plelemlq.cpp

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

  vector w,gp,t(nne),sig(tncomp),r(ndofe);
  matrix gm(tncomp,ndofe),grm(4,ndofe),d(tncomp,tncomp),s(4,4);
  
  //  element nodes
  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);
  
  //  component setting to zero
  fillm (0.0,sm);
  
  //  array for weights of integration points
  allocv (intordsm[0][0],w);
  //  array for coordinates of integration points
  allocv (intordsm[0][0],gp);
  
  //  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];
      
      //
      //  linear stiffness matrix and inital deformation matrix
      //
      
      //  strain-displacement matrix
      gngeom_matrix (gm,r,x,y,xi,eta,jac);
      
      //  stiffness matrix of the material
      Mm->matstiff (d,ipp);
      
      //  thickness in integration point
      thick = approx (xi,eta,t);
      
      jac*=thick*w[i]*w[j];
      
      //  contribution to the stiffness matrix of the element
      bdbjac (sm,gm,d,gm,jac);
      
      
      //
      //  initial stress matrix
      //
      
      //  gradient matrix
      gnl_grmatrix (grm,x,y,xi,eta,jac2);
      
      //  stresses
      Mm->givestress (lcid,ipp,sig);
      
      s[0][0]=sig[0];  s[0][1]=sig[2];
      s[1][0]=sig[2];  s[1][1]=sig[1];

      s[2][2]=sig[0];  s[2][3]=sig[2];
      s[3][2]=sig[2];  s[3][3]=sig[1];

      //  contribution to the stiffness matrix of the element
      bdbjac (sm,grm,s,grm,jac);
      
      ipp++;
    }
  }
  
  destrv (gp);  destrv (w);
  
}

/**
   function computes stiffness %matrix of quadrilateral element
   
   @param lcid - load case id
   @param eid - element id
   @param sm - stiffness %matrix
   
   JK
*/
void planeelemlq::res_stiffness_matrix (long lcid,long eid,matrix &sm)
{
  long transf;
  ivector nodes(nne);
  vector x(nne),y(nne);

  Mt->give_node_coord2d (x,y,eid);

  
  gl_stiffness_matrix (eid,0,0,sm,x,y);
  //gnl_stiffness_matrix (lcid,eid,0,0,sm,x,y);
  
  //  transformation of stiffness 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 (sm,tmat);
  }
}

/**
   function computes mass %matrix of the plane stress rectangular
   finite element with bilinear approximation functions
   
   this function is used in plane stress/strain elements (function is called
   by function res_mass_matrix) and shell elements

   @param eid - number of element
   @param mm - mass %matrix
   
   JK, 24.6.2001
*/
void planeelemlq::mass_matrix (long eid,matrix &mm,vector &x,vector &y)
{
  long i,j;
  double jac,xi,eta,thick,rho;
  ivector nodes(nne);
  vector w(intordmm),gp(intordmm),t(nne),dens(nne);
  matrix n(napfun,ndofe);

  Mt->give_elemnodes (eid,nodes);
  Mc->give_thickness (eid,nodes,t);
  Mc->give_density (eid,nodes,dens);
  gauss_points (gp.a,w.a,intordmm);
  
  fillm (0.0,mm);

  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);
      
      thick = approx (xi,eta,t);
      rho = approx (xi,eta,dens);
      jac*=w[i]*w[j]*thick*rho;
      
      nnj (mm.a,n.a,jac,n.m,n.n);
    }
  }
  
}

/**
   function assembles mass %matrix of plane stress rectangular
   finite element with biquadratic approximation functions
   
   @param eid - element id
   @param mm - mass %matrix
   
   JK
*/
void planeelemlq::res_mass_matrix (long eid,matrix &mm)
{
  long transf;
  ivector nodes(nne);
  vector x(nne),y(nne);
  
  Mt->give_node_coord2d (x,y,eid);

  mass_matrix (eid,mm,x,y);
  
  //  transformation of mass 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 (mm,tmat);
  }
}






/**
   function computes strains at integration points
   
   @param lcid - load case id
   @param eid - element id
   
   JK
*/
void planeelemlq::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
  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);
  }
  
  gl_ip_strains (lcid,eid,0,0,x,y,r);
  //gnl_ip_strains (lcid,eid,0,0,x,y,r);
  
}

/**
   function computes strains at integration points of element
   function is used in geometrically linear problems
   
   @param lcid - load case id
   @param eid - element id
   @param ri,ci - row and column indices
   @param ii - number of block
   @param x,y - arrays with node coordinates
   @param r - %vector of nodal displacements
   
   JK, 10.5.2002
*/
void planeelemlq::gl_ip_strains (long lcid,long eid,long ri,long ci,vector &x,vector &y,vector &r)
{
  long i,j,ii,ipp;
  double xi,eta,jac;
  vector gp,w,eps,epscum;
  matrix gm;
  
  //  loop over blocks
  for (ii=0;ii<nb;ii++){
    
    allocv (intordsm[ii][ii],gp);
    allocv (intordsm[ii][ii],w);
    allocv (ncomp[ii],eps);
    allocm (ncomp[ii],ndofe,gm);
    
    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];
	
	geom_matrix_block (gm,ii,x,y,xi,eta,jac);
	mxv (gm,r,eps);
	
	Mm->storestrain (lcid,ipp,cncomp[ii],eps);
	ipp++;
      }
    }
    
    destrm (gm);  destrv (eps);  destrv (w);  destrv (gp);
  }
  
  // ********************************************
  //  exchange of values at integration points
  // ********************************************
  //  values from 4 points to 1 point
  ipp=Mt->elements[eid].ipp[ri][ci];
  allocv (ncomp[0],epscum);
  allocv (ncomp[0],eps);
  for (i=0;i<intordsm[0][0];i++){
    for (j=0;j<intordsm[0][0];j++){
      Mm->givestrain (lcid,ipp,cncomp[0],eps);
      addv (eps,epscum,epscum);
      ipp++;
    }
  }
  
  cmulv (1.0/4.0,epscum,epscum);
  ipp=Mt->elements[eid].ipp[ri+1][ci+1];
  Mm->storestrain (lcid,ipp,epscum);
  destrv (eps);
  destrv (epscum);

  //  value from 1 point to 4 points
  allocv (ncomp[1],eps);
  Mm->givestrain (lcid,ipp,cncomp[1],eps);
  ipp=Mt->elements[eid].ipp[ri][ci];
  Mm->storestrain (lcid,ipp,cncomp[1],eps);  ipp++;
  Mm->storestrain (lcid,ipp,cncomp[1],eps);  ipp++;
  Mm->storestrain (lcid,ipp,cncomp[1],eps);  ipp++;
  Mm->storestrain (lcid,ipp,cncomp[1],eps);  ipp++;
  destrv (eps);
}

/**
   function computes strains at integration points of element
   function is used in geometrically linear problems
   
   @param lcid - load case id
   @param eid - element id
   @param ri,ci - row and column indices
   @param ii - number of block
   @param x,y - arrays with node coordinates
   @param r - %vector of nodal displacements
   
   JK, 24.9.2005
*/
void planeelemlq::gnl_ip_strains (long lcid,long eid,long ri,long ci,vector &x,vector &y,vector &r)
{
  long i,j,ipp;
  double xi,eta,jac,b11r,b12r,b21r,b22r;
  vector gp,w,eps,b11(ndofe),b12(ndofe),b21(ndofe),b22(ndofe);
  
  allocv (intordsm[0][0],gp);
  allocv (intordsm[0][0],w);
  allocv (tncomp,eps);
  
  gauss_points (gp.a,w.a,intordsm[0][0]);
  
  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];
      
      bvectors (x,y,xi,eta,jac,b11,b12,b21,b22);

      scprd (b11,r,b11r);
      scprd (b12,r,b12r);
      scprd (b21,r,b21r);
      scprd (b22,r,b22r);
      
      eps[0]=b11r+0.5*b11r*b11r+0.5*b21r*b21r;
      eps[1]=b22r+0.5*b12r*b12r+0.5*b22r*b22r;
      eps[2]=b12r+b21r+b11r*b12r+b21r*b22r;
      
      
      Mm->storestrain (lcid,ipp,eps);
      ipp++;
    }
  }
  
  destrv (eps);  destrv (w);  destrv (gp);
  
}


/**
   function computes strains in 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_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);
  }
  
}

/**
   function computes nodal strains directly
   
   @param lcid - load case id
   @param eid - element id
   @param stra - array for strain components
   
   JK, 25.9.2004
*/
void planeelemlq::nod_strains_comp (long lcid,long eid,double **stra)
{
  long i,j;
  double jac;
  ivector cn(ndofe),nodes(nne);
  vector x(nne),y(nne),nxi(nne),neta(nne),r(ndofe),eps(tncomp),aux;
  matrix tmat,gm(tncomp,ndofe);
  
  //  node coordinates
  Mt->give_node_coord2d (x,y,eid);
  //  node numbers
  Mt->give_elemnodes (eid,nodes);
  //  code numbers of the element
  Mt->give_code_numbers (eid,cn.a);
  //  nodal displacements
  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);
  }
  
  //  natural coordinates of element nodes
  //  (function is from the file GEFEL/ordering.cpp)
  nodcoord_planelq (nxi,neta);
  
  //  loop over nodes
  for (i=0;i<nne;i++){
    //  geometric matrix
    geom_matrix (gm,x,y,nxi[i],neta[i],jac);
    //  strain computation
    mxv (gm,r,eps);
    
    for (j=0;j<eps.n;j++){
      stra[i][j]=eps[j];
    }
  }

}



/**
   function computes strains at strain points
   
   @param lcid - load case id
   @param eid - element id
   @param ri,ci - row and column indices
   
   JK
*/
void planeelemlq::strains (long lcid,long eid,long ri,long ci)
{
  long i,naep,ncp,sid;
  vector coord,eps;

  switch (Mm->stra.tape[eid]){
  case nowhere:{
    break;
  }
  case intpts:{
    //allip_strains (lcid,eid,ri,ci);
    break;
  }
  case enodes:{
    nod_strains_ip (lcid,eid,ri,ci);
    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 planeelemlq::strains (%s, line %d).\n",__FILE__,__LINE__);
  }
  }
  
}


/**
   function computes stresses at integration points
   
   @param lcid - load case id
   @param eid - element id
   
   JK
*/
void planeelemlq::res_ip_stresses (long lcid,long eid)
{
  ip_stresses (lcid,eid,0,0);
}

/**
   function computes stresses at integration points of element
   
   @param lcid - load case id
   @param eid - element id
   @param ri,ci - row and column indices
   
   function can be used when all strain components are known
   at all integration points
   
   JK, 10.5.2002
*/
void planeelemlq::ip_stresses (long lcid,long eid,long ri,long ci)
{
  long i,j,ii,jj,ipp;
  vector sig,sigcum;

  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++;
	}
      }
    }
  }
  
  
  // ********************************************
  //  exchange of values at integration points
  // ********************************************
  //  values from 4 points to 1 point
  ipp=Mt->elements[eid].ipp[ri][ci];
  allocv (ncomp[0],sigcum);
  allocv (ncomp[0],sig);
  for (i=0;i<intordsm[0][0];i++){
    for (j=0;j<intordsm[0][0];j++){
      Mm->givestress (lcid,ipp,cncomp[0],sig);
      addv (sig,sigcum,sigcum);
      ipp++;
    }
  }
  
  cmulv (1.0/4.0,sigcum,sigcum);
  ipp=Mt->elements[eid].ipp[ri+1][ci+1];
  Mm->storestress (lcid,ipp,sigcum);
  destrv (sig);
  destrv (sigcum);

  //  value from 1 point to 4 points
  allocv (ncomp[1],sig);
  Mm->givestrain (lcid,ipp,cncomp[1],sig);
  ipp=Mt->elements[eid].ipp[ri][ci];
  Mm->storestrain (lcid,ipp,cncomp[1],sig);  ipp++;
  Mm->storestrain (lcid,ipp,cncomp[1],sig);  ipp++;
  Mm->storestrain (lcid,ipp,cncomp[1],sig);  ipp++;
  Mm->storestrain (lcid,ipp,cncomp[1],sig);  ipp++;
  destrv (sig);
}

/**
   function computes stresses in integration points of element
   
   @param lcid - load case id
   @param eid - element id
   @param ri,ci - row and column indices
   
   function can be used when all strain components are known
   at all integration points
   
   10.5.2002
*/
void planeelemlq::ip_elast_stresses (long lcid,long eid,long ri,long ci)
{
  long i,j,ii,jj,ipp;
  double xi,eta;
  vector gp,w,eps,epst,epstt,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],gp);
    allocv (intordsm[ii][ii],w);
    
    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);
	
	fillv (0.0,sig);
	for (jj=0;jj<nb;jj++){
	  allocv (ncomp[jj],eps);
	  allocm (ncomp[ii],ncomp[jj],dd);
	  
	  //  block of strains