plelemrotlq.cpp

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

  vector x(nne),y(nne);
  Mt->give_node_coord2d (x,y,eid);
  Mt->give_elemnodes (eid,nodes);

  stiffness_matrix (eid,0,0,sm,x,y);

  //  transformation of stiffness matrix
  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 quadrilateral
   finite element with rotationale degrees of freedom wtih
   bilinear approximation functions

   @param eid - number of element
   @param mm - mass matrix

   8.12.2001
*/
void planeelemrotlq::mass_matrix (long eid,matrix &mm,vector &x,vector &y)
{
  long i,j;
  double jac,xi,eta,w1,w2,thick,rho;
  ivector nodes(nne);
  vector l(nne),nx(nne),ny(nne),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);
  auxdata (x,y,l,nx,ny);
  gauss_points (gp.a,w.a,intordmm);
  
  fillm (0.0,mm);

  for (i=0;i<intordmm;i++){
    xi=gp[i];  w1=w[i];
    for (j=0;j<intordmm;j++){
      eta=gp[j];  w2=w[i];
      jac_2d (jac,x,y,xi,eta);
      bf_matrix (n,xi,eta,l,nx,ny);
      
      thick = approx (xi,eta,t);
      rho = approx (xi,eta,dens);
      jac*=w1*w2*thick*rho;
      
      nnj (mm.a,n.a,jac,n.m,n.n);
    }
  }
  
}

void planeelemrotlq::res_mass_matrix (long eid,matrix &mm)
{
  vector x(nne),y(nne);
  Mt->give_node_coord2d (x,y,eid);
  mass_matrix (eid,mm,x,y);
}


/**
   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

   25.7.2001
*/
void planeelemrotlq::load_matrix (long eid,matrix &lm)
{
  long i,j;
  double jac,xi,eta,w1,w2,thick;
  ivector nodes(nne);
  vector x(nne),y(nne),l(nne),nx(nne),ny(nne),w(intordmm),gp(intordmm),t(nne);
  matrix n(napfun,ndofe);
  
  Mt->give_elemnodes (eid,nodes);
  Mc->give_thickness (eid,nodes,t);
  Mt->give_node_coord2d (x,y,eid);
  auxdata (x,y,l,nx,ny);
  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,l,nx,ny);
      
      thick = approx (xi,eta,t);
      jac*=w1*w2*thick;
      
      nnj (lm.a,n.a,jac,n.m,n.n);
    }
  }
  
}



void planeelemrotlq::res_mainip_strains (long lcid,long eid)
{
  long i;
  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);
  }

  for (i=0;i<nb;i++){
    mainip_strains (lcid,eid,0,0,i,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
   @param ii - number of block
   @param x,y - arrays with node coordinates
   @param r - %vector of nodal displacements
   
   10.5.2002
*/
void planeelemrotlq::mainip_strains (long lcid,long eid,long ri,long ci,long ii,vector &x,vector &y,vector &r)
{
  long i,j,ipp;
  double xi,eta,jac;
  vector gp,w,eps,nx(ned),ny(ned),l(ned);
  matrix gm;

  auxdata (x,y,l,nx,ny);
  
  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,l,nx,ny,jac);
      mxv (gm,r,eps);
      
      Mm->storestrain (lcid,ipp,cncomp[ii],ncomp[ii],eps);
      ipp++;
    }
  }
  
  destrm (gm);  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 planeelemrotlq::nod_strains_ip (long lcid,long eid,long ri,long ci)
{
  long i,j;
  ivector ipnum(nne),nod(nne);
  vector eps(tncomp);
  
  //  numbers of integration points closest to nodes
  nodipnum (eid,ri,ci,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 strains in nodes of element
   
   @param lcid - load case id
   @param eid - element id
   
   10.5.2002
*/
void planeelemrotlq::nod_strains_comp (long lcid,long eid,double **stra)
{
  long i,j;
  double jac;
  ivector cn(ndofe),nodes(nne);
  vector x(nne),y(nne),l(nne),nx(nne),ny(nne),nxi(nne),neta(nne),r(ndofe),eps(tncomp),natcoord(2),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
  nodecoord (nxi,neta);

  auxdata (x,y,l,nx,ny);

  //  loop over nodes
  for (i=0;i<nne;i++){
    //  geometric matrix
    geom_matrix (gm,x,y,nxi[i],neta[i],l,nx,ny,jac);
    //  strain computation
    mxv (gm,r,eps);
    
    for (j=0;j<eps.n;j++){
      stra[i][j]=eps[j];
    }
  }

}


/**
   function computes all strain components at all integration points
   
   @param lcid - load case id
   @param eid - element id
   
   JK, 26.9.2004
*/
void planeelemrotlq::res_allip_strains (long lcid,long eid)
{
  //  blocks of strain components at integration points
  res_mainip_strains (lcid,eid);
  //  all strain components at all integration points
  allip_strains (lcid,eid,0,0);
}

/**
   function assembles all values at all integration points
   
   @param lcid - load case id
   @param eid - element id
   @param ri,ci - row and column indices
   
   JK, 25.9.2004
*/
void planeelemrotlq::allip_strains (long lcid,long eid,long ri,long ci)
{
  long i,j,ipp;
  vector eps(tncomp),epsnor(ncomp[0]),epsshear(ncomp[1]),aux(tncomp);
  
  ipp=Mt->elements[eid].ipp[ri+1][ci+1];
  Mm->givestrain (lcid,ipp,cncomp[1],epsshear);
  
  ipp=Mt->elements[eid].ipp[ri][ci];
  
  for (i=0;i<intordsm[0][0];i++){
    for (j=0;j<intordsm[0][0];j++){
      
      Mm->givestrain (lcid,ipp,cncomp[0],ncomp[0],eps);
      eps[2]=epsshear[0];
      
      Mm->storestrain (lcid,ipp,eps);
      
      addv (aux,eps,aux);
      ipp++;
    }
  }
  
  cmulv(0.25,aux,eps);
  Mm->storestrain (lcid,ipp,eps);
}

/**
   function computes strains at strain points
   
   @param lcid - load case id
   @param eid - element id
   @param ri,ci - row and column indices
   
   JK
*/
void planeelemrotlq::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 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 planeelemrotlq::nodecoord (vector &xi,vector &eta)
{
  xi[0] =  1.0;  eta[0] =  1.0;
  xi[1] = -1.0;  eta[1] =  1.0;
  xi[2] = -1.0;  eta[2] = -1.0;
  xi[3] =  1.0;  eta[3] = -1.0;
}

/**
   function returns numbers of integration point closest to element nodes
   
   @param eid - element id
   @param ri,ci - row and column indices
   @param ipnum - array of numbers
   
   JK, 25.9.2004
*/
void planeelemrotlq::nodipnum (long eid,long ri,long ci,ivector &ipnum)
{
  long i,j;
  
  j=intordsm[0][0];
  i=Mt->elements[eid].ipp[ri][ci];

  ipnum[0]=i+j*(j-1)+j-1;
  ipnum[1]=i+j-1;
  ipnum[2]=i;
  ipnum[3]=i+j*(j-1);
}





/**
   function computes stresses in integration points of element
   
   @param eid - element id
   @param ri - row index
   @param ci - column index
   
   10.5.2002
*/
void planeelemrotlq::mainip_stresses (long lcid,long eid,long ri,long ci)
{
  long i,j,ii,jj,ipp;
  double xi,eta;
  vector gp,w,eps,sig,auxsig;
  matrix d,dd;

  allocm (tncomp,tncomp,d);

  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);
	  //appstrain (lcid,eid,xi,eta,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 (gp);  destrv (auxsig);  destrv (sig);
  }
  
}

void planeelemrotlq::nod_stresses (long lcid,long eid,long ri,long ci)
{
  long i,j,ii,jj,ipp;
  double xi,eta,*lsm,*lhs,*rhs;
  vector nxi(nne),neta(nne),gp,w,eps,sig,auxsig,natcoord(2);
  ivector nodes(nne);