linhex_nb1.cpp

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

  ivector nodes(nne),cn(ndofe);
  vector x(nne),y(nne),z(nne),w,gp,r(ndofe),eps(tncomp),sig,contr(ndofe),v(ndofe);
  matrix gm,tmat (ndofe,ndofe);

  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 nodal displacements
  Mt->give_elemnodes (eid,nodes);
  transf = Mt->locsystems (nodes);
  if (transf>0){
    transf_matrix (nodes,tmat);
    copyv (r,v);
    locglobtransf (r,v,tmat);
  }
  
  
  fillv (0.0,ifor);
  
  for (ii=0;ii<nb;ii++){
    if (intordsm[ii][ii]==0)  continue;
    
    allocv (intordsm[ii][ii],gp);
    allocv (intordsm[ii][ii],w);
    allocm (ncomp[ii],ndofe,gm);
    allocv (ncomp[ii],sig);
    
    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];
	for (k=0;k<intordsm[ii][ii];k++){
	  zeta=gp[k];
	  
	  geom_matrix (gm,x,y,z,xi,eta,zeta,jac);
	  
	  mxv (gm,r,eps);
	  
	  Mm->storestrain (lcid,ipp,eps);
	  
	  Mm->computenlstresses (ipp);
	  
	  Mm->givestress (lcid,ipp,cncomp[ii],ncomp[ii],sig);
	  
	  geom_matrix (gm,x,y,z,xi,eta,zeta,jac);
	  mtxv (gm,sig,contr);
	  
	  cmulv (jac*w[i]*w[j]*w[k],contr);
	  
	  for (l=0;l<contr.n;l++){
	    ifor[l]+=contr[l];
	  }
	  
	  ipp++;
	}
      }
    }
    destrv (sig);  destrm (gm);  destrv (w);  destrv (gp);
  }
  
  //  transformation of nodal forces
  if (transf>0){
    transf_matrix (nodes,tmat);
    globloctransf (ifor,v,tmat);
    copyv (v,ifor);
  }
  
}

/**
   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
   
   JK, 24.9.2005
*/
void linhex::gnl_internal_forces (long lcid,long eid,long ri,long ci,vector &ifor)
{
  long i,j,k,l,ipp;
  double xi,eta,zeta,jac;
  ivector cn(ndofe);
  vector w,gp,x(nne),y(nne),z(nne),sig(tncomp),contr(ndofe),r(ndofe);
  matrix gm(tncomp,ndofe);
  
  //  node coordinates
  Mt->give_node_coord3d (x,y,z,eid);
  //  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];
      for (k=0;k<intordsm[0][0];k++){
	zeta=gp[k];
	
	//  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,z,xi,eta,zeta,jac);
	
	mtxv (gm,sig,contr);
	
	cmulv (jac*w[i]*w[j]*w[k],contr);
	
	for (l=0;l<contr.n;l++){
	  ifor[l]+=contr[l];
	}
	
	ipp++;
      }
    }
  }
  destrv (w);  destrv (gp);
}


void linhex::res_internal_forces (long lcid,long eid,vector &ifor)
{
  gl_internal_forces (lcid,eid,0,0,ifor);
  //gnl_internal_forces (lcid,eid,0,0,ifor);
}

/**
   function computes internal forces

   @param lcid - number of load case
   @param eid - element id
   @param ri,ci - row and column indices
   @param ifor - vector of internal forces
   
   28.7.2001
*/
void linhex::local_values (long lcid,long eid,long ri,long ci)
{
  long i,j,k,ii,ipp;
  double xi,eta,zeta;
  double **stra;
  vector w,gp,eps(tncomp);
  matrix gm;

  stra = new double* [nne];
  for (i=0;i<nne;i++){
    stra[i] = new double [tncomp];
  }
  //elem_strains (stra,lcid,eid,ri,ci);

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

    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];
	for (k=0;k<intordsm[ii][ii];k++){
	  zeta=gp[k];
	  
	  //appval (xi,eta,zeta,0,tncomp,eps,stra);
	  
	  Mm->storestrain (lcid,ipp,eps);
	  
	  Mm->computenlstresses (ipp);
	  
	  ipp++;
	}
      }
    }
    destrv (w);  destrv (gp);
  }

  for (i=0;i<nne;i++){
    delete [] stra[i];
  }
  delete [] stra;
}


/**
   function computes internal forces

   @param lcid - number of load case
   @param eid - element id
   @param ri,ci - row and column indices
   @param ifor - vector of internal forces
   
   28.7.2001
*/
void linhex::nonloc_internal_forces (long lcid,long eid,long ri,long ci,vector &ifor)
{
  long i,j,k,l,ii,ipp;
  double xi,eta,zeta,jac;
  vector x(nne),y(nne),z(nne),w,gp,sig,contr(ndofe);
  matrix gm;


  Mt->give_node_coord3d (x,y,z,eid);
  
  fillv (0.0,ifor);

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

    allocv (intordsm[ii][ii],gp);
    allocv (intordsm[ii][ii],w);
    allocm (ncomp[ii],ndofe,gm);
    allocv (ncomp[ii],sig);
    
    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];
	for (k=0;k<intordsm[ii][ii];k++){
	  zeta=gp[k];
	  
	  Mm->compnonloc_nlstresses (ipp);
	  
	  Mm->givestress (lcid,ipp,cncomp[ii],ncomp[ii],sig);
	  
	  geom_matrix (gm,x,y,z,xi,eta,zeta,jac);
	  mtxv (gm,sig,contr);
	  
	  cmulv (jac*w[i]*w[j]*w[k],contr);
	  
	  for (l=0;l<contr.n;l++){
	    ifor[l]+=contr[l];
	  }
	  
	  ipp++;
	}
      }
    }
    destrv (sig);  destrm (gm);  destrv (w);  destrv (gp);
  }

}


/**
   function returns coordinates of integration points
   
   @param eid - element id
   @param ipp - integration point pointer
   @param coord - vector of coordinates
   
   10.1.2002
*/
void linhex::ipcoord (long eid,long ipp,long ri,long ci,vector &coord)
{
  long i,j,k,ii;
  double xi,eta,zeta;
  vector x(nne),y(nne),z(nne),w(intordsm[ri][ci]),gp(intordsm[ri][ci]);
  
  gauss_points (gp.a,w.a,intordsm[ri][ci]);
  Mt->give_node_coord3d (x,y,z,eid);
  ii=Mt->elements[eid].ipp[ri][ci];
  
  for (i=0;i<intordsm[ri][ci];i++){
    xi=gp[i];
    for (j=0;j<intordsm[ri][ci];j++){
      eta=gp[j];
      for (k=0;k<intordsm[ri][ci];k++){
	zeta=gp[k];
	if (ii==ipp){
	  coord[0]=approx (xi,eta,zeta,x);
	  coord[1]=approx (xi,eta,zeta,y);
	  coord[2]=approx (xi,eta,zeta,z);
	}
	ii++;
      }
    }
  }
}



void linhex::inicipval(long eid, long ri, long ci, matrix &nodval, inictype *ictn)
{
  long i, j, k, l, m, ipp;
  long ii, jj, nv = nodval.n;
  long nstra;
  double xi, eta, zeta, ipval;
  vector w, gp, anv(nne);

  nstra = 0;
  for (j = 0; j < nv; j++) // for all initial values
  {
    for(i = 0; i < nne; i++) // for all nodes on element
      anv[i] = nodval[i][j];
    for (ii = 0; ii < nb; ii++)
    {
      for (jj = 0; jj < nb; jj++)
      {
        ipp=Mt->elements[eid].ipp[ri+ii][ci+jj];
        if (intordsm[ii][jj] == 0)
          continue;
        allocv (intordsm[ii][jj],gp);
        allocv (intordsm[ii][jj],w);
        gauss_points (gp.a,w.a,intordsm[ii][jj]);
        for (k = 0; k < intordsm[ii][jj]; k++)
        {
          xi=gp[k];
          for (l = 0; l < intordsm[ii][jj]; l++)
          {
            eta=gp[l];
            for (m = 0; m < intordsm[ii][jj]; m++)
            {
              zeta=gp[m];
              //  value in integration point
              ipval = approx (xi,eta,zeta,anv);
              if ((ictn[i] & inistrain) && (j < Mm->ip[ipp].ncompstr))
              {
                Mm->ip[ipp].strain[j] += ipval;
                ipp++;
                continue;
              }
              if ((ictn[i] & inistress) && (j < nstra + Mm->ip[ipp].ncompstr))
              {
                Mm->ip[ipp].stress[j] += ipval;
                ipp++;
                continue;
              }
              if ((ictn[i] & iniother) && (j < nv))
              {
                Mm->ip[ipp].other[j] += ipval;
                ipp++;
                continue;
              }
              ipp++;
            }
          }
        }
        destrv (gp);  destrv (w);
      }
    }
    if (ictn[i] & inistrain) nstra++;
  }
}

/**
   function computes volume appropriate to integration point
   
   2.3.2004, JK
*/
void linhex::ipvolume (long eid,long ri,long ci)
{
  long i,j,k,ii,jj,ipp;
  double xi,eta,zeta,jac;
  vector x(nne),y(nne),z(nne),w,gp;
  
  Mt->give_node_coord3d (x,y,z,eid);
  
  for (ii=0;ii<nb;ii++){
    for (jj=0;jj<nb;jj++){
      if (intordsm[ii][jj]==0)  continue;

      allocv (intordsm[ii][jj],w);
      allocv (intordsm[ii][jj],gp);
      
      gauss_points (gp.a,w.a,intordsm[ii][jj]);
      
      ipp=Mt->elements[eid].ipp[ri+ii][ci+jj];
      
      for (i=0;i<intordsm[ii][jj];i++){
	xi=gp[i];
	for (j=0;j<intordsm[ii][jj];j++){
	  eta=gp[j];
	  for (k=0;k<intordsm[ii][jj];k++){
	    zeta=gp[k];
	    
	    jac_3d (jac,x,y,z,xi,eta,zeta);
	    jac=fabs(jac);
	    
	    jac*=w[i]*w[j]*w[k];
	    
	    Mm->storeipvol (ipp,jac);
	    ipp++;
	  }
	}
      }
      destrv (gp);  destrv (w);
    }
  }
  
}

/**
   function computes nodal forces caused by presure on surface
   
   @param eid - element id
   @param ri,ci - row and column indices
   @param nfor - vector of presure 
   @param eis - surface id 
   
   27.1.2006
*/
void linhex::node_forces_surf (long lcid,long eid,long *is,double *nv,vector &nf)
{
  long i,j;
  double xi,eta,zeta,jac;
  double *tnv;
  vector x(nne),y(nne),z(nne),gp,w,av(ndofe),v(ndofe);
  matrix n(napfun,ndofe),an(napfun,ndofe),am(ndofe,ndofe),tran(3,3);
  
  tnv = new double [12];

  //  coordinates of element nodes
  Mt->give_node_coord3d (x,y,z,eid);
  
  allocv (intordb,w);
  allocv (intordb,gp);
  gauss_points (gp.a,w.a,intordb);
  
  //  surface number 1

  if (is[0]>0 ){
    xi=1.0;
    for (i=0;i<intordb;i++){
      eta=gp[i];
      for (j=0;j<intordb;j++){
	zeta=gp[j];
	
	jac2d_3d (jac,x,y,z,eta,zeta,0);
	bf_matrix (n,xi,eta,zeta);
	jac = jac*w[i]*w[j];
	nnj (am.a,n.a,jac,n.m,n.n);
      }
    }
    
    if (is[0]==1){
      av[0] = nv[0*3+0];
      av[1] = nv[0*3+1];
      av[2] = nv[0*3+2];
      
      av[9] = nv[1*3+0];
      av[10] = nv[1*3+1];
      av[11] = nv[1*3+2];
      
      av[21] = nv[2*3+0];
      av[22] = nv[2*3+1];
      av[23] = nv[2*3+2];

      av[12] = nv[3*3+0];
      av[13] = nv[3*3+1];
      av[14] = nv[3*3+2];
    }


    if (is[0]==2){
      
      av[0] = nv[0*3+0];
      av[1] = nv[0*3+1];
      av[2] = nv[0*3+2];
      
      av[3] = nv[1*3+0];
      av[4] = nv[1*3+1];
      av[5] = nv[1*3+2];
      
      av[6] = nv[2*3+0];
      av[7] = nv[2*3+1];
      av[8] = nv[2*3+2];

      av[9]  = nv[3*3+0];
      av[10] = nv[3*3+1];
      av[11] = nv[3*3+2];
      
      locglob_nodeval (0,av,tnv,x,y,z);
      
      av[0] = tnv[0*3+0];
      av[1] = tnv[0*3+1];
      av[2] = tnv[0*3+2];
      
      av[9] = tnv[1*3+0];
      av[10] = tnv[1*3+1];
      av[11] = tnv[1*3+2];
      
      av[21] = tnv[2*3+0];
      av[22] = tnv[2*3+1];
      av[23] = tnv[2*3+2];

      av[12] = tnv[3*3+0];
      av[13] = tnv[3*3+1];
      av[14] = tnv[3*3+2];
    }


    mxv (am,av,v);
    addv (v,nf,nf);
  }


  //  surface number 2

  if (is[1]>0 ){
    eta=1.0;
    for (i=0;i<intordb;i++){
      xi=gp[i];
      for (j=0;j<intordb;j++){
	zeta=gp[j];
	
	jac2d_3d (jac,x,y,z,xi,zeta,1);
	bf_matrix (n,xi,eta,zeta);
	jac = jac*w[i]*w[j];
	nnj (am.a,n.a,jac,n.m,n.n);
      }
    }
    
    if (is[1]==1){
      av[3] = nv[12+0*3+0];
      av[4] = nv[12+0*3+1];
      av[5] = nv[12+0*3+2];
      
      av[0] = nv[12+1*3+0];
      av[1] = nv[12+1*3+1];
      av[2] = nv[12+1*3+2];
      
      av[12] = nv[12+2*3+0];
      av[13] = nv[12+2*3+1];
      av[14] = nv[12+2*3+2];

      av[15] = nv[12+3*3+0];
      av[16] = nv[12+3*3+1];
      av[17] = nv[12+3*3+2];
    }


    if (is[1]==2){
      
      av[0] = nv[12+0*3+0];
      av[1] = nv[12+0*3+1];
      av[2] = nv[12+0*3+2];
      
      av[3] = nv[12+1*3+0];
      av[4] = nv[12+1*3+1];
      av[5] = nv[12+1*3+2];
      
      av[6] = nv[12+2*3+0];
      av[7] = nv[12+2*3+1];
      av[8] = nv[12+2*3+2];

      av[9]  = nv[12+3*3+0];
      av[10] = nv[12+3*3+1];
      av[11] = nv[12+3*3+2];
      
      locglob_nodeval (1,av,tnv,x,y,z);
      
      av[3] = tnv[0*3+0];
      av[4] = tnv[0*3+1];
      av[5] = tnv[0*3+2];
      
      av[0] = tnv[1*3+0];
      av[1] = tnv[1*3+1];
      av[2] = tnv[1*3+2];
      
      av[12] = tnv[2*3+0];
      av[13] = tnv[2*3+1];
      av[14] = tnv[2*3+2];

      av[15] = tnv[3*3+0];
      av[16] = tnv[3*3+1];
      av[17] = tnv[3*3+2];

    }

    mxv (am,av,v);
    addv (v,nf,nf);
  }

  //  surface number 3

  if (is[2]>0 ){
    xi=-1.0;
    for (i=0;i<intordb;i++){
      eta=gp[i];