axisymlq-nb3.cpp

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

  nodecoord (nxi,neta);
  Mt->give_elemnodes (eid,nodes);
  Mt->give_node_coord2d (x,y,eid);
  Mt->give_code_numbers (eid,cn.a);
  eldispl (lcid,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);
    copyv (aux,r);
    destrv (aux);
    destrm (tmat);
  }

  for (ii=0;ii<nb;ii++){
    if (intordsm[ii][ii]==0)  continue;
    
    allocv (intordsm[ii][ii],gp);
    allocv (intordsm[ii][ii],w);
    allocv (ncomp[ii],eps);
    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->givestrain (lcid,ipp,cncomp[ii],ncomp[ii],eps);
	
	natcoord[0]=xi;  natcoord[1]=eta;
	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 (gp);
  }
  
  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 axisymlq::elem_strains (double **stra,long lcid,long eid,long ri,long ci)
{
  long i,j,ii,ipp;
  double xi,eta,*lsm,*lhs,*rhs;
  vector nxi(nne),neta(nne),gp,w,eps,aux,natcoord(2);

  lsm = new double [9];

  nodecoord (nxi,neta);
  
  for (ii=0;ii<nb;ii++){
    allocv (intordsm[ii][ii],gp);
    allocv (intordsm[ii][ii],w);
    allocv (ncomp[ii],eps);
    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->givestrain (lcid,ipp,cncomp[ii],ncomp[ii],eps);
	
	natcoord[0]=xi;  natcoord[1]=eta;
	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 (gp);
  }
  
  delete [] lsm;
}


/**
   function computes strains 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 eps - array containing strains
   
   11.5.2002
*/
void axisymlq::appstrain (long lcid,long eid,double xi,double eta,long fi,long ncomp,vector &eps)
{
  long i,j,k;
  ivector nodes;
  vector nodval;
  
  if (ncomp != eps.n){
    fprintf (stderr,"\n\n wrong interval of indices in function strain (%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]].strain[lcid*tncomp+i];
    }
    eps[k]=approx (xi,eta,nodval);
    k++;
  }
  
  destrv (nodes);  destrv (nodval);
}

/**
   function computes all strain components at all integration points
   
   @param lcid - load case id
   @param eid - element id
   
   JK, 26.9.2004
*/
void axisymlq::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 computes strains in all integration points
   
   @param lcid - load case id
   @param eid - element id
   @param ri,ci - row and column indices
   
   10.5.2002
*/
void axisymlq::allip_strains (long lcid,long eid,long ri,long ci)
{
  long i,j,ipp1,ipp2,ipp3;
  vector eps(tncomp),aux(tncomp);
  
  ipp1=Mt->elements[eid].ipp[ri+0][ci+0];
  ipp2=Mt->elements[eid].ipp[ri+1][ci+1];
  ipp3=Mt->elements[eid].ipp[ri+2][ci+2];

  for (i=0;i<intordsm[0][0];i++){
    for (j=0;j<intordsm[0][0];j++){
      
      Mm->givestrain (lcid,ipp1,cncomp[0],ncomp[0],eps);
      Mm->givestrain (lcid,ipp2,cncomp[1],ncomp[1],eps);
      Mm->givestrain (lcid,ipp3,cncomp[2],ncomp[2],eps);
      
      Mm->storestrain (lcid,ipp1,eps);
      Mm->storestrain (lcid,ipp2,eps);
      
      addv (aux,eps,aux);

      ipp1++;  ipp2++;
    }
  }

  cmulv(0.25,aux,eps);
  Mm->storestrain (lcid,ipp3,eps);
  
}



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

/**
   function computes stresses at integration points
   
   @param lcid - load case id
   @param eid - element id
   
   JK
*/
void axisymlq::res_mainip_stresses (long lcid,long eid)
{
  long i;
  
  //  loop over blocks
  for (i=0;i<nb;i++){
    mainip_stresses (lcid,eid,0,0,i);
  }
}

/**
   function computes stresses in main 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 axisymlq::mainip_stresses (long lcid,long eid,long ri,long ci,long ii)
{
  long i,j,jj,ipp;
  double xi,eta;
  vector gp,w,eps,epst,epstt,sig,auxsig;
  matrix d(tncomp,tncomp),dd;

  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
	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],ncomp[ii],sig);
      
      ipp++;
    }
  }
  
  destrv (w);  destrv (gp);  destrv (auxsig);  destrv (sig);
}


/**
   function computes stresses in nodes
   
   @param lcid - load case id
   @param eid - element id
   @param ri,ci - row and column indices
   
   10.5.2002
*/
void axisymlq::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),r(ndofe),gp,w,eps,epst,epstt,sig,auxsig,natcoord(2);
  ivector nodes(nne);
  matrix d(tncomp,tncomp),dd;

  lsm = new double [9];

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

  for (ii=0;ii<nb;ii++){
    if (intordsm[ii][ii]==0)  continue;

    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)
	    Mm->givestrain (lcid,ipp,cncomp[jj],ncomp[jj],eps);
	  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);
	  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]);
    Mt->stress_nodal_values (nodes,nxi,neta,nxi,lhs,2,cncomp[ii],ncomp[ii],lcid);
    
    
    delete [] lhs;  delete [] rhs;
    destrv (auxsig);  destrv (sig);  destrv (eps);  destrv (w);  destrv (gp);
  }
  delete [] lsm;
}

void axisymlq::elem_stresses (double **stra,double **stre,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,epst,epstt,sig,auxsig,natcoord(2);
  matrix d(tncomp,tncomp),dd;

  lsm = new double [9];

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