quadhex.cpp

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

#include "quadhex.h"
#include "linhex.h"
#include "global.h"
#include "globmat.h"
#include "genfile.h"
#include "node.h"
#include "element.h"
#include "loadcase.h"
#include "intpoints.h"
#include <stdlib.h>


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

  //  number of nodes on element
  nne=20;
  //  number of DOFs on element
  ndofe=60;
  //  number of strain/stress components
  tncomp=6;
  //  number of functions approximated
  napfun=3;
  //  order of numerical integration of mass matrix
  intordmm=2;
  //  number of edges on element
  ned=12;
  //  number of nodes on one edge
  nned=3;
  //  order of numerical integration on element edges (boundaries)
  intordb=3;
  //  number of surfaces on element
  nsurf=6;
  //  number of nodes on one surface
  nnsurf=8;
  //  strain/stress state
  ssst=spacestress;
  
  //  number of blocks (parts of geometric matrix)
  nb=1;

  //  number of strain/stress components
  ncomp = new long [nb];
  ncomp[0]=6;
  
  //  cumulative number of components approximated
  cncomp = new long [nb];
  cncomp[0]=0;

  //  number of integration points
  //  order of numerical integration of stiffness matrix
  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]=27;
  
  //  total number of integration points
  tnip=0;
  for (i=0;i<nb;i++){
    for (j=0;j<nb;j++){
      tnip+=nip[i][j];
    }
  }

  intordsm[0][0]=3;

}

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

void quadhex::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 xi,eta,zeta - natural coordinates
   @param nodval - nodal values
   
   JK, 20.8.2001
*/
double quadhex::approx (double xi,double eta,double zeta,vector &nodval)
{
  double f;
  vector bf(nne);
  
  bf_quad_hex_3d (bf.a,xi,eta,zeta);
  
  scprd (bf,nodval,f);
  
  return f;
}

/**
   function assembles %matrix of base functions
   
   @param n - %matrix of base functions
   @param xi,eta,zeta - coordinates

   JK, 16.8.2001
*/
void quadhex::bf_matrix (matrix &n,double xi,double eta,double zeta)
{
  long i,j,k,l;
  vector bf(nne);
  
  fillm (0.0,n);

  bf_quad_hex_3d (bf.a,xi,eta,zeta);
  
  j=0;  k=1;  l=2;
  for (i=0;i<nne;i++){
    n[0][j]=bf[i];  j+=3;
    n[1][k]=bf[i];  k+=3;
    n[2][l]=bf[i];  l+=3;
  }
}

/**
   function computes strain-displacement (geometric) %matrix

   @param gm - geometric %matrix
   @param x,y,z - vectors containing element node coordinates
   @param xi,eta,zeta - coordinates
   @param jac - Jacobian

   JK, 16.8.2001
*/
void quadhex::geom_matrix (matrix &gm,vector &x,vector &y,vector &z,
			   double xi,double eta,double zeta,double &jac)
{
  long i,j,k,l;
  vector dx(nne),dy(nne),dz(nne);

  dx_bf_quad_hex_3d (dx.a,xi,eta,zeta);
  dy_bf_quad_hex_3d (dy.a,xi,eta,zeta);
  dz_bf_quad_hex_3d (dz.a,xi,eta,zeta);

  derivatives_3d (dx,dy,dz,jac,x,y,z,xi,eta,zeta);

  fillm (0.0,gm);

  j=0;  k=1;  l=2;
  for (i=0;i<nne;i++){
    gm[0][j]=dx[i];
    gm[1][k]=dy[i];
    gm[2][l]=dz[i];
    
    gm[3][k]=dz[i];
    gm[3][l]=dy[i];
    
    gm[4][j]=dz[i];
    gm[4][l]=dx[i];
    
    gm[5][j]=dy[i];
    gm[5][k]=dx[i];
    
    j+=3;  k+=3;  l+=3;
  }
}



/**
   function assembles transformation %matrix from local nodal coordinate
   system to the global coordinate system x_g = T x_l
   
   @param nodes - nodes of element
   @param tmat - transformation %matrix
   
   JK
*/
void quadhex::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

   JK, 16.8.2001
*/
void quadhex::stiffness_matrix (long eid,long ri,long ci,matrix &sm)
{
  long i,j,k,ipp;
  double xi,eta,zeta,jac;
  vector x(nne),y(nne),z(nne),w,gp;
  matrix gm(tncomp,ndofe),d(tncomp,tncomp);
  
  Mt->give_node_coord3d (x,y,z,eid);
  fillm (0.0,sm);

  allocv (intordsm[0][0],w);
  allocv (intordsm[0][0],gp);
  
  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];
      for (k=0;k<intordsm[0][0];k++){
	zeta=gp[k];
	
	//  geometric matrix
	geom_matrix (gm,x,y,z,xi,eta,zeta,jac);
	
	//  stiffness matrix of the material
	Mm->matstiff (d,ipp);  ipp++;
	
	jac*=w[i]*w[j]*w[k];
	
	bdbjac (sm,gm,d,gm,jac);
      }
    }
  }
  
  destrv (gp);  destrv (w);
  
  
}

/**
   function computes stiffness %matrix of one element

   @param eid - number of element
   @param sm - stiffness %matrix

   JK, 16.8.2001
*/
void quadhex::res_stiffness_matrix (long eid,matrix &sm)
{
  long transf;
  ivector nodes (nne);
  
  stiffness_matrix (eid,0,0,sm);
  
  //  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
   
   @param eid - number of element
   @param mm - mass %matrix

   JK, 16.8.2001
*/
void quadhex::mass_matrix (long eid,matrix &mm)
{
  long i,j,k;
  double jac,xi,eta,zeta,w1,w2,w3,rho;
  ivector nodes (nne);
  vector x(nne),y(nne),z(nne),w(intordmm),gp(intordmm),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 (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[j];
      for (k=0;k<intordmm;k++){
	zeta=gp[k];  w3=w[k];
	
	jac_3d (jac,x,y,z,xi,eta,zeta);

	bf_matrix (n,xi,eta,zeta);

	rho = approx (xi,eta,zeta,dens);
	
	jac*=w1*w2*w3*rho;
	
	nnj (mm.a,n.a,jac,n.m,n.n);
      }
    }
  }
  
}

/**
   function computes mass %matrix
   
   @param eid - number of element
   @param mm - mass %matrix

   JK, 16.8.2001
*/
void quadhex::res_mass_matrix (long eid,matrix &mm)
{
  long transf;
  ivector nodes(nne);
  
  mass_matrix (eid,mm);
  
  //  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 load %matrix
   
   @param eid - number of element
   @param lm - load %matrix
   
   JK, 16.8.2001
*/
void quadhex::load_matrix (long eid,matrix &lm)
{
  long i,j,k;
  double jac,xi,eta,zeta,w1,w2,w3;
  ivector nodes (nne);
  vector x(nne),y(nne),z(nne),w(intordmm),gp(intordmm);
  matrix n(napfun,ndofe);
  
  Mt->give_elemnodes (eid,nodes);
  Mt->give_node_coord3d (x,y,z,eid);
  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];
      for (k=0;k<intordmm;k++){
	zeta=gp[k];  w3=w[k];
	
	jac_3d (jac,x,y,z,xi,eta,zeta);

	bf_matrix (n,xi,eta,zeta);

	jac*=w1*w2*w3;
	
	nnj (lm.a,n.a,jac,n.m,n.n);
      }
    }
  }
  
}

/**
   function computes load %matrix
   
   @param eid - number of element
   @param lm - load %matrix
   
   JK, 16.8.2001
*/
void quadhex::res_load_matrix (long eid,matrix &lm)
{
  long transf;
  ivector nodes(nne);

  load_matrix (eid,lm);
  
  //  transformation of load 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 (lm,tmat);
  }

}



/**
   function computes strains at integration points
   
   @param lcid - load case id
   @param eid - element id
   
   JK, modified 23.11.2006
*/
void quadhex::res_ip_strains (long lcid,long eid)
{
  vector x(nne),y(nne),z(nne),r(ndofe),gp,w,eps,aux;
  ivector nodes(nne),cn(ndofe);
  matrix gm,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);
  }

  ip_strains (lcid,eid,0,0,x,y,z,r);
}

/**
   function computes strains at integration points of element
   
   @param lcid - load case id
   @param eid - element id
   @param ri - row index
   @param ci - column index
   @param x,y,z - %vectors of nodal coordinates
   @param r - %vector of nodal displacements
   
   JK, 10.5.2002, modified 27.11.2006
*/
void quadhex::ip_strains (long lcid,long eid,long ri,long ci,vector &x,vector &y,vector &z,vector &r)
{
  long i,j,k,ii,ipp;
  double xi,eta,zeta,jac;
  vector gp,w,eps,aux;
  ivector nodes(nne),cn(ndofe);
  matrix gm,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);
    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];
	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,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
   
   JK, 27.9.2005
*/
void quadhex::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_quadhex (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 strains in nodes of element
   
   @param lcid - load case id
   @param eid - element id
   @param stra - array for strain components
   
   stra[i][j] - the j-th strain component at the i-th node

   JK, 10.5.2002
*/
void quadhex::nod_strains_comp (long lcid,long eid,double **stra)
{
  long i,j;
  double jac;
  vector x(nne),y(nne),z(nne),nxi(nne),neta(nne),nzeta(nne),eps(tncomp),r(ndofe),aux;
  ivector cn(ndofe),nodes(nne);
  matrix gm(tncomp,ndofe),tmat;

  //  node coordinates
  Mt->give_node_coord3d (x,y,z,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_quadhex (nxi,neta,nzeta);

  //  loop over nodes