lintet.cpp

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

#include <stdlib.h>
#include <math.h>
#include "lintet.h"
#include "gadaptivity.h"
#include "global.h"
#include "globmat.h"
#include "genfile.h"
#include "intpoints.h"
#include "node.h"
#include "element.h"
#include "loadcase.h"




lintet::lintet (void)
{
  long i,j;

  //  number nodes on element
  nne=4;
  //  number of DOFs on element
  ndofe=12;
  //  number of strain/stress components
  tncomp=6;
  //  number of functions approximated
  napfun=3;
  //  order of numerical integration of mass matrix
  intordmm=1;
  //  number of edges on element
  ned=6;
  //  number of nodes on one edge
  nned=2;
  nsurf=4;
  nnsurf=3;
  //  order of numerical integration on element edges (boundaries)
  intordb=3;
  ssst=spacestress;
  
  //  number of blocks (parts of geometric matrix)
  nb=1;
  
  ncomp = new long [nb];
  ncomp[0]=6;
  
  cncomp = new long [nb];
  cncomp[0]=0;
  
  nip = new long* [nb];
  intordsm = new long* [nb];
  for (i=0;i<nb;i++){
    nip[i] = new long [nb];
    intordsm[i] = new long [nb];
  }
  
  nip[0][0]=1;

  tnip=0;
  for (i=0;i<nb;i++){
    for (j=0;j<nb;j++){
      tnip+=nip[i][j];
    }
  }

  intordsm[0][0]=1;

}

lintet::~lintet (void)
{
  long i;
  
  for (i=0;i<nb;i++){
    delete [] nip[i];
    delete [] intordsm[i];
  }
  delete [] nip;
  delete [] intordsm;
  
  delete [] cncomp;
  delete [] ncomp;
}

void lintet::eleminit (long eid)
{
  long ii,jj;
  Mt->elements[eid].nb=nb;
  Mt->elements[eid].intordsm = new long* [nb];
  Mt->elements[eid].nip = new long* [nb];

  for (ii=0;ii<nb;ii++){
    Mt->elements[eid].intordsm[ii] = new long [nb];
    Mt->elements[eid].nip[ii] = new long [nb];
    for (jj=0;jj<nb;jj++){
      Mt->elements[eid].intordsm[ii][jj]=intordsm[ii][jj];
      Mt->elements[eid].nip[ii][jj]=nip[ii][jj];
    }
  }
}

/**
   function approximates function defined by nodal values
   
   @param volcoord - volume coordinates
   @param nodval - nodal values
   
   20.8.2001
*/
double lintet::approx (vector &volcoord,vector &nodval)
{
  double f;

  scprd (volcoord,nodval,f);
  
  return f;
}

/**
   function approximates function defined by nodal values
   
   @param volcoord - volume coordinates
   @param nodval - nodal values
   
   20.8.2001
*/
double lintet::approx_nat (double xi,double eta,double zeta,vector &nodval)
{
  double f;
  vector volcoord(4);
  
  volcoord[0]=xi;
  volcoord[1]=eta;
  volcoord[2]=zeta;
  volcoord[3]=1.0-volcoord[0]-volcoord[1]-volcoord[2];
  
  scprd (volcoord,nodval,f);
  
  return f;
}

/**
   function assembles matrix of base functions

   @param n - matrix of base functions
   @param volcoord - volume coordinates
   
   24.8.2001
*/
void lintet::bf_matrix (matrix &n,vector &volcoord)
{
  fillm (0.0,n);
  
  n[0][0]=volcoord[0];  n[0][3]=volcoord[1];  n[0][6]=volcoord[2];  n[0][9] =volcoord[3];
  n[1][1]=volcoord[0];  n[1][4]=volcoord[1];  n[1][7]=volcoord[2];  n[1][10]=volcoord[3];
  n[2][2]=volcoord[0];  n[2][5]=volcoord[1];  n[2][8]=volcoord[2];  n[2][11]=volcoord[3];
}
void lintet::bf_matrix (matrix &n,double xi,double eta,double zeta)
{
  fillm (0.0,n);
  
  n[0][0]=xi;  n[0][3]=eta;  n[0][6]=zeta;  n[0][9] =1.0-xi-eta-zeta;
  n[1][1]=xi;  n[1][4]=eta;  n[1][7]=zeta;  n[1][10]=1.0-xi-eta-zeta;
  n[2][2]=xi;  n[2][5]=eta;  n[2][8]=zeta;  n[2][11]=1.0-xi-eta-zeta;
}

/**
   function assembles geometric matrix
   vector of strains has following ordering
   eps=(e_xx, e_yy, e_zz, e_yz, e_zx, e_xy)
   
   @param gm - geometric matrix
   @param x,y,z - vectors of node coordinates
   
   24.8.2001
*/
void lintet::geom_matrix (matrix &gm,vector &x,vector &y,vector &z)
{
  long i,i1,i2,i3,i4,i5,i6,i7,i8,i9;
  double det;
  vector b(4),c(4),d(4);
  
  det = det3d (x.a,y.a,z.a);
  
  volb_3d (b.a,y.a,z.a,det);
  volc_3d (c.a,x.a,z.a,det);
  vold_3d (d.a,x.a,y.a,det);
  
  i1=0;  i2=1;  i3=2;  i4=1;  i5=2;  i6=0;  i7=2;  i8=0;  i9=1;
  for (i=0;i<4;i++){
    gm[0][i1]=b[i];  i1+=3;
    gm[1][i2]=c[i];  i2+=3;
    gm[2][i3]=d[i];  i3+=3;
    
    gm[3][i4]=d[i];  i4+=3;
    gm[3][i5]=c[i];  i5+=3;
    
    gm[4][i6]=d[i];  i6+=3;
    gm[4][i7]=b[i];  i7+=3;
    
    gm[5][i8]=c[i];  i8+=3;
    gm[5][i9]=b[i];  i9+=3;
  }
  
}


/**
   function assembles transformation matrix
   
   @param nodes - nodes of element
   @param tmat - transformation matrix
   
*/
void lintet::transf_matrix (ivector &nodes,matrix &tmat)
{
  long i,n,m;

  fillm (0.0,tmat);

  n=nodes.n;
  m=tmat.m;
  for (i=0;i<m;i++){
    tmat[i][i]=1.0;
  }
  
  for (i=0;i<n;i++){
    if (Mt->nodes[nodes[i]].transf>0){
      tmat[i*3+0][i*3]=Mt->nodes[nodes[i]].e1[0];
      tmat[i*3+1][i*3]=Mt->nodes[nodes[i]].e1[1];
      tmat[i*3+2][i*3]=Mt->nodes[nodes[i]].e1[2];

      tmat[i*3+0][i*3+1]=Mt->nodes[nodes[i]].e2[0];
      tmat[i*3+1][i*3+1]=Mt->nodes[nodes[i]].e2[1];
      tmat[i*3+2][i*3+1]=Mt->nodes[nodes[i]].e2[2];

      tmat[i*3+0][i*3+2]=Mt->nodes[nodes[i]].e3[0];
      tmat[i*3+1][i*3+2]=Mt->nodes[nodes[i]].e3[1];
      tmat[i*3+2][i*3+2]=Mt->nodes[nodes[i]].e3[2];
    }
  }
}


/**
   function computes stiffness matrix of one element

   @param eid - number of element
   @param ri,ci - row and column indices
   @param sm - stiffness matrix

   19.7.2001
*/
void lintet::stiffness_matrix (long eid,long ri,long ci,matrix &sm)
{
  long ipp;
  double det,jac;
  vector x(nne),y(nne),z(nne);
  matrix gm(tncomp,ndofe),d(tncomp,tncomp);

  Mt->give_node_coord3d (x,y,z,eid);
  fillm (0.0,sm);
  det = det3d (x.a,y.a,z.a);

  ipp=Mt->elements[eid].ipp[ri][ci];

  geom_matrix (gm,x,y,z);
  Mm->matstiff (d,ipp);

  jac=fabs(det)/6.0;
  //jac=det/6.0;
  if (jac<0.0) fprintf (stdout,"\n zaporny jakobian");

  //jac=det/6.0;

  bdbjac (sm,gm,d,gm,jac);

}

/**
   function assembles resulting stiffness matrix of the element

   @param eid - element id
   @param sm - stiffness matrix

   JK, 9.5.2002
*/
void lintet::res_stiffness_matrix (long eid,matrix &sm)
{
  stiffness_matrix (eid,0,0,sm);
}

/**
   function computes mass matrix
   
   @param eid - number of element
   @param mm - mass matrix
   
   26.8.2001
*/
void lintet::mass_matrix (long eid,matrix &mm)
{
  long i;
  double det,jac,rho;
  ivector nodes (nne);
  vector x(nne),y(nne),z(nne),w(intordmm),gp1(intordmm),gp2(intordmm),gp3(intordmm),volcoord(4),dens(nne);
  matrix n(napfun,ndofe);
  
  Mt->give_elemnodes (eid,nodes);
  Mc->give_density (eid,nodes,dens);
  Mt->give_node_coord3d (x,y,z,eid);

  gauss_points_tet (gp1.a,gp2.a,gp3.a,w.a,intordmm);

  det = det3d (x.a,y.a,z.a);
  
  fillm (0.0,mm);
  
  for (i=0;i<intordmm;i++){
    volcoord[0]=gp1[i];
    volcoord[1]=gp2[i];
    volcoord[2]=gp3[i];
    volcoord[3]=1.0-gp1[i]-gp2[i]-gp3[i];
    
    bf_matrix (n,volcoord);
    rho = approx (volcoord,dens);
    
    jac=det*w[i]*rho;
    
    nnj (mm.a,n.a,jac,n.m,n.n);
  }
  
}

/**
   function computes load matrix
   
   @param eid - number of element
   @param lm - load matrix

   26.8.2001
*/
void lintet::load_matrix (long eid,matrix &lm)
{
  long i;
  double det,jac;
  ivector nodes (nne);
  vector x(nne),y(nne),z(nne),w(intordmm),gp1(intordmm),gp2(intordmm),gp3(intordmm),volcoord(4);
  matrix n(napfun,ndofe);
  
  Mt->give_elemnodes (eid,nodes);
  Mt->give_node_coord3d (x,y,z,eid);

  gauss_points_tet (gp1.a,gp2.a,gp3.a,w.a,intordmm);

  det = det3d (x.a,y.a,z.a);

  fillm (0.0,lm);

  for (i=0;i<intordmm;i++){
    volcoord[0]=gp1[i];
    volcoord[1]=gp2[i];
    volcoord[2]=gp3[i];
    volcoord[3]=1.0-gp1[i]-gp2[i]-gp3[i];

    bf_matrix (n,volcoord);

    jac=det*w[i];

    nnj (lm.a,n.a,jac,n.m,n.n);
  }
}





void lintet::res_mainip_strains (long lcid,long eid)
{
  mainip_strains (lcid,eid,0,0);
}

/**
   function computes strains 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 lintet::mainip_strains (long lcid,long eid,long ri,long ci)
{
  long ipp;
  vector x(nne),y(nne),z(nne),r(ndofe),eps(tncomp),aux;
  ivector nodes(nne),cn(ndofe);
  matrix gm(tncomp,ndofe),tmat;

  Mt->give_elemnodes (eid,nodes);
  Mt->give_node_coord3d (x,y,z,eid);
  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);
  }

  ipp=Mt->elements[eid].ipp[ri][ci];
  
  geom_matrix (gm,x,y,z);
  mxv (gm,r,eps);
  Mm->storestrain (lcid,ipp,eps);
  
}

/**
   function computes strains in nodes of element
   
   @param lcid - load case id
   @param eid - element id
   
   10.5.2002
*/
void lintet::nod_strains (long lcid,long eid,long ri,long ci)
{
  long ipp;
  double *lsm,*lhs,*rhs;
  vector nxi(nne),neta(nne),nzeta(nne),eps(tncomp),natcoord(3);
  ivector nodes(nne);
  
  lsm = new double [16];

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

  lhs = new double [ncomp[0]*4];
  rhs = new double [ncomp[0]*4];
  
  nullv (lsm,16);
  nullv (lhs,ncomp[0]*4);
  nullv (rhs,ncomp[0]*4);
    
  ipp=Mt->elements[eid].ipp[ri][ci];
  Mm->givestrain (lcid,ipp,cncomp[0],ncomp[0],eps);
  
  natcoord[0]=0.25;  natcoord[1]=0.25;  natcoord[2]=0.25;
  matassem_lsm (lsm,natcoord);
  rhsassem_lsm (rhs,natcoord,eps);
  
  solve_lsm (lsm,lhs,rhs,Mp->zero,4,ncomp[0]);
  Mt->strain_nodal_values (nodes,nxi,neta,nzeta,lhs,3,cncomp[0],ncomp[0],lcid);
  
  /*
  lhs[0]=eps[0];
  lhs[2]=eps[1];
  lhs[4]=eps[2];
  lhs[6]=eps[3];
  lhs[8]=eps[4];
  lhs[10]=eps[5];

  Mt->strain_nodal_values (nodes,nxi,neta,nzeta,lhs,3,ncomp[0],ncomp[0],lcid);
  */
  
  delete [] lsm;  delete [] lhs;  delete [] rhs;
}

/**
   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 lintet::elem_strains (double **stra,long lcid,long eid,long ri,long ci)
{
  long i,ii,ipp;
  double xi,eta,zeta,*lsm,*lhs,*rhs;
  vector nxi(nne),neta(nne),nzeta(nne),gp1,gp2,gp3,w,eps,natcoord(3);

  lsm = new double [16];

  nodecoord (nxi,neta,nzeta);

  for (ii=0;ii<nb;ii++){
    allocv (intordsm[ii][ii],gp1);
    allocv (intordsm[ii][ii],gp2);
    allocv (intordsm[ii][ii],gp3);
    allocv (intordsm[ii][ii],w);
    allocv (ncomp[ii],eps);
    lhs = new double [ncomp[ii]*4];
    rhs = new double [ncomp[ii]*4];
    gauss_points_tet (gp1.a,gp2.a,gp3.a,w.a,intordsm[ii][ii]);

    nullv (lsm,16);
    nullv (rhs,ncomp[ii]*4);
    
    ipp=Mt->elements[eid].ipp[ri+ii][ci+ii];
    for (i=0;i<intordsm[ii][ii];i++){
      xi=gp1[i];
      eta=gp2[i];
      zeta=gp3[i];
      
      Mm->givestrain (lcid,ipp,cncomp[ii],ncomp[ii],eps);
      
      natcoord[0]=xi;  natcoord[1]=eta;  natcoord[2]=zeta;
      matassem_lsm (lsm,natcoord);
      rhsassem_lsm (rhs,natcoord,eps);
      
      ipp++;
    }
    
    solve_lsm (lsm,lhs,rhs,Mp->zero,4,ncomp[ii]);
    nodal_values (stra,nxi,neta,nzeta,lhs,3,cncomp[ii],ncomp[ii]);

    delete [] lhs;  delete [] rhs;
    destrv (eps);  destrv (w);  destrv (gp1);  destrv (gp2);  destrv (gp3);
  }
  
  delete [] lsm;
}

/**
   function computes strains in arbitrary point on element
   
   @param lcid - load case id
   @param eid - element id
   @param volcoord - area coordinates of the point
   @param fi,li - first and last indices
   @param eps - array containing strains
   
   11.5.2002
*/
void lintet::appstrain (long lcid,long eid,double xi,double eta,double zeta,long fi,long ncomp,vector &eps)
{
  long i,j,k;
  ivector nodes(nne);
  vector nodval(nne),volcoord(4);
  
  if (ncomp != eps.n){
    fprintf (stderr,"\n\n wrong interval of indices in function strain (%s, line %d).\n",__FILE__,__LINE__);
    abort ();
  }
  
  volcoord[0]=xi;
  volcoord[1]=eta;
  volcoord[2]=zeta;
  volcoord[3]=1.0-volcoord[0]-volcoord[1]-volcoord[2];
  
  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 (volcoord,nodval);
    k++;
  }
}

/**
   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 lintet::allip_strains (double **stra,long lcid,long eid,long ri,long ci)
{
  long ipp;
  double xi,eta,zeta;
  vector eps(tncomp);
  
  xi=0.25;
  eta=0.25;
  zeta=0.25;
  
  ipp=Mt->elements[eid].ipp[ri][ci];

  if (Mp->strainaver==0)
    appval (xi,eta,zeta,0,tncomp,eps,stra);
  if (Mp->strainaver==1)
    appstrain (lcid,eid,xi,eta,zeta,0,tncomp,eps);
  
  Mm->storestrain (lcid,ipp,eps);
}

void lintet::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 (3,coord);
    for (i=0;i<naep;i++){
      Mm->stra.give_aepcoord (sid,i,coord);
      
      if (Mp->strainaver==0)
	appval (coord[0],coord[1],coord[2],0,ncp,eps,stra);
      if (Mp->strainaver==1)
	appstrain (lcid,eid,coord[0],coord[1],coord[2],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 planeelemlt::strains (%s, line %d).\n",__FILE__,__LINE__);
  }
  }

}

/**
   function assembles natural coordinates of nodes of element
   
   @param xi - array containing natural coordinates xi