes of element
   
   @param lcid - load case id
   @param eid - element id
   
   10.5.2002
*/
void planeelemrotlt::nod_strains (long lcid,long eid,long ri,long ci)
{
  long i,ii,ipp;
  double *lsm,*lhs,*rhs;
  vector nxi(nne),neta(nne),gp1,gp2,w,eps,aux,natcoord(2),areacoord(3);
  ivector nodes(nne);

  lsm = new double [9];

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


  for (ii=0;ii<nb;ii++){
    allocv (intordsm[ii][ii],gp1);
    allocv (intordsm[ii][ii],gp2);
    allocv (intordsm[ii][ii],w);
    allocv (ncomp[ii],eps);
    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++){
      areacoord[0]=gp1[i];
      areacoord[1]=gp2[i];
      areacoord[2]=1.0-gp1[i]-gp2[i];
      
      Mm->givestrain (lcid,ipp,cncomp[ii],ncomp[ii],eps);
      
      natcoord[0]=areacoord[0];  natcoord[1]=areacoord[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;
}

/**
   function computes strains on element
   
   @param val - array containing strains on element
   @param lcid - load case id
   @param eid - element id
   
   15.7.2002
*/
void planeelemrotlt::elem_strains (double **stra,long lcid,long eid,long ri,long ci)
{
  long i,ii,ipp;
  double *lsm,*lhs,*rhs;
  vector nxi(nne),neta(nne),gp1,gp2,w,eps,aux,natcoord(2),areacoord(3);
  ivector nodes(nne);

  lsm = new double [9];
  nodecoord (nxi,neta);
  Mt->give_elemnodes (eid,nodes);

  for (ii=0;ii<nb;ii++){
    allocv (intordsm[ii][ii],gp1);
    allocv (intordsm[ii][ii],gp2);
    allocv (intordsm[ii][ii],w);
    allocv (ncomp[ii],eps);
    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++){
      areacoord[0]=gp1[i];
      areacoord[1]=gp2[i];
      areacoord[2]=1.0-areacoord[0]-areacoord[1];
      
      Mm->givestrain (lcid,ipp,cncomp[ii],ncomp[ii],eps);
      
      natcoord[0]=areacoord[0];  natcoord[1]=areacoord[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;
}

/**
   function computes strains in arbitrary point on element
   
   @param eid - element id
   @param xi, eta - natural coordinates of the point
   @param fi,li - first and last indices
   @param eps - array containing strains
   
   11.5.2002
*/
void planeelemrotlt::appstrain (long lcid,long eid,double xi,double eta,long fi,long ncomp,vector &eps)
{
  long i,j,k;
  ivector nodes(nne);
  vector nodval(nne),areacoord(3);
  
  if (ncomp != eps.n){
    fprintf (stderr,"\n\n wrong interval of indices in function strain (%s, line %d).\n",__FILE__,__LINE__);
    abort ();
  }

  areacoord[0]=xi;
  areacoord[1]=eta;
  areacoord[2]=1.0-areacoord[0]-areacoord[1];

  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]=approx (areacoord,nodval);
    k++;
  }
  
}

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

  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++){
        
        if (Mp->strainaver==0)
          appval (gp1[i],gp2[i],0,tncomp,eps,stra);
        if (Mp->strainaver==1)
          appstrain (lcid,eid,gp1[i],gp2[i],0,tncomp,eps);
        
        Mm->storestrain (lcid,ipp,eps);
        ipp++;
      }
      destrv (w);  destrv (gp2);  destrv (gp1);
    }
  }
  destrv (eps);
}

void planeelemrotlt::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 planeelemrotlt::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 planeelemrotlt::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 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 planeelemrotlt::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_nat (xi,eta,nodval);
    k++;
  }
  
  destrv (nodval);
}

/**
   function computes stresses in integration points of element
   
   @param eid - element id
   @param ri - row index
   @param ci - column index
   
   10.5.2002
*/
void planeelemrotlt::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,cncomp[ii],ncomp[ii],sig);
      
      ipp++;
    }
    destrv (w);  destrv (gp1);  destrv (gp2);  destrv (auxsig);  destrv (sig);
  }
  
}

void planeelemrotlt::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];

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