dkt.cpp

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

#include "dkt.h"
#include "gadaptivity.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>

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

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

  nb=1;

  ncomp = new long [nb];
  ncomp[0]=3;
  cncomp = new long [nb];
  cncomp[0]=0;

  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]=3;

  tnip=0;
  for (i=0;i<nb;i++){
    for (j=0;j<nb;j++){
      tnip+=nip[i][j];
    }
  }

  intordsm[0][0]=3;
}

dktelem::~dktelem (void)
{
  long i;

  for (i=0;i<nb;i++){
    delete [] nip[i];
    delete [] intordsm[i];
  }
  delete [] nip;
  delete [] intordsm;

  delete [] ncomp;
  delete [] cncomp;
}

void dktelem::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 dktelem::geom_matrix (matrix &gm,vector &x,vector &y,vector &l)
{
  double det,dx1,dy1,dx12,dy12,dx31,dy31;
  vector sx(3),sy(3),q(3),pb(3),pc(3),dl(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]));
  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 . det
  sx[0]=x[2]-x[1];  sx[1]=x[0]-x[2];  sx[2]=x[1]-x[0];
  //   der   dL(1)/dx . det
  sy[0]=y[1]-y[2];  sy[1]=y[2]-y[0];  sy[2]=y[0]-y[1];
  // dl0= betwen node 1,2
  q[0]=dl[0]*dl[0];
  q[1]=dl[1]*dl[1];
  q[2]=dl[2]*dl[2];
  pb[0]=(sy[0]*sy[0]/4.-sx[0]*sx[0]/2.)/q[1];
  pb[1]=(sy[1]*sy[1]/4.-sx[1]*sx[1]/2.)/q[2];
  pb[2]=(sy[2]*sy[2]/4.-sx[2]*sx[2]/2.)/q[0];
  pc[0]=(sx[0]*sx[0]/4.-sy[0]*sy[0]/2.)/q[1];
  pc[1]=(sx[1]*sx[1]/4.-sy[1]*sy[1]/2.)/q[2];
  pc[2]=(sx[2]*sx[2]/4.-sy[2]*sy[2]/2.)/q[0];
  
  dx1= sy[0]*(l[0]-1./4.)/det;
  dy1= sx[0]*(l[0]-1./4.)/det;
  dx12=(sy[0]*l[1]+sy[1]*l[0])/det;
  dy12=(sx[0]*l[1]+sx[1]*l[0])/det;
  dx31=(sy[2]*l[0]+sy[0]*l[2])/det;
  dy31=(sx[2]*l[0]+sx[0]*l[2])/det;       
  gm[0][0]= 6.*(sx[2]/q[0]*dx12-sx[1]/q[2]*dx31);
  gm[0][1]=-3.*(sx[1]*sy[1]/q[2]*dx31+sx[2]*sy[2]/q[0]*dx12);
  gm[0][2]= 4.*(dx1-pc[1]*dx31-pc[2]*dx12);
  gm[1][0]=-6.*(sy[2]/q[0]*dy12-sy[1]/q[2]*dy31);
  gm[1][1]=-4.*(dy1-pb[1]*dy31-pb[2]*dy12);
  gm[1][2]= 3.*(sx[1]*sy[1]/q[2]*dy31+sx[2]*sy[2]/q[0]*dy12);
  gm[2][0]= 6.*(sx[2]/q[0]*dy12-sx[1]/q[2]*dy31 -sy[2]/q[0]*dx12+sy[1]/q[2]*dx31);
  gm[2][1]=-3.*(sx[1]*sy[1]/q[2]*dy31+sx[2]*sy[2]/q[0]*dy12) -4.*(dx1-pb[1]*dx31-pb[2]*dx12);
  gm[2][2]= 4.*(dy1-pc[1]*dy31-pc[2]*dy12) +3.*(sx[1]*sy[1]/q[2]*dx31+sx[2]*sy[2]/q[0]*dx12);
  
  dx1= sy[1]*(l[1]-1./4.)/det;
  dy1= sx[1]*(l[1]-1./4.)/det;
  dx12=(sy[1]*l[2]+sy[2]*l[1])/det;
  dy12=(sx[1]*l[2]+sx[2]*l[1])/det;
  dx31=(sy[0]*l[1]+sy[1]*l[0])/det;
  dy31=(sx[0]*l[1]+sx[1]*l[0])/det;       
  gm[0][3]= 6.*(sx[0]/q[1]*dx12-sx[2]/q[0]*dx31);
  gm[0][4]=-3.*(sx[2]*sy[2]/q[0]*dx31+sx[0]*sy[0]/q[1]*dx12);
  gm[0][5]= 4.*(dx1-pc[2]*dx31-pc[0]*dx12);
  gm[1][3]=-6.*(sy[0]/q[1]*dy12-sy[2]/q[0]*dy31);
  gm[1][4]=-4.*(dy1-pb[2]*dy31-pb[0]*dy12);
  gm[1][5]= 3.*(sx[2]*sy[2]/q[0]*dy31+sx[0]*sy[0]/q[1]*dy12);
  gm[2][3]= 6.*(sx[0]/q[1]*dy12-sx[2]/q[0]*dy31 -sy[0]/q[1]*dx12+sy[2]/q[0]*dx31);
  gm[2][4]=-3.*(sx[2]*sy[2]/q[0]*dy31+sx[0]*sy[0]/q[1]*dy12) -4.*(dx1-pb[2]*dx31-pb[0]*dx12);
  gm[2][5]= 4.*(dy1-pc[2]*dy31-pc[0]*dy12) +3.*(sx[2]*sy[2]/q[0]*dx31+sx[0]*sy[0]/q[1]*dx12);
  
  dx1= sy[2]*(l[2]-1./4.)/det;
  dy1= sx[2]*(l[2]-1./4.)/det;
  dx12=(sy[2]*l[0]+sy[0]*l[2])/det;
  dy12=(sx[2]*l[0]+sx[0]*l[2])/det;
  dx31=(sy[1]*l[2]+sy[2]*l[1])/det;
  dy31=(sx[1]*l[2]+sx[2]*l[1])/det;       
  gm[0][6]= 6.*(sx[1]/q[2]*dx12-sx[0]/q[1]*dx31);
  gm[0][7]=-3.*(sx[0]*sy[0]/q[1]*dx31+sx[1]*sy[1]/q[2]*dx12);
  gm[0][8]= 4.*(dx1-pc[0]*dx31-pc[1]*dx12);
  gm[1][6]=-6.*(sy[1]/q[2]*dy12-sy[0]/q[1]*dy31);
  gm[1][7]=-4.*(dy1-pb[0]*dy31-pb[1]*dy12);
  gm[1][8]= 3.*(sx[0]*sy[0]/q[1]*dy31+sx[1]*sy[1]/q[2]*dy12);
  gm[2][6]= 6.*(sx[1]/q[2]*dy12-sx[0]/q[1]*dy31 -sy[1]/q[2]*dx12+sy[0]/q[1]*dx31);
  gm[2][7]=-3.*(sx[0]*sy[0]/q[1]*dy31+sx[1]*sy[1]/q[2]*dy12) -4.*(dx1-pb[0]*dx31-pb[1]*dx12);
  gm[2][8]= 4.*(dy1-pc[0]*dy31-pc[1]*dy12) +3.*(sx[0]*sy[0]/q[1]*dx31+sx[1]*sy[1]/q[2]*dx12);
  
}

void dktelem::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 dktelem::dbmat (matrix &d,matrix &db,double t)
{
  double c;

  c=t*t*t;

  db[0][0] = c*d[0][0];  db[0][1] = c*d[0][1];  db[0][2] = c*d[0][2];
  db[1][0] = c*d[1][0];  db[1][1] = c*d[1][1];  db[1][2] = c*d[1][2];
  db[2][0] = c*d[2][0];  db[2][1] = c*d[2][1];  db[2][2] = c*d[2][2];
}

/**
   function computes stiffness matrix of dkt element

   @param eid - element id
   @param ri,ci - row and column indices
   @param sm - stiffness matrix

   15.3.2002
*/
void dktelem::stiffness_matrix (long eid,long ri,long ci,matrix &sm,vector &x,vector &y)
{
  long i,ii;
  double jac,det,thick;
  ivector nodes(nne);
  vector gp1(intordsm[0][0]),gp2(intordsm[0][0]),w(intordsm[0][0]),l(3),t(nne);
  matrix gm(3,ndofe),d(5,5),db(3,3);

  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);

  ii=Mt->elements[eid].ipp[ri][ci];

  gauss_points_tr (gp1.a,gp2.a,w.a,intordsm[0][0]);

  for (i=0;i<intordsm[0][0];i++){
    l[0]=gp1[i];  l[1]=gp2[i];  l[2]=1.0-l[0]-l[1];

    geom_matrix (gm,x,y,l);

    Mm->matstiff (d,ii);  ii++;
    thick = t[0]*l[0]+t[1]*l[1]+t[2]*l[2];
    dbmat (d,db,thick);
    jac=det*w[i];
    bdbj (sm.a,gm.a,db.a,jac,gm.m,gm.n);
  }


//  fprintf (Out,"\n\n prvek cislo %ld",eid);
//  for (i=0;i<ndofe;i++){
//    fprintf (Out,"\n %4ld   %20.10e",i,sm[i][i]);
//  }

}

void dktelem::res_stiffness_matrix (long eid,matrix &sm)
{
  long transf;
  vector x(nne),y(nne);
  ivector nodes(nne);
  Mt->give_elemnodes (eid,nodes);
  Mt->give_node_coord2d (x,y,eid);

  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);
  }
}


void dktelem::nodecoord (vector &xi,vector &eta)
{
  xi[0] = 0.0;  eta[0] = 0.0;
  xi[1] = 1.0;  eta[1] = 0.0;
  xi[2] = 0.0;  eta[2] = 1.0;
}


void dktelem::appval (vector &l, long fi,long nc,vector &eps,double **val)
{
  long i,j,k;
  vector nodval;
  
  k=0;
  allocv (nne,nodval);
  for (i=fi;i<fi+nc;i++){
    for (j=0;j<nne;j++){
      nodval[j]=val[j][i];
    }
    eps[k] = nodval[0]*l[0]+nodval[1]*l[1]+nodval[2]*l[2];
    k++;
  }
  
  destrv (nodval);
}

/**
   function computes strains in arbitrary point on element
   
   @param xi, eta - natural coordinates of the point
   @param eps - array containing strains
   @param val - array containing values on element
   
   11.5.2002
*/

void dktelem::res_mainip_strains (long lcid,long eid)
{
  vector aux,x(nne),y(nne),r(ndofe);
  ivector cn(ndofe),nodes(nne);
  matrix tmat;

  Mt->give_node_coord2d (x,y,eid);
  Mt->give_elemnodes (eid,nodes);
  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);
  }

  mainip_strains (lcid,eid,0,0,x,y,r);
}
/**
   function computes strains in integration points of element
   
   @param lcid - load case id
   @param eid - element id
   @param ri - row index
   @param ci - column index
   
   10.5.2002
*/
void dktelem::mainip_strains (long lcid,long eid,long ri,long ci,vector &x,vector &y,vector &r)
{
  long i,ipp,ij;
  vector l(3),eps(ncomp[0]),gp1(intordsm[0][0]),gp2(intordsm[0][0]),w(intordsm[0][0]);
  matrix gm(ncomp[0],ndofe);
  
  gauss_points_tr (gp1.a,gp2.a,w.a,intordsm[0][0]);
  fprintf (Out,"\n\n eps");
  fprintf (Out,"\n\n prvek cislo %ld",eid);
  
  ipp=Mt->elements[eid].ipp[ri][ci];
  for (i=0;i<intordsm[0][0];i++){
    l[0]=gp1[i];  l[1]=gp2[i];  l[2]=1.0-l[0]-l[1];	
    geom_matrix (gm,x,y,l);
    mxv (gm,r,eps);
    Mm->storestrain (lcid,ipp,cncomp[0],ncomp[0],eps);
           fprintf (Out,"\n");
		  for (ij=0;ij<ncomp[0];ij++){ fprintf (Out,"%20.10e",eps[ij]);	}
   ipp++;
  }
  
}

void dktelem::nod_strains (long lcid,long eid,long ri,long ci)
{
  long i,ipp;
  double *lsm,*lhs,*rhs;
  vector nxi(nne),neta(nne),natcoord(2),l(3);
  vector eps(ncomp[0]),gp1(intordsm[0][0]),gp2(intordsm[0][0]),w(intordsm[0][0]);
  ivector nodes;

  lsm = new double [9];
  allocv (nne,nodes);

  Mt->give_elemnodes (eid,nodes);
  nodecoord (nxi,neta);
  
  lhs = new double [ncomp[0]*3];
  rhs = new double [ncomp[0]*3];
  gauss_points_tr (gp1.a,gp2.a,w.a,intordsm[0][0]);
  
  nullv (lsm,9);
  nullv (rhs,ncomp[0]*3);

  ipp=Mt->elements[eid].ipp[ri][ci];
  for (i=0;i<intordsm[0][0];i++){
    l[0]=gp1[i];  l[1]=gp2[i];  l[2]=1.0-l[0]-l[1];   
	Mm->givestrain (lcid,ipp,cncomp[0],ncomp[0],eps);
    natcoord[0]=l[0];  natcoord[1]=l[1];
    matassem_lsm (lsm,natcoord);
    rhsassem_lsm (rhs,natcoord,eps);
	ipp++;
  }
  
  solve_lsm (lsm,lhs,rhs,Mp->zero,3,ncomp[0]);
  Mt->strain_nodal_values (nodes,nxi,neta,nxi,lhs,2,cncomp[0],ncomp[0],lcid);

  delete [] lhs;  delete [] rhs;
  
  destrv (nodes);
  delete [] lsm;
}

/**
   function computes strains on element
   
   @param val - array containing strains on element
   @param lcid - load case id
   @param eid - element id
   
   15.7.2002
*/
void dktelem::elem_strains (double **stra,long lcid,long eid,long ri,long ci)
{
  long i,ipp;
  double *lsm,*lhs,*rhs;
  vector nxi(nne),neta(nne),natcoord(2),l(3);
  vector eps(ncomp[0]),gp1(intordsm[0][0]),gp2(intordsm[0][0]),w(intordsm[0][0]);
  ivector nodes;

  lsm = new double [9];

  nodecoord (nxi,neta);
  
  lsm = new double [9];
  allocv (nne,nodes);

  Mt->give_elemnodes (eid,nodes);
  nodecoord (nxi,neta);
  
  lhs = new double [ncomp[0]*3];
  rhs = new double [ncomp[0]*3];
  gauss_points_tr (gp1.a,gp2.a,w.a,intordsm[0][0]);
  
  nullv (lsm,9);
  nullv (rhs,ncomp[0]*3);

  ipp=Mt->elements[eid].ipp[ri][ci];
  for (i=0;i<intordsm[0][0];i++){
    l[0]=gp1[i];  l[1]=gp2[i];  l[2]=1.0-l[0]-l[1];   
	Mm->givestrain (lcid,ipp,cncomp[0],ncomp[0],eps);
    natcoord[0]=l[0];  natcoord[1]=l[1];
    matassem_lsm (lsm,natcoord);
    rhsassem_lsm (rhs,natcoord,eps);
	ipp++;
  }   
    
  solve_lsm (lsm,lhs,rhs,Mp->zero,3,ncomp[0]);
  nodal_values (stra,nxi,neta,nxi,lhs,2,cncomp[0],ncomp[0]);
    
  delete [] lhs;  delete [] rhs;
  destrv (nodes);
  
  delete [] lsm;
}




/**
   function computes strains DKT
*/
/**
   function computes strains in arbitrary point on element
   
   @param lcid - load case id
   @param eid - element id
   @param areacoord - area coordinates of the point
   @param fi,li - first and last indices
   @param eps - array containing strains
   
   11.5.2002
*/
void dktelem::appstrain (long lcid,long eid,vector &l,long fi,long ncomp,vector &eps)
{
  long i,j,k;
  ivector nodes;
  vector nodval;
  
  if (ncomp != eps.n){
    fprintf (stderr,"\n\n wrong interval of indices in function strain (%s, line %d).\n",__FILE__,__LINE__);
    abort ();
  }


  allocv (nne,nodes);
  allocv (nne,nodval);
  Mt->give_elemnodes (eid,nodes);
  k=0;
  for (i=fi;i<fi+ncomp;i++){
    for (j=0;j<nne;j++){
      nodval[j]=Mt->nodes[nodes[j]].strain[lcid*tncomp+i];
    }
    eps[k] = nodval[0]*l[0]+nodval[1]*l[1]+nodval[2]*l[2];
//    eps[k]=approx (areacoord,nodval);
    k++;
  }
  
  destrv (nodes);  destrv (nodval);