linhex.cpp

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

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




linhex::linhex ()
{
  long i,j;

  //  number of nodes on element
  nne=8;
  //  number of DOFs on element
  ndofe=24;
  //  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=2;
  //  order of numerical integration on element edges (boundaries)
  intordb=2;
  //  number of surfaces on element
  nsurf=6;
  //  number of nodes on one surface
  nnsurf=4;
  //  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]=8;
  
  //  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]=2;
}

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

void linhex::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 linhex::approx (double xi,double eta,double zeta,vector &nodval)
{
  double f;
  vector bf(nne);
  
  bf_lin_hex_3d (bf.a,xi,eta,zeta);
  
  scprd (bf,nodval,f);

  return f;
}

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

   JK, 19.7.2001
*/
void linhex::bf_matrix (matrix &n,double xi,double eta,double zeta)
{
  long i,j,k,l;
  vector bf(nne);

  fillm (0.0,n);

  bf_lin_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 assembles strain-displacement (geometric) %matrix

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

   JK, 19.7.2001
*/
void linhex::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_lin_hex_3d (dx.a,eta,zeta);
  dy_bf_lin_hex_3d (dy.a,xi,zeta);
  dz_bf_lin_hex_3d (dz.a,xi,eta);

  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 auxiliary vectors B for evaluation of stiffness %matrix
   in geometrically nonlinear problems
   
   @param x,y,z - array containing node coordinates
   @param xi,eta,zeta - natural coordinates
   @param jac - Jacobian
   @param b11,b12,b13,b21,b22,b23,b31,b32,b33 - vectors of derivatives of shape functions
   
   JK, 24.9.2005
*/
void linhex::bvectors (vector &x,vector &y,vector &z,double xi,double eta,double zeta,double &jac,
		       vector &b11,vector &b12,vector &b13,
		       vector &b21,vector &b22,vector &b23,
		       vector &b31,vector &b32,vector &b33)
{
  vector dx(nne),dy(nne),dz(nne);
  
  dx_bf_lin_hex_3d (dx.a,eta,zeta);
  dy_bf_lin_hex_3d (dy.a,xi,zeta);
  dz_bf_lin_hex_3d (dz.a,xi,eta);
  
  derivatives_3d (dx,dy,dz,jac,x,y,z,xi,eta,zeta);
  
  fillv (0.0,b11);
  fillv (0.0,b12);
  fillv (0.0,b13);
  fillv (0.0,b21);
  fillv (0.0,b22);
  fillv (0.0,b23);
  fillv (0.0,b31);
  fillv (0.0,b32);
  fillv (0.0,b33);

  //  du/dx
  b11[0]=dx[0];  b11[3]=dx[1];  b11[6]=dx[2];  b11[9]=dx[3];   b11[12]=dx[4];  b11[15]=dx[5];  b11[18]=dx[6];  b11[21]=dx[7];
  //  du/dy
  b12[0]=dy[0];  b12[3]=dy[1];  b12[6]=dy[2];  b12[9]=dy[3];   b12[12]=dy[4];  b12[15]=dy[5];  b12[18]=dy[6];  b12[21]=dy[7];
  //  du/dz
  b13[0]=dz[0];  b13[3]=dz[1];  b13[6]=dz[2];  b13[9]=dz[3];   b13[12]=dz[4];  b13[15]=dz[5];  b13[18]=dz[6];  b13[21]=dz[7];

  //  dv/dx
  b21[1]=dx[0];  b21[4]=dx[1];  b21[7]=dx[2];  b21[10]=dx[3];  b21[13]=dx[4];  b21[16]=dx[5];  b21[19]=dx[6];  b21[22]=dx[7];
  //  dv/dy
  b22[1]=dy[0];  b22[4]=dy[1];  b22[7]=dy[2];  b22[10]=dy[3];  b22[13]=dy[4];  b22[16]=dy[5];  b22[19]=dy[6];  b22[22]=dy[7];
  //  dv/dz
  b23[1]=dz[0];  b23[4]=dz[1];  b23[7]=dz[2];  b23[10]=dz[3];  b23[13]=dz[4];  b23[16]=dz[5];  b23[19]=dz[6];  b23[22]=dz[7];

  //  dw/dx
  b31[2]=dx[0];  b31[5]=dx[1];  b31[8]=dx[2];  b31[11]=dx[3];  b31[14]=dx[4];  b31[17]=dx[5];  b31[20]=dx[6];  b31[23]=dx[7];
  //  dw/dy
  b32[2]=dy[0];  b32[5]=dy[1];  b32[8]=dy[2];  b32[11]=dy[3];  b32[14]=dy[4];  b32[17]=dy[5];  b32[20]=dy[6];  b32[23]=dy[7];
  //  dw/dz
  b33[2]=dz[0];  b33[5]=dz[1];  b33[8]=dz[2];  b33[11]=dz[3];  b33[14]=dz[4];  b33[17]=dz[5];  b33[20]=dz[6];  b33[23]=dz[7];

}

/**
   function computes strain-displacement %matrix for geometrically nonlinear problems
   
   @param gm - strain-displacement %matrix
   @param r - array of nodal displacements
   @param x,y,z - array containing node coordinates
   @param xi,eta,zeta - natural coordinates
   @param jac - Jacobian

   JK, 24.9.2005
*/
void linhex::gngeom_matrix (matrix &gm,vector &r,vector &x,vector &y,vector &z,double xi,double eta,double zeta,double &jac)
{
  long i;
  double b11r,b12r,b13r,b21r,b22r,b23r,b31r,b32r,b33r;
  vector b11(ndofe),b12(ndofe),b13(ndofe),b21(ndofe),b22(ndofe),b23(ndofe),b31(ndofe),b32(ndofe),b33(ndofe),av(ndofe);
  
  fillm (0.0,gm);
  
  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);
  
  
  // *******
  //  E_11
  // *******
  
  //  B11 dr
  for (i=0;i<ndofe;i++){
    gm[0][i]+=b11[i];
  }
  
  //  r B11 B11 dr
  cmulv(b11r,b11,av);
  for (i=0;i<ndofe;i++){
    gm[0][i]+=av[i];
  }
  
  //  r B21 B21 dr
  cmulv(b21r,b21,av);
  for (i=0;i<ndofe;i++){
    gm[0][i]+=av[i];
  }

  //  r B31 B31 dr
  cmulv(b31r,b31,av);
  for (i=0;i<ndofe;i++){
    gm[0][i]+=av[i];
  }

  
  // *******
  //  E_22
  // *******
  
  //  B22 dr
  for (i=0;i<ndofe;i++){
    gm[1][i]+=b22[i];
  }
  
  //  r B12 B12 dr
  cmulv(b12r,b12,av);
  for (i=0;i<ndofe;i++){
    gm[1][i]+=av[i];
  }
  
  //  r B22 B22 dr
  cmulv(b22r,b22,av);
  for (i=0;i<ndofe;i++){
    gm[1][i]+=av[i];
  }
  
  //  r B32 B32 dr
  cmulv(b32r,b32,av);
  for (i=0;i<ndofe;i++){
    gm[1][i]+=av[i];
  }
  
  // *******
  //  E_33
  // *******
  
  //  B33 dr
  for (i=0;i<ndofe;i++){
    gm[2][i]+=b22[i];
  }
  
  //  r B13 B13 dr
  cmulv(b13r,b13,av);
  for (i=0;i<ndofe;i++){
    gm[2][i]+=av[i];
  }
  
  //  r B23 B23 dr
  cmulv(b23r,b23,av);
  for (i=0;i<ndofe;i++){
    gm[2][i]+=av[i];
  }
  
  //  r B33 B33 dr
  cmulv(b33r,b33,av);
  for (i=0;i<ndofe;i++){
    gm[2][i]+=av[i];
  }
  

  // **************
  //  E_23 = E_32
  // **************
  
  //  (B23 + B32) dr
  for (i=0;i<ndofe;i++){
    gm[3][i]+=b23[i]+b32[i];
  }
  
  //  r B13 B12 dr
  cmulv(b13r,b12,av);
  for (i=0;i<ndofe;i++){
    gm[3][i]+=av[i];
  }
  
  //  r B12 B13 dr
  cmulv(b12r,b13,av);
  for (i=0;i<ndofe;i++){
    gm[3][i]+=av[i];
  }

  //  r B23 B22 dr
  cmulv(b23r,b22,av);
  for (i=0;i<ndofe;i++){
    gm[3][i]+=av[i];
  }
  
  //  r B22 B23 dr
  cmulv(b22r,b23,av);
  for (i=0;i<ndofe;i++){
    gm[3][i]+=av[i];
  }
  
  //  r B33 B32 dr
  cmulv(b33r,b32,av);
  for (i=0;i<ndofe;i++){
    gm[3][i]+=av[i];
  }
  
  //  r B32 B33 dr
  cmulv(b32r,b33,av);
  for (i=0;i<ndofe;i++){
    gm[3][i]+=av[i];
  }
  
  // **************
  //  E_31 = E_13
  // **************
  
  //  (B31 + B13) dr
  for (i=0;i<ndofe;i++){
    gm[4][i]+=b31[i]+b13[i];
  }
  
  //  r B11 B13 dr
  cmulv(b11r,b13,av);
  for (i=0;i<ndofe;i++){
    gm[4][i]+=av[i];
  }
  
  //  r B13 B11 dr
  cmulv(b13r,b11,av);
  for (i=0;i<ndofe;i++){
    gm[4][i]+=av[i];
  }

  //  r B21 B23 dr
  cmulv(b21r,b23,av);
  for (i=0;i<ndofe;i++){
    gm[4][i]+=av[i];
  }
  
  //  r B23 B21 dr
  cmulv(b23r,b21,av);
  for (i=0;i<ndofe;i++){
    gm[4][i]+=av[i];
  }
  
  //  r B31 B33 dr
  cmulv(b31r,b33,av);
  for (i=0;i<ndofe;i++){
    gm[4][i]+=av[i];
  }
  
  //  r B33 B31 dr
  cmulv(b33r,b31,av);
  for (i=0;i<ndofe;i++){
    gm[4][i]+=av[i];
  }


  // **************
  //  E_12 = E_21
  // **************
  
  //  (B12 + B21) dr
  for (i=0;i<ndofe;i++){
    gm[5][i]+=b12[i]+b21[i];
  }
  
  //  r B12 B11 dr
  cmulv(b12r,b11,av);
  for (i=0;i<ndofe;i++){
    gm[5][i]+=av[i];
  }
  
  //  r B11 B12 dr
  cmulv(b11r,b12,av);
  for (i=0;i<ndofe;i++){
    gm[5][i]+=av[i];
  }

  //  r B22 B21 dr
  cmulv(b22r,b21,av);
  for (i=0;i<ndofe;i++){
    gm[5][i]+=av[i];
  }
  
  //  r B21 B22 dr
  cmulv(b21r,b22,av);
  for (i=0;i<ndofe;i++){
    gm[5][i]+=av[i];
  }
  
  //  r B32 B31 dr
  cmulv(b32r,b31,av);
  for (i=0;i<ndofe;i++){
    gm[5][i]+=av[i];
  }
  
  //  r B31 B32 dr
  cmulv(b31r,b32,av);
  for (i=0;i<ndofe;i++){
    gm[5][i]+=av[i];
  }
  


}


/**
   function computes gradient %matrix for geometrically nonlinear problems
   
   @param grm - gradient %matrix
   @param x,y,z - array containing node coordinates
   @param xi,eta,zeta - natural coordinates
   @param jac - Jacobian

   JK, 24.9.2005
*/
void linhex::gnl_grmatrix (matrix &grm,vector &x,vector &y,vector &z,double xi,double eta,double zeta,double &jac)
{
  long i;
  vector b11(ndofe),b12(ndofe),b13(ndofe),b21(ndofe),b22(ndofe),b23(ndofe),b31(ndofe),b32(ndofe),b33(ndofe);
  
  bvectors (x,y,z,xi,eta,zeta,jac,b11,b12,b13,b21,b22,b23,b31,b32,b33);
  
  for (i=0;i<ndofe;i++){
    grm[0][i]=b11[i];
    grm[1][i]=b12[i];
    grm[2][i]=b13[i];
    grm[3][i]=b21[i];
    grm[4][i]=b22[i];
    grm[5][i]=b23[i];
    grm[6][i]=b31[i];
    grm[7][i]=b32[i];
    grm[8][i]=b33[i];
  }
}




/**
   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 linhex::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

   function computes stiffness %matrix for geometrically linear problems

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

   JK, 19.7.2001
*/
void linhex::gl_stiffness_matrix (long eid,long ri,long ci,matrix &sm)
{
  long i,j,k,ii,jj,ipp,transf;
  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++){