linhex_nb1.cpp

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

  double xi,eta,zeta,jac;
  vector x(nne),y(nne),z(nne),w,gp;
  matrix gm,d(tncomp,tncomp);
  
  Mt->give_node_coord3d (x,y,z,eid);
  
  fillm (0.0,sm);

  for (ii=0;ii<nb;ii++){
    allocm (ncomp[ii],ndofe,gm);
    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];
	    
	    //  geometric matrices
	    geom_matrix (gm,x,y,z,xi,eta,zeta,jac);
	    
	    Mm->matstiff (d,ipp);  ipp++;
	    
	    jac*=w[i]*w[j]*w[k];
	    
	    //  contribution to the stiffness matrix of the element
	    bdbjac (sm,gm,d,gm,jac);
	    
	  }
	}
      }
      destrv (gp);  destrv (w);
    }
    destrm (gm);
  }
  
  //  transformation of stiffness matrix
  ivector nodes (nne);
  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 stiffness %matrix of quadrilateral finite element
   
   function computes stiffness %matrix for geometrically nonlinear problems
   
   @param lcid - load case id
   @param eid - element id
   @param ri,ci - row and column indices
   @param sm - stiffness %matrix
   @param x,y - vectors of nodal coordinates
   
   JK, 21.9.2005
*/
void linhex::gnl_stiffness_matrix (long lcid,long eid,long ri,long ci,matrix &sm)
{
  long i,j,k,ipp;
  double xi,eta,zeta,jac,jac2;
  ivector cn(ndofe);
  vector w,gp,sig(tncomp),r(ndofe),x(nne),y(nne),z(nne);
  matrix gm(tncomp,ndofe),grm(9,ndofe),d(tncomp,tncomp),s(9,9);
  
  //  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);
  
  //  component setting to zero
  fillm (0.0,sm);
  
  //  array for weights of integration points
  allocv (intordsm[0][0],w);
  //  array for coordinates of integration points
  allocv (intordsm[0][0],gp);
  
  //  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];
	
	//
	//  linear stiffness matrix and inital deformation matrix
	//
	
	//  strain-displacement matrix
	gngeom_matrix (gm,r,x,y,z,xi,eta,zeta,jac);
	
	//  stiffness matrix of the material
	Mm->matstiff (d,ipp);
	
	jac*=w[i]*w[j]*w[k];
	
	//  contribution to the stiffness matrix of the element
	bdbjac (sm,gm,d,gm,jac);
	
	
	//
	//  initial stress matrix
	//
	
	//  gradient matrix
	gnl_grmatrix (grm,x,y,z,xi,eta,zeta,jac2);
	
	//  stresses
	Mm->givestress (lcid,ipp,sig);
	
	s[0][0]=sig[0];  s[0][1]=sig[5];  s[0][2]=sig[4];
	s[1][0]=sig[5];  s[1][1]=sig[1];  s[1][2]=sig[3];
	s[2][0]=sig[4];  s[2][1]=sig[3];  s[2][2]=sig[2];
	
	s[3][3]=sig[0];  s[3][4]=sig[5];  s[3][5]=sig[4];
	s[4][3]=sig[5];  s[4][4]=sig[1];  s[4][5]=sig[3];
	s[5][3]=sig[4];  s[5][4]=sig[3];  s[5][5]=sig[2];
	
	s[6][6]=sig[0];  s[6][7]=sig[5];  s[6][8]=sig[4];
	s[7][6]=sig[5];  s[7][7]=sig[1];  s[7][8]=sig[3];
	s[8][6]=sig[4];  s[8][7]=sig[3];  s[8][8]=sig[2];
	
	
	
	//  contribution to the stiffness matrix of the element
	bdbjac (sm,grm,s,grm,jac);
	
	ipp++;
      }
    }
  }
  
  destrv (gp);  destrv (w);
  
}


/**
   function assembles resulting stiffness matrix of the element
   
   @param lcid - load case id
   @param eid - element id
   @param sm - stiffness matrix
   
   JK, 9.5.2002
*/
void linhex::res_stiffness_matrix (long lcid,long eid,matrix &sm)
{
  gl_stiffness_matrix (eid,0,0,sm);
  //gnl_stiffness_matrix (lcid,eid,0,0,sm);
}

/**
   function computes mass matrix

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

   19.7.2001
*/
void linhex::mass_matrix (long eid,matrix &mm)
{
  long i,j,k;
  double jac,xi,eta,zeta,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];
    for (j=0;j<intordmm;j++){
      eta=gp[j];
      for (k=0;k<intordmm;k++){
	zeta=gp[k];
	
	jac_3d (jac,x,y,z,xi,eta,zeta);
	
	jac=fabs(jac);

	bf_matrix (n,xi,eta,zeta);

	rho = approx (xi,eta,zeta,dens);
	
	jac*=w[i]*w[j]*w[k]*rho;
	
	nnj (mm.a,n.a,jac,n.m,n.n);
      }
    }
  }
  
}

/**
   function computes load matrix

   @param eid - number of element
   @param lm - load matrix
   
   25.7.2001
*/
void linhex::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;
	
	//jac=fabs(jac);
	//if (jac<0.0)  fprintf (stderr,"\n zaporny jakobian ve funkci load_matrix");

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





/**
   function computes strains at integration points
   
   @param lcid - load case id
   @param eid - element id
   
   JK
*/
void linhex::res_mainip_strains (long lcid,long eid)
{
  long i;
  ivector nodes(nne),cn(ndofe);
  vector x(nne),y(nne),z(nne),r(ndofe),aux;
  matrix 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);
    copyv (aux,r);
    destrv (aux);
    destrm (tmat);
  }
  
  gl_mainip_strains (lcid,eid,0,0,x,y,z,r);
  //gnl_mainip_strains (lcid,eid,0,0,x,y,z,r);
  
}


/**
   function computes block of 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
   
   10.5.2002
*/
void linhex::gl_mainip_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;
  matrix gm;
  
  for (ii=0;ii<nb;ii++){
    
    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],eps);
	  
	  ipp++;
	}
      }
    }
    
    destrm (gm);  destrv (w);  destrv (gp);
    destrv (eps);
  }
}

/**
   function computes strains at integration points of element
   function is used in geometrically linear problems
   
   @param lcid - load case id
   @param eid - element id
   @param ri,ci - row and column indices
   @param ii - number of block
   @param x,y,z - arrays with node coordinates
   @param r - %vector of nodal displacements
   
   JK, 24.9.2005
*/
void linhex::gnl_mainip_strains (long lcid,long eid,long ri,long ci,vector &x,vector &y,vector &z,vector &r)
{
  long i,j,k,ipp;
  double xi,eta,zeta,jac,b11r,b12r,b13r,b21r,b22r,b23r,b31r,b32r,b33r;
  vector gp,w,eps;
  vector b11(ndofe),b12(ndofe),b13(ndofe),b21(ndofe),b22(ndofe),b23(ndofe),b31(ndofe),b32(ndofe),b33(ndofe);
  
  allocv (intordsm[0][0],gp);
  allocv (intordsm[0][0],w);
  allocv (tncomp,eps);
  
  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];
	
	bvectors (x,y,z,xi,eta,zeta,jac,b11,b12,b13,b21,b22,b23,b31,b32,b33);
	
	scprd (b11,r,b11r);
	scprd (b12,r,b12r);
	scprd (b13,r,b13r);
	scprd (b21,r,b21r);
	scprd (b22,r,b22r);
	scprd (b23,r,b23r);
	scprd (b31,r,b31r);
	scprd (b32,r,b32r);
	scprd (b33,r,b33r);
	
	eps[0] = b11r + 0.5*b11r*b11r + 0.5*b21r*b21r + 0.5*b31r*b31r;
	eps[1] = b22r + 0.5*b12r*b12r + 0.5*b22r*b22r + 0.5*b32r*b32r;
	eps[2] = b33r + 0.5*b13r*b13r + 0.5*b23r*b23r + 0.5*b33r*b33r;

	eps[3] = b23r+b32r + b12r*b13r + b22r*b23r + b32r*b33r;
	eps[4] = b31r+b13r + b13r*b11r + b23r*b21r + b33r*b31r;
	eps[5] = b12r+b21r + b11r*b12r + b21r*b22r + b31r*b32r;
	
	
	Mm->storestrain (lcid,ipp,eps);
	ipp++;
      }
    }
  }
  
  destrv (eps);  destrv (w);  destrv (gp);
  
}



/**
   function computes strains in nodes of element
   
   @param lcid - load case id
   @param eid - element id
   
   10.5.2002
*/
void linhex::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 nodal strains directly
   
   @param lcid - load case id
   @param eid - element id
   @param stra - array for strain components
   
   JK, 26.9.2004
*/
void linhex::nod_strains_comp (long lcid,long eid,double **stra)
{
  long i,j;
  double jac;
  ivector cn(ndofe),nodes(nne);
  vector x(nne),y(nne),z(nne),nxi(nne),neta(nne),nzeta(nne),r(ndofe),eps(tncomp),aux;
  matrix tmat,gm(tncomp,ndofe);
  
  //  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);
    copyv (aux,r);
    destrv (aux);
    destrm (tmat);
  }
  
  //  natural coordinates of element nodes
  nodecoord (nxi,neta,nzeta);
  
  //  loop over nodes
  for (i=0;i<nne;i++){
    //  geometric matrix
    geom_matrix (gm,x,y,z,nxi[i],neta[i],nzeta[i],jac);
    //  strain computation
    mxv (gm,r,eps);
    
    for (j=0;j<eps.n;j++){
      stra[i][j]=eps[j];
    }
  }

}

/**
   function computes strains on element
   
   @param val - array containing strains on element
   @param lcid - load case id
   @param eid - element id
   
   19.9.2002
*/
/*  zruseno 26.9.2004
void linhex::elem_strains (double **stra,long lcid,long eid,long ri,long ci)
{
  long i,j,k,ii,ipp;
  double xi,eta,zeta,*lsm,*lhs,*rhs;
  vector nxi(nne),neta(nne),nzeta(nne),gp,w,eps,natcoord(3);

  lsm = new double [16];

  nodecoord (nxi,neta,nzeta);
  
  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]*4];
    rhs = new double [ncomp[ii]*4];
    gauss_points (gp.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=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->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 (gp);
  }
  
  delete [] lsm;
}
*/


/**
   function computes strains in arbitrary point on element
   
   @param lcid - load case id
   @param eid - element id
   @param xi, eta, zeta - natural coordinates of the point
   @param fi - first index
   @param ncomp - number of components
   @param eps - array containing strains
   
   11.5.2002
*/
void linhex::appstrain (long lcid,long eid,double xi,double eta,double zeta,long fi,long ncomp,vector &eps)
{
  long i,j,k;
  ivector nod(nne);
  vector nodval(nne);
  
  if (ncomp != eps.n){
    fprintf (stderr,"\n\n wrong interval of indices in function strain (%s, line %d).\n",__FILE__,__LINE__);
    abort ();
  }

  Mt->give_elemnodes (eid,nod);
  k=0;
  for (i=fi;i<fi+ncomp;i++){
    for (j=0;j<nne;j++){
      nodval[j]=Mt->nodes[nod[j]].strain[lcid*tncomp+i];
    }
    eps[k]=approx (xi,eta,zeta,nodval);
    k++;
  }
}

/**