plelemlq.cpp

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

	  Mm->givestrain (lcid,ipp,cncomp[jj],eps);
	  //  block of stiffness matrix of material
	  dmatblock (ii,jj,d,dd);
	  //  stress contributions
	  mxv (dd,eps,auxsig);
	  //  summation of contributions
	  addv (auxsig,sig,sig);
	  
	  destrm (dd);  destrv (eps);
	}
	
	//  storage of block of stress
	Mm->storestress (lcid,ipp,cncomp[ii],sig);
	
	ipp++;
      }
    }
    
    destrv (w);  destrv (gp);  destrv (auxsig);  destrv (sig);
  }
}

/**
   function computes stresses at nodes of element

   @param lcid - load case id
   @param eid - element id
   @param ri,ci - row and column indices
   
   10.5.2002
*/
void planeelemlq::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);
  }
  
}

/**
   function computes nodal stresses directly
   
   @param lcid - load case id
   @param eid - element id
   @param stra - array for strain components
   
   JK, 25.9.2004
*/
void planeelemlq::nod_stresses_comp (long lcid,long eid,long ri,long ci,double **stra,double **stre)
{
  long i,j,ipp;
  vector eps(tncomp),sig(tncomp);
  matrix d(tncomp,tncomp);
  
  //  number of the first integration point on the element
  ipp=Mt->elements[eid].ipp[ri][ci];
  //  stiffness matrix of the material
  Mm->matstiff (d,ipp);
  
  //  loop over nodes
  for (i=0;i<nne;i++){
    for (j=0;j<eps.n;j++){
      eps[j]=stra[i][j];
    }
    mxv (d,eps,sig);
    for (j=0;j<eps.n;j++){
      stre[i][j]=sig[j];
    }
  }
}









void planeelemlq::stresses (long lcid,long eid,long ri,long ci)
{
  long i,naep,ncp,sid;
  vector coord,sig;
  
  //  computation of blocks of stresses at integration points
  res_ip_stresses (lcid,eid);
  
  
  switch (Mm->stre.tape[eid]){
  case nowhere:{
    break;
  }
  case intpts:{
    //allip_stresses (lcid,eid,ri,ci);
    break;
  }
  case enodes:{
    nod_stresses_ip (lcid,eid,ri,ci);
    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__);
  }
  }

}

/**
   function computes other values in nodes of element

   @param lcid - load case id
   @param eid - element id
   
   10.5.2002
*/
void planeelemlq::nod_eqother_ip (long lcid,long eid,long ri,long ci)
{
  long i,j,ipp,ncompo;
  ivector ipnum(nne),nod(nne);
  vector eqother;
  
  //  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++){
    ncompo = Mm->givencompeqother (ipnum[i],0);
    allocv (ncompo,eqother);
    Mm->giveeqother (ipnum[i],0,ncompo,eqother.a);
    
    //  storage of strains to the node
    j=nod[i];
    Mt->nodes[j].storeother (lcid,0,ncompo,eqother);
    
    destrv (eqother);
  }
}





/**
   function computes load %matrix of the plane stress rectangular
   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
   @param x,y - node coordinates
   
   JK, 25.7.2001
*/
void planeelemlq::load_matrix (long eid,matrix &lm,vector &x,vector &y)
{
  long i,j;
  double jac,xi,eta,w1,w2,thick;
  ivector nodes(nne);
  vector w(intordmm),gp(intordmm),t(nne);
  matrix n(napfun,ndofe);
  
  Mt->give_elemnodes (eid,nodes);
  Mc->give_thickness (eid,nodes,t);

  gauss_points (gp.a,w.a,intordmm);
  
  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];
      jac_2d (jac,x,y,xi,eta);
      bf_matrix (n,xi,eta);
      
      thick = approx (xi,eta,t);
      jac*=w1*w2*thick;
      
      nnj (lm.a,n.a,jac,n.m,n.n);
    }
  }
  
}

/**
   function computes load %matrix of the plane stress rectangular
   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
   
   JK, 25.7.2001
*/
void planeelemlq::res_load_matrix (long eid,matrix &lm)
{
  long transf;
  ivector nodes(nne);
  vector x(nne),y(nne);
  
  Mt->give_node_coord2d (x,y,eid);

  load_matrix (eid,lm,x,y);

  //  transformation of load matrix
  //  (in the case of nodal coordinate systems)
  Mt->give_elemnodes (eid,nodes);
  transf = Mt->locsystems (nodes);
  if (transf>0){
    matrix tmat (ndofe,ndofe);
    transf_matrix (nodes,tmat);
    glmatrixtransf (lm,tmat);
  }

}













/**
   function computes correct stresses at integration points on element

   @param lcid - number of load case
   @param eid - element id
   @param ri,ci - row and column indices
   
   JK, 27.11.2006
*/
void planeelemlq::compute_nlstress (long lcid,long eid,long ri,long ci)
{
  long i,j,ii,jj,ipp;
  
  for (ii=0;ii<nb;ii++){
    for (jj=0;jj<nb;jj++){
      if (intordsm[ii][jj]==0)  continue;
      
      ipp=Mt->elements[eid].ipp[ri+ii][ci+jj];
      
      for (i=0;i<intordsm[ii][jj];i++){
	for (j=0;j<intordsm[ii][jj];j++){
	  
	  //  computation of correct stresses
	  if (Mp->strcomp==1)
	    Mm->computenlstresses (ipp);
	  
	  ipp++;
	}
      }
    }
  }
}

/**
   function computes nonlocal correct stresses at integration points on element
   
   @param lcid - number of load case
   @param eid - element id
   @param ri,ci - row and column indices
   
   JK, 27.11.2006
*/
void planeelemlq::compute_nonloc_nlstress (long lcid,long eid,long ri,long ci)
{
  long i,j,ii,jj,ipp;
  
  for (ii=0;ii<nb;ii++){
    for (jj=0;jj<nb;jj++){
      if (intordsm[ii][jj]==0)  continue;
      
      ipp=Mt->elements[eid].ipp[ri+ii][ci+jj];
      
      for (i=0;i<intordsm[ii][jj];i++){
	for (j=0;j<intordsm[ii][jj];j++){
	  
	  //  computation of correct stresses
	  if (Mp->strcomp==1)
	    Mm->compnonloc_nlstresses (ipp);
	  
	  ipp++;
	}
      }
    }
  }
}

/**
   function computes nonlocal correct stresses at integration points on element
   
   @param lcid - number of load case
   @param eid - element id
   @param ri,ci - row and column indices
   
   JK, 27.11.2006
*/
void planeelemlq::compute_eigstress (long lcid,long eid,long ri,long ci)
{
  long i,j,ii,jj,ipp;
  vector eigstr(tncomp),sig(tncomp);
  matrix d(tncomp,tncomp);
  
  for (ii=0;ii<nb;ii++){
    for (jj=0;jj<nb;jj++){
      if (intordsm[ii][jj]==0)  continue;
      
      ipp=Mt->elements[eid].ipp[ri+ii][ci+jj];
      
      for (i=0;i<intordsm[ii][jj];i++){
	for (j=0;j<intordsm[ii][jj];j++){
	  
	  Mm->giveeigstrain (ipp,eigstr);
	  
	  //  matrix of stiffness of the material
	  Mm->matstiff (d,ipp);
	  
	  mxv (d,eigstr,sig);
	  
	  Mm->storeeigstress (ipp,sig);
	  
	  ipp++;
	}
      }
    }
  }
}

/**
   function integrates selected quantity over the finite element
   it results in nodal values
   
   @param iq - type of integrated quantity (see alias.h)
   @param lcid - number of load case
   @param eid - element id
   @param ri,ci - row and column indices
   @param nv - nodal values
   @param x,y - node coordinates
   
   JK, 27.11.2006
*/
void planeelemlq::elem_integration (integratedquant iq,long lcid,long eid,long ri,long ci,vector &nv,vector &x,vector &y)
{
  long i,j,ii,ipp;
  double xi,eta,jac,thick;
  ivector nodes(nne);
  vector w,gp,t(nne),ipv,contr(ndofe);
  matrix gm;
  
  Mc->give_thickness (eid,nodes,t);
  
  fillv (0.0,nv);
  
  for (ii=0;ii<nb;ii++){
    allocv (intordsm[ii][ii],gp);
    allocv (intordsm[ii][ii],w);
    allocm (ncomp[ii],ndofe,gm);
    allocv (ncomp[ii],ipv);
    
    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];
	thick = approx (xi,eta,t);
	
	
	switch (iq){
	case locstress:{
	  //  stress reading from integration point
	  Mm->givestress (lcid,ipp,cncomp[ii],ipv);
	  break;
	}
	case nonlocstress:{
	  //  stress reading from integration point
	  Mm->givestress (lcid,ipp,cncomp[ii],ipv);
	  break;
	}
	case eigstress:{
	  //  eigenstress reading from integration point
	  Mm->giveeigstress (ipp,ncomp[ii],cncomp[ii],ipv);
	  break;
	}
	default:{
	  fprintf (stderr,"\n\n unknown type of quantity is required in function plelemqq::elem_integration (file %s, line %d).\n",__FILE__,__LINE__);
	}
	}
	
	
	//  strain-displacement (geometric) matrix
	geom_matrix_block (gm,ii,x,y,xi,eta,jac);
	
	//  contribution to the nodal values
	mtxv (gm,ipv,contr);
	
	cmulv (jac*w[i]*w[j]*thick,contr);
	
	//  summation
	addv(contr,nv,nv);
	
	ipp++;
      }
    }
    destrm (gm);  destrv (ipv);  destrv (w);  destrv (gp);
  }
}



/**
   function computes contributions from eigenstrains to the right hand side
   
   @param lcid - load case id
   @param eid - element id
   @param nfor - %vector of internal forces

   JK, 28.7.2001
*/
void planeelemlq::res_eigstrain_forces (long lcid,long eid,vector &nfor)
{
  long transf;
  ivector nodes (nne);
  vector v(ndofe),x(nne),y(nne);
  
  Mt->give_node_coord2d (x,y,eid);
  
  eigstrain_forces (lcid,eid,0,0,nfor,x,y);
  
  //  transformation of nodal forces
  //  (in the case of nodal coordinate systems)
  Mt->give_elemnodes (eid,nodes);
  transf = Mt->locsystems (nodes);
  if (transf>0){
    matrix tmat (ndofe,ndofe);
    transf_matrix (nodes,tmat);
    //globloctransf (nfor,v,tmat);
    glvectortransf (nfor,v,tmat);
    copyv (v,nfor);
  }
}

/**
   function computes contributions from eigenstrains to the right hand side
   
   @param eid - element id
   @param ri,ci - row and column indices
   @param ifor - vector of nodal forces
   @param x,y - vectors of nodal coordinates

   JK, 28.7.2001
*/
void planeelemlq::eigstrain_forces (long lcid,long eid,long ri,long ci,vector &nfor,vector &x,vector &y)
{
  integratedquant iq;
  iq=eigstress;
  
  //  computation of eigenstresses
  compute_eigstress (lcid,eid,ri,ci);
  
  //  integration of stresses over the element
  elem_integration (iq,lcid,eid,ri,ci,nfor,x,y);
}




/**
   function computes internal forces (from correct stresses)
   
   @param lcid - number of load case
   @param eid - element id
   @param ri,ci - row and column indices
   @param ifor - vector of internal forces
   @param x,y - vectors of nodal coordinates
   
   JK, 28.7.2001
*/
void planeelemlq::gl_internal_forces (long lcid,long eid,long ri,long ci,vector &ifor,vector &x,vector &y)
{
  integratedquant iq;
  iq=locstress;
  
  //  computation of stresses
  compute_nlstress (lcid,eid,ri,ci);
  
  //  integration of stresses over the element
  elem_integration (iq,lcid,eid,ri,ci,ifor,x,y);
}

/**
   function computes internal forces (from correct stresses)
   
   @param lcid - number of load case
   @param eid - element id
   @param ri,ci - row and column indices
   @param ifor - vector of internal forces
   @param x,y - vectors of nodal coordinates
   
   JK, 22.9.2005
*/
void planeelemlq::gnl_internal_forces (long lcid,long eid,long ri,long ci,vector &ifor,vector &x,vector &y)
{
  long i,j,k,ipp;
  double xi,eta,jac,thick;
  ivector cn(ndofe),nodes(nne);
  vector w,gp,t(nne),sig(tncomp),contr(ndofe),r(ndofe);
  matrix gm(tncomp,ndofe);
  
  //  element nodeds
  Mt->give_elemnodes (eid,nodes);
  //  thickness of element
  Mc->give_thickness (eid,nodes,t);
  //  code numbers of element
  Mt->give_code_numbers (eid,cn.a);
  //  nodal displacements
  eldispl (lcid,eid,r.a,cn.a,ndofe);
  
  
  fillv (0.0,ifor);
  
  //  array for coordinates of integration points
  allocv (intordsm[0][0],gp);
  //  array for weights of integration points
  allocv (intordsm[0][0],w);
  
  //  coordinates and weights of integration points
  gauss_points (gp.a,w.a,intordsm[0][0]);
  
  //  number of the first integration point on element
  ipp=Mt->elements[eid].ipp[ri][ci];
  
  
  for (i=0;i<intordsm[0][0];i++){
    xi=gp[i];
    for (j=0;j<intordsm[0][0];j++){
      eta=gp[j];
      
      //  thickness at integration point
      thick = approx (xi,eta,t);
      
      //  computation of stress
      if (Mp->strcomp==1)
	Mm->computenlstresses (ipp);
      
      Mm->givestress (lcid,ipp,sig);
      
      //  strain-displacement (geometric) matrix
      gngeom_matrix (gm,r,x,y,xi,eta,jac);
      
      mtxv (gm,sig,contr);
      
      cmulv (jac*w[i]*w[j]*thick,contr);
      
      for (k=0;k<contr.n;k++){
	ifor[k]+=contr[k];
      }
      
      ipp++;
    }
  }
  
  destrv (w);  destrv (gp);
}


/**
   function computes internal forces
   
   @param lcid - load case id
   @param eid - element id
   @param ifor - %vector of internal forces
   
   JK, 22.9.2005
*/
void planeelemlq::res_internal_forces (long lcid,long eid,vector &ifor)
{
  long transf;