cct.cpp

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

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

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

  nne=3;  ndofe=9;  tncomp=5;  napfun=3;  ned=3;  nned=2;
  intordmm=3;  ssst=plate;

  nb=2;

  ncomp = new long [nb];
  ncomp[0]=3;
  ncomp[1]=2;

  cncomp = new long [nb];
  cncomp[0]=0;
  cncomp[1]=3;
  
  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;  nip[0][1]=0;
  nip[1][0]=0;  nip[1][1]=1;
  
  tnip=0;
  for (i=0;i<nb;i++){
    for (j=0;j<nb;j++){
      tnip+=nip[i][j];
    }
  }
  
  intordsm[0][0]=1;  intordsm[0][1]=0;
  intordsm[1][0]=0;  intordsm[1][1]=1;
}

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

  delete [] cncomp;
  delete [] ncomp;
}

void cctelem::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 areacoord - vector containing area coordinates
   @param nodval - nodal values

   28.3.2002
*/
double cctelem::approx (vector &areacoord,vector &nodval)
{
  double f;
  scprd (areacoord,nodval,f);
  return f;
}

/**
   function approximates function defined by nodal values

   @param xi,eta - natural coordinates
   @param nodval - nodal values

*/
double cctelem::approx_nat (double xi,double eta,vector &nodval)
{
  double f;
  vector areacoord(3);
  areacoord[0]=xi;
  areacoord[1]=eta;
  areacoord[2]=1.0-areacoord[0]-areacoord[1];
  scprd (areacoord,nodval,f);
  return f;
}


/**
   function assembles %matrix of approximation functions
   
   @param n - %matrix of approximation functions
   @param x,y - array containing node coordinates
   @param areacoord - array of area coordinates
   
   JK, 19.7.2001
*/
void cctelem::bf_matrix (matrix &n,vector &x,vector &y,vector &areacoord)
{
  vector bf(9),sx(3),sy(3);
  
  sx[0]=x[1]-x[0];  sx[1]=x[2]-x[1];  sx[2]=x[0]-x[2];
  sy[0]=y[1]-y[0];  sy[1]=y[2]-y[1];  sy[2]=y[0]-y[2];
  
  bf_cct (bf.a,areacoord.a,sx.a,sy.a);
  
  fillm (0.0,n);
  
  n[0][0]=bf[0];
  n[0][1]=bf[1];
  n[0][2]=bf[2];
  n[0][3]=bf[3];
  n[0][4]=bf[4];
  n[0][5]=bf[5];
  n[0][6]=bf[6];
  n[0][7]=bf[7];
  n[0][8]=bf[8];
  
  n[1][1]=bf[0];
  n[1][4]=bf[3];
  n[1][7]=bf[6];

  n[2][2]=bf[0];
  n[2][5]=bf[3];
  n[2][8]=bf[6];

}

/**
   function assembles part of geometric %matrix
   
   @param gm - geometric %matrix
   @param x,y - array containing node coordinates
   @param areacoord - area coordinates
   
   JK, 19.7.2001
*/
void cctelem::geom_matrix_block (matrix &gm,long bi,vector &x,vector &y,vector &areacoord)
{
  double det;
  vector sx(3),sy(3),b(3),c(3),bf(9),dx(9),dy(9);

  sx[0]=x[1]-x[0];  sx[1]=x[2]-x[1];  sx[2]=x[0]-x[2];
  sy[0]=y[1]-y[0];  sy[1]=y[2]-y[1];  sy[2]=y[0]-y[2];
  
  //  det is equal to double area of the element
  det = (x[1]-x[0])*(y[2]-y[0])-(x[2]-x[0])*(y[1]-y[0]);  
  
  plsb (b.a,y.a,det);
  plsc (c.a,x.a,det);
  
  bf_cct (bf.a,areacoord.a,sx.a,sy.a);
  dx_cct (dx.a,areacoord.a,b.a,sx.a,sy.a);
  dy_cct (dy.a,areacoord.a,c.a,sx.a,sy.a);
  
  fillm (0.0,gm);
  
  if (bi==0){
    gm[0][2]=dx[0];
    gm[0][5]=dx[3];
    gm[0][8]=dx[6];
    
    gm[1][1]=0.0-dy[0];
    gm[1][4]=0.0-dy[3];
    gm[1][7]=0.0-dy[6];
    
    gm[2][1]=0.0-dx[0];
    gm[2][2]=dy[0];
    gm[2][4]=0.0-dx[3];
    gm[2][5]=dy[3];
    gm[2][7]=0.0-dx[6];
    gm[2][8]=dy[6];
  }
  if (bi==1){
    gm[0][0]=dy[0];
    gm[0][1]=dy[1]-bf[0];
    gm[0][2]=dy[2];
    gm[0][3]=dy[3];
    gm[0][4]=dy[4]-bf[3];
    gm[0][5]=dy[5];
    gm[0][6]=dy[6];
    gm[0][7]=dy[7]-bf[6];
    gm[0][8]=dy[8];
    
    gm[1][0]=dx[0];
    gm[1][1]=dx[1];
    gm[1][2]=dx[2]+bf[0];
    gm[1][3]=dx[3];
    gm[1][4]=dx[4];
    gm[1][5]=dx[5]+bf[3];
    gm[1][6]=dx[6];
    gm[1][7]=dx[7];
    gm[1][8]=dx[8]+bf[6];
  }
  
}

/**
   function assembles geometric %matrix of the cct element
   
   @param gm - geometric %matrix
   @param x,y - array of node coordinates
   @param areacoord - area coordinates
   
   JK, 19.7.2001
*/
void cctelem::geom_matrix (matrix &gm,vector &x,vector &y,vector &areacoord)
{
  double det;
  vector sx(3),sy(3),b(3),c(3),bf(9),dx(9),dy(9);
  
  sx[0]=x[1]-x[0];  sx[1]=x[2]-x[1];  sx[2]=x[0]-x[2];
  sy[0]=y[1]-y[0];  sy[1]=y[2]-y[1];  sy[2]=y[0]-y[2];

  //  det is equal to double area of the element
  det = (x[1]-x[0])*(y[2]-y[0])-(x[2]-x[0])*(y[1]-y[0]);  

  plsb (b.a,y.a,det);
  plsc (c.a,x.a,det);
  
  bf_cct (bf.a,areacoord.a,sx.a,sy.a);
  dx_cct (dx.a,areacoord.a,b.a,sx.a,sy.a);
  dy_cct (dy.a,areacoord.a,c.a,sx.a,sy.a);

  fillm (0.0,gm);
  
  gm[0][2]=dx[0];
  gm[0][5]=dx[3];
  gm[0][8]=dx[6];
  
  gm[1][1]=0.0-dy[0];
  gm[1][4]=0.0-dy[3];
  gm[1][7]=0.0-dy[6];
  
  gm[2][1]=0.0-dx[0];
  gm[2][2]=dy[0];
  gm[2][4]=0.0-dx[3];
  gm[2][5]=dy[3];
  gm[2][7]=0.0-dx[6];
  gm[2][8]=dy[6];
  
  gm[3][0]=dy[0];
  gm[3][1]=dy[1]-bf[0];
  gm[3][2]=dy[2];
  gm[3][3]=dy[3];
  gm[3][4]=dy[4]-bf[3];
  gm[3][5]=dy[5];
  gm[3][6]=dy[6];
  gm[3][7]=dy[7]-bf[6];
  gm[3][8]=dy[8];
  
  gm[4][0]=dx[0];
  gm[4][1]=dx[1];
  gm[4][2]=dx[2]+bf[0];
  gm[4][3]=dx[3];
  gm[4][4]=dx[4];
  gm[4][5]=dx[5]+bf[3];
  gm[4][6]=dx[6];
  gm[4][7]=dx[7];
  gm[4][8]=dx[8]+bf[6];
}

/**
   function extracts blocks from stiffness %matrix of the material
   
   @param ri,ci - row and column indices
   @param d - stiffness %matrix of the material
   @param dd - required block from stiffness %matrix of material
   @param t - thickness of plate
   
   JK, 19.7.2001
*/
void cctelem::dmatblock (long ri,long ci,matrix &d,matrix &dd,double t)
{
  double c;
  
  c=t*t*t;
  fillm (0.0,dd);
  
  if (ri==0 && ci==0){
    dd[0][0] = c*d[0][0];  dd[0][1] = c*d[0][1];  dd[0][2] = c*d[0][2];
    dd[1][0] = c*d[1][0];  dd[1][1] = c*d[1][1];  dd[1][2] = c*d[1][2];
    dd[2][0] = c*d[2][0];  dd[2][1] = c*d[2][1];  dd[2][2] = c*d[2][2];
  }
  if (ri==1 && ci==1){
    dd[0][0] = t*d[3][3]*5.0/6.0;  dd[0][1] = 0.0;
    dd[1][0] = 0.0;                dd[1][1] = t*d[4][4]*5.0/6.0;
  }

}

void cctelem::dmat (matrix &d,double t)
{
  double c;
  
  c=t*t*t;
  
  d[0][0] = c*d[0][0];  d[0][1] = c*d[0][1];  d[0][2] = c*d[0][2];
  d[1][0] = c*d[1][0];  d[1][1] = c*d[1][1];  d[1][2] = c*d[1][2];
  d[2][0] = c*d[2][0];  d[2][1] = c*d[2][1];  d[2][2] = c*d[2][2];
  
  d[3][3] = t*d[3][3]*5.0/6.0;
  d[4][4] = t*d[4][4]*5.0/6.0;
}

/**
   nutna kontrola

   function assembles transformation %matrix 
*/
void cctelem::transf_matrix (ivector &nodes,matrix &tmat)
{
  long i,n,m;
  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+1][i*3+1]=Mt->nodes[nodes[i]].e1[0];  tmat[i*3+1][i*3+2]=Mt->nodes[nodes[i]].e2[0];
      tmat[i*3+2][i*3+1]=Mt->nodes[nodes[i]].e1[1];  tmat[i*3+2][i*3+2]=Mt->nodes[nodes[i]].e2[1];
    }
  }
}

/**
   function computes stiffness %matrix of cct element
   
   @param eid - element id
   @param ri,ci - row and column indices
   @param sm - stiffness %matrix
   
   JK, 19.7.2001
*/
void cctelem::stiffness_matrix (long eid,long ri,long ci,matrix &sm,vector &x,vector &y)
{
  long i,ii,jj,ipp;
  double jac,det,thick;
  ivector nodes(nne);
  vector l(3),t(nne),gp1,gp2,w,areacoord(3);
  matrix gmr,gmc,dd,d(tncomp,tncomp);
  
  Mt->give_elemnodes (eid,nodes);
  Mc->give_thickness (eid,nodes,t);

  //  det is equal to double area of the element
  det = (x[1]-x[0])*(y[2]-y[0])-(x[2]-x[0])*(y[1]-y[0]);  

  fillm (0.0,sm);
  

  for (ii=0;ii<nb;ii++){
    allocm (ncomp[ii],ndofe,gmr);
    for (jj=0;jj<nb;jj++){
      if (intordsm[ii][jj]==0)  continue;

      allocv (intordsm[ii][jj],w);
      allocv (intordsm[ii][jj],gp1);
      allocv (intordsm[ii][jj],gp2);
      
      allocm (ncomp[jj],ndofe,gmc);
      allocm (ncomp[ii],ncomp[jj],dd);
      
      gauss_points_tr (gp1.a,gp2.a,w.a,intordsm[ii][jj]);
      
      ipp=Mt->elements[eid].ipp[ri+ii][ci+jj];
      
      for (i=0;i<intordsm[ii][jj];i++){
	areacoord[0]=gp1[i];
	areacoord[1]=gp2[i];
	areacoord[2]=1.0-areacoord[0]-areacoord[1];
	
	thick = approx (areacoord,t);

	//  geometric matrix
	geom_matrix_block (gmr,ii,x,y,areacoord);
	geom_matrix_block (gmc,jj,x,y,areacoord);
	
	//  matrix of stiffness of the material
	Mm->matstiff (d,ipp);
	dmatblock (ii,jj,d,dd,thick);
	
	jac=w[i]*det;
	
	//  contribution to the stiffness matrix of the element
	bdbjac (sm,gmr,dd,gmc,jac);
	
	ipp++;
      }

      destrm (dd);  destrm (gmc);  destrv (gp2);  destrv (gp1);  destrv (w);
    }
    destrm (gmr);
  }

}

/**
   function assembles resulting stiffness %matrix of the element
   
   @param eid - element id
   @param sm - stiffness %matrix
   
   JK, 9.5.2002
*/
void cctelem::res_stiffness_matrix (long eid,matrix &sm)
{
  long transf;
  ivector nodes(nne);
  vector x(nne),y(nne);
  Mt->give_node_coord2d (x,y,eid);
  Mt->give_elemnodes (eid,nodes);

  stiffness_matrix (eid,0,0,sm,x,y);

  //  transformation of stiffness %matrix
  transf = Mt->locsystems (nodes);
  if (transf>0){
    matrix tmat (ndofe,ndofe);
    transf_matrix (nodes,tmat);
    glmatrixtransf (sm,tmat);
  }
}

/**
   function computes mass %matrix of the cct element
   
   @param eid - element id
   @param mm - mass %matrix
   
   JK, 19.7.2001
*/
void cctelem::mass_matrix (long eid,matrix &mm,vector &x,vector &y)
{
  long i;
  double det,ww,thick,rho;
  ivector nodes(nne);
  vector l(3),gp1(intordmm),gp2(intordmm),w(intordmm),t(nne),dens(nne);
  matrix n(3,ndofe);

  Mt->give_elemnodes (eid,nodes);
  Mc->give_thickness (eid,nodes,t);