dst.cpp

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

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

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

  nne=3;  ndofe=9;  tncomp=5;  napfun=3; ned=3;  nned=2;  
  intordmm=3; intordb=2; ssst=plate;
  nb=3; 
  
  ncomp = new long [nb];
  ncomp[0]=3;
  ncomp[1]=3;
  ncomp[2]=2;
  
  cncomp = new long [nb];
  cncomp[0]=0;
  cncomp[1]=0;
  cncomp[2]=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[0][2]=0;
  nip[1][0]=0;  nip[1][1]=3;  nip[1][2]=0;
  nip[2][0]=0;  nip[2][1]=0;  nip[2][2]=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[0][2]=0;
  intordsm[1][0]=0;  intordsm[1][1]=3; intordsm[1][2]=0;
  intordsm[2][0]=0;  intordsm[2][1]=0; intordsm[2][2]=1;
}

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

  delete [] cncomp;
  delete [] ncomp;
}

void dstelem::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 assembles matrix of base functions
   
   @param gm - geometric matrix
   @param x,y - array containing node coordinates
   @param l - areacoordinates
   
   15.3.2002
*/

void dstelem::tran_matrix (matrix &a,matrix &ct,long eid)
{
  double det,dj,gg,thick;
  long i,ipp;
  ivector nodes(nne);
  vector x(3),y(3),ax(3),ay(3),dl(3),t(nne);
  matrix dbx(3,3),dby(3,3),b(2,3),ba(3,3),dd(3,3),d(tncomp,tncomp);
  
  //  det is equal to double area of the element
  Mt->give_elemnodes (eid,nodes);
  Mt->give_node_coord2d (x,y,eid);
  ipp=Mt->elements[eid].ipp[0][0];
  Mm->matstiff (d,ipp);
  Mc->give_thickness (eid,nodes,t);
  thick = (t[0]+t[1]+t[2])/3.0;
  det = ((x[1]-x[0])*(y[2]-y[0])-(x[2]-x[0])*(y[1]-y[0]))/2.0;
  dl[0] = sqrt((x[1]-x[0])*(x[1]-x[0])+(y[1]-y[0])*(y[1]-y[0]));
  dl[1] = sqrt((x[2]-x[1])*(x[2]-x[1])+(y[2]-y[1])*(y[2]-y[1]));
  dl[2] = sqrt((x[0]-x[2])*(x[0]-x[2])+(y[0]-y[2])*(y[0]-y[2]));
  // matrix vector of sides {cos,sin} 
  ct[0][0]=(x[1]-x[0])/dl[0];
  ct[0][1]=(y[1]-y[0])/dl[0];
  ct[1][0]=(x[2]-x[1])/dl[1];
  ct[1][1]=(y[2]-y[1])/dl[1];
  ct[2][0]=(x[0]-x[2])/dl[2];
  ct[2][1]=(y[0]-y[2])/dl[2];
  //   der   dL(1)/dy
  ax[0]=(x[2]-x[1])/2./det;  ax[1]=(x[0]-x[2])/2./det;  ax[2]=(x[1]-x[0])/2./det;
  //   der   dL(1)/dx
  ay[0]=(y[1]-y[2])/2./det;  ay[1]=(y[2]-y[0])/2./det;  ay[2]=(y[0]-y[1])/2./det;
  // dl0= betwen node 1,2
  dj=ay[1]*ax[0]+ay[0]*ax[1];
  dbx[0][0]= 8.*ct[0][0]*ay[0]*ay[1];
  dbx[1][0]= 4.*ct[0][1]*dj;
  dbx[2][0]= 4.*ct[0][0]*dj +8.*ct[0][1]*ay[0]*ay[1];
  dby[0][0]= 4.*ct[0][0]*dj;
  dby[1][0]= 8.*ct[0][1]*ax[0]*ax[1];
  dby[2][0]= 8.*ct[0][0]*ax[0]*ax[1] +4.*ct[0][1]*dj;

  dj=ay[2]*ax[1]+ay[1]*ax[2];
  dbx[0][1]= 8.*ct[1][0]*ay[1]*ay[2];
  dbx[1][1]= 4.*ct[1][1]*dj;
  dbx[2][1]= 4.*ct[1][0]*dj +8.*ct[1][1]*ay[1]*ay[2];
  dby[0][1]= 4.*ct[1][0]*dj;
  dby[1][1]= 8.*ct[1][1]*ax[1]*ax[2];
  dby[2][1]= 8.*ct[1][0]*ax[1]*ax[2] +4.*ct[1][1]*dj;

  dj=ay[0]*ax[2]+ay[2]*ax[0];
  dbx[0][2]= 8.*ct[2][0]*ay[2]*ay[0];
  dbx[1][2]= 4.*ct[2][1]*dj;
  dbx[2][2]= 4.*ct[2][0]*dj +8.*ct[2][1]*ay[2]*ay[0];
  dby[0][2]= 4.*ct[2][0]*dj;
  dby[1][2]= 8.*ct[2][1]*ax[2]*ax[0];
  dby[2][2]= 8.*ct[2][0]*ax[2]*ax[0] +4.*ct[2][1]*dj;

  dmatblock (dd, d,0,0,thick);

//  dd[0][0]=0.45733E+06; dd[0][1]=0.11433E+06; dd[1][0]=0.11433E+06;
//  dd[1][1]=0.45733E+06; dd[2][2]=0.28583E+06;
//  dd[0][2]=0.0; dd[2][0]=0.0;dd[1][2]=0.0; dd[2][1]=0.0;
  gg=dd[2][2]/thick/thick*10.;
  for (i=0;i<3;i++){
     b[0][i]=(dd[0][0]*dbx[0][i]+dd[2][0]*dby[0][i]
             +dd[0][1]*dbx[1][i]+dd[2][1]*dby[1][i]
             +dd[0][2]*dbx[2][i]+dd[2][2]*dby[2][i])/gg;
     b[1][i]=(dd[1][0]*dby[0][i]+dd[2][0]*dbx[0][i]
             +dd[1][1]*dby[1][i]+dd[2][1]*dbx[1][i]
             +dd[1][2]*dby[2][i]+dd[2][2]*dbx[2][i])/gg;
  }

// vypocet matice transformace alfa-parametru do koncovych posunu
  dbx[0][0]=-.5*dl[0];
  dbx[1][0]=-dl[1]*(ct[0][0]*ct[1][0]+ct[0][1]*ct[1][1])/6.;
  dbx[2][0]=-dl[2]*(ct[0][0]*ct[2][0]+ct[0][1]*ct[2][1])/6.;
  dbx[0][1]=-dl[0]*(ct[1][0]*ct[0][0]+ct[1][1]*ct[0][1])/6.;
  dbx[1][1]=-.5*dl[1];
  dbx[2][1]=-dl[2]*(ct[1][0]*ct[2][0]+ct[1][1]*ct[2][1])/6.;
  dbx[0][2]=-dl[0]*(ct[2][0]*ct[0][0]+ct[2][1]*ct[0][1])/6.;
  dbx[1][2]=-dl[1]*(ct[2][0]*ct[1][0]+ct[2][1]*ct[1][1])/6.;
  dbx[2][2]=-.5*dl[2];

  for (i=0;i<3;i++){
     dbx[i][0]=dbx[i][0]+dl[i]*(ct[i][0]*b[0][0]+ct[i][1]*b[1][0]);
     dbx[i][1]=dbx[i][1]+dl[i]*(ct[i][0]*b[0][1]+ct[i][1]*b[1][1]);
     dbx[i][2]=dbx[i][2]+dl[i]*(ct[i][0]*b[0][2]+ct[i][1]*b[1][2]);
  }

   det= dbx[0][0]*dbx[1][1]*dbx[2][2]+dbx[0][1]*dbx[1][2]*dbx[2][0]+dbx[0][2]*dbx[1][0]*dbx[2][1]
       -dbx[0][1]*dbx[1][0]*dbx[2][2]-dbx[0][0]*dbx[1][2]*dbx[2][1]-dbx[0][2]*dbx[1][1]*dbx[2][0];
   ba[0][0]=(dbx[1][1]*dbx[2][2]-dbx[1][2]*dbx[2][1])/det;
   ba[0][1]=(dbx[0][2]*dbx[2][1]-dbx[0][1]*dbx[2][2])/det;
   ba[0][2]=(dbx[0][1]*dbx[1][2]-dbx[0][2]*dbx[1][1])/det;
   ba[1][0]=(dbx[1][2]*dbx[2][0]-dbx[1][0]*dbx[2][2])/det;
   ba[1][1]=(dbx[0][0]*dbx[2][2]-dbx[0][2]*dbx[2][0])/det;
   ba[1][2]=(dbx[0][2]*dbx[1][0]-dbx[0][0]*dbx[1][2])/det;
   ba[2][0]=(dbx[1][0]*dbx[2][1]-dbx[1][1]*dbx[2][0])/det;
   ba[2][1]=(dbx[0][1]*dbx[2][0]-dbx[0][0]*dbx[2][1])/det;
   ba[2][2]=(dbx[0][0]*dbx[1][1]-dbx[0][1]*dbx[1][0])/det;

  for (i=0;i<3;i++){
     a[i][0]=(-ba[i][0]+ba[i][2]);
     a[i][1]=-(ba[i][0]*ct[0][1]*dl[0]+ba[i][2]*ct[2][1]*dl[2])/2.;
     a[i][2]= (ba[i][0]*ct[0][0]*dl[0]+ba[i][2]*ct[2][0]*dl[2])/2.;
     a[i][3]=( ba[i][0]-ba[i][1]);
     a[i][4]=-(ba[i][0]*ct[0][1]*dl[0]+ba[i][1]*ct[1][1]*dl[1])/2.;
     a[i][5]= (ba[i][0]*ct[0][0]*dl[0]+ba[i][1]*ct[1][0]*dl[1])/2.;
     a[i][6]=( ba[i][1]-ba[i][2]);
     a[i][7]=-(ba[i][1]*ct[1][1]*dl[1]+ba[i][2]*ct[2][1]*dl[2])/2.;
     a[i][8]= (ba[i][1]*ct[1][0]*dl[1]+ba[i][2]*ct[2][0]*dl[2])/2.;
  }
/*
  fprintf (Out,"\n\n prvek cislo %ld",eid);
  for (j=0;j<3;j++){
		fprintf (Out,"\n");
	for (i=0;i<ndofe;i++){
		fprintf (Out," %20.10le",a[j][i]);
	}
  }
*/
}




void dstelem::geom_matrix_bconst (matrix &gm,vector &x,vector &y)
{
  double det;
  long i,i1,i2;
  vector ax(3),ay(3);
  
  //  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]))/2.;
  //   der   dL(1)/dy
  ax[0]=(x[2]-x[1])/2./det;  ax[1]=(x[0]-x[2])/2./det;  ax[2]=(x[1]-x[0])/2./det;
  //   der   dL(1)/dx
  ay[0]=(y[1]-y[2])/2./det;  ay[1]=(y[2]-y[0])/2./det;  ay[2]=(y[0]-y[1])/2./det;

  
  
  for (i=0;i<3;i++){
     i2=3*i+2;
     i1=i2-1;
     gm[0][i2]+=ay[i];
     gm[1][i1]+=-ax[i];
     gm[2][i2]+=ax[i];
     gm[2][i1]+=-ay[i];
  }
  
}
void dstelem::geom_matrix_b (matrix &gm,matrix &a,matrix &ct,vector &x,vector &y,vector &l)
{
  double det;
  long i,i2,i3;
  vector ax(3),ay(3);
  matrix ba(3,3);
  
  //  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]))/2.;
  //   der   dL(1)/dy
  ax[0]=(x[2]-x[1])/2./det;  ax[1]=(x[0]-x[2])/2./det;  ax[2]=(x[1]-x[0])/2./det;
  //   der   dL(1)/dx
  ay[0]=(y[1]-y[2])/2./det;  ay[1]=(y[2]-y[0])/2./det;  ay[2]=(y[0]-y[1])/2./det;
  
  for (i=0;i<3;i++){
     i2=i+1;
	 if (i2>2){i2=i2-3;}
     i3=i+2;
	 if (i3>2){i3=i3-3;}
	 ba[0][i]= 4.*ct[i][0]*( l[i2]*ay[i]+l[i]*ay[i2]+ay[i3]/3.);
     ba[1][i]= 4.*ct[i][1]*( l[i2]*ax[i]+l[i]*ax[i2]+ax[i3]/3.);
     ba[2][i]= 4.*ct[i][0]*( l[i2]*ax[i]+l[i]*ax[i2]+ax[i3]/3.)+4.*ct[i][1]*( l[i2]*ay[i]+l[i]*ay[i2]+ay[i3]/3.);
  }
  
  for (i=0;i<9;i++){
     gm[0][i]=ba[0][0]*a[0][i]+ba[0][1]*a[1][i]+ba[0][2]*a[2][i];
     gm[1][i]=ba[1][0]*a[0][i]+ba[1][1]*a[1][i]+ba[1][2]*a[2][i];
     gm[2][i]=ba[2][0]*a[0][i]+ba[2][1]*a[1][i]+ba[2][2]*a[2][i];

  }

  
}

void dstelem::geom_matrix_shear (matrix &gs,matrix &a,matrix &ct,long eid)
{
  double det,dj,gg,thick;
  long i,ipp;
  ivector nodes(nne);
  vector x(3),y(3),ax(3),ay(3),dl(3),t(nne);
  matrix dbx(3,3),dby(3,3),dd(3,3),b(2,3),d(tncomp,tncomp);
  
  Mt->give_elemnodes (eid,nodes);
  Mt->give_node_coord2d (x,y,eid);
  ipp=Mt->elements[eid].ipp[0][0];
  Mm->matstiff (d,ipp);
  Mc->give_thickness (eid,nodes,t);
  thick = (t[0]+t[1]+t[2])/3.;
//  thick=0.7;
  //  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]))/2.;
  dl[0] = sqrt((x[1]-x[0])*(x[1]-x[0])+(y[1]-y[0])*(y[1]-y[0]));
  dl[1] = sqrt((x[2]-x[1])*(x[2]-x[1])+(y[2]-y[1])*(y[2]-y[1]));
  dl[2] = sqrt((x[0]-x[2])*(x[0]-x[2])+(y[0]-y[2])*(y[0]-y[2]));
  //   der   dL(1)/dy
  ax[0]=(x[2]-x[1])/2./det;  ax[1]=(x[0]-x[2])/2./det;  ax[2]=(x[1]-x[0])/2./det;
  //   der   dL(1)/dx
  ay[0]=(y[1]-y[2])/2./det;  ay[1]=(y[2]-y[0])/2./det;  ay[2]=(y[0]-y[1])/2./det;
  // dl0= betwen node 1,2
  dj=ay[1]*ax[0]+ay[0]*ax[1];
  dbx[0][0]= 8.*ct[0][0]*ay[0]*ay[1];
  dbx[1][0]= 4.*ct[0][1]*dj;
  dbx[2][0]= 4.*ct[0][0]*dj +8.*ct[0][1]*ay[0]*ay[1];
  dby[0][0]= 4.*ct[0][0]*dj;
  dby[1][0]= 8.*ct[0][1]*ax[0]*ax[1];
  dby[2][0]= 8.*ct[0][0]*ax[0]*ax[1] +4.*ct[0][1]*dj;

  dj=ay[2]*ax[1]+ay[1]*ax[2];
  dbx[0][1]= 8.*ct[1][0]*ay[1]*ay[2];
  dbx[1][1]= 4.*ct[1][1]*dj;
  dbx[2][1]= 4.*ct[1][0]*dj +8.*ct[1][1]*ay[1]*ay[2];
  dby[0][1]= 4.*ct[1][0]*dj;
  dby[1][1]= 8.*ct[1][1]*ax[1]*ax[2];
  dby[2][1]= 8.*ct[1][0]*ax[1]*ax[2] +4.*ct[1][1]*dj;

  dj=ay[0]*ax[2]+ay[2]*ax[0];
  dbx[0][2]= 8.*ct[2][0]*ay[2]*ay[0];
  dbx[1][2]= 4.*ct[2][1]*dj;
  dbx[2][2]= 4.*ct[2][0]*dj +8.*ct[2][1]*ay[2]*ay[0];
  dby[0][2]= 4.*ct[2][0]*dj;
  dby[1][2]= 8.*ct[2][1]*ax[2]*ax[0];
  dby[2][2]= 8.*ct[2][0]*ax[2]*ax[0] +4.*ct[2][1]*dj;

  dmatblock (dd, d,0,0,thick);
//  dd[0][0]=0.45733E+06; dd[0][1]=0.11433E+06; dd[1][0]=0.11433E+06;
//  dd[1][1]=0.45733E+06; dd[2][2]=0.28583E+06;
//  dd[0][2]=0.0; dd[2][0]=0.0;dd[1][2]=0.0; dd[2][1]=0.0;
  gg=dd[2][2]/thick/thick*10.;
  for (i=0;i<3;i++){
     b[0][i]=(dd[0][0]*dbx[0][i]+dd[2][0]*dby[0][i]
              +dd[0][1]*dbx[1][i]+dd[2][1]*dby[1][i]
              +dd[0][2]*dbx[2][i]+dd[2][2]*dby[2][i])/gg;
     b[1][i]=(dd[1][0]*dby[0][i]+dd[2][0]*dbx[0][i]
              +dd[1][1]*dby[1][i]+dd[2][1]*dbx[1][i]
              +dd[1][2]*dby[2][i]+dd[2][2]*dbx[2][i])/gg;
  }
  for (i=0;i<9;i++){
     gs[0][i]=b[0][0]*a[0][i]+b[0][1]*a[1][i]+b[0][2]*a[2][i];
     gs[1][i]=b[1][0]*a[0][i]+b[1][1]*a[1][i]+b[1][2]*a[2][i];
  }

}

  
  
void dstelem::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 extracts components of the shear
   part of stiffness matrix of the material to the matrix ds
   20.3.2002
*/
void dstelem::dmatblock (matrix &dd,matrix &d,long ri, long ci, double t)
{
  double c;
  
  c=t*t*t;
  fillm (0.0,dd);

  if ((ri==0 && ci==0)||(ri==1 && ci==1)){
  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==2 && ci==2){
    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;
  }
}

/**
   function computes stiffness matrix of dst element
   
   @param eid - element id
   @param sm - stiffness matrix

   15.3.2002
*/