dkt.cpp

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

}


void dktelem::allip_strains (double **stra,long lcid,long eid,long ri,long ci)
{
  long i,ipp;
  vector l(3);
  vector eps(ncomp[0]),gp1(intordsm[0][0]),gp2(intordsm[0][0]),w(intordsm[0][0]);
  
  gauss_points_tr (gp1.a,gp2.a,w.a,intordsm[0][0]);
  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];   
	if (Mp->strainaver==0)
		appval (l,0,tncomp,eps,stra);
	if (Mp->strainaver==1)
	    appstrain (lcid,eid,l,0,tncomp,eps);
	Mm->storestrain (lcid,ipp,eps);
	ipp++;
  }
}

void dktelem::strains (long lcid,long eid,long ri,long ci)
{
  long i,naep,ncp,sid;
  double **stra;
  vector coord,eps,l(3);
  
  if (Mp->strainaver==0){
    stra = new double* [nne];
    for (i=0;i<nne;i++){
      stra[i] = new double [tncomp];
    }
    elem_strains (stra,lcid,eid,ri,ci);
  }

  switch (Mm->stra.tape[eid]){
  case nowhere:{
    break;
  }
  case intpts:{
    allip_strains (stra,lcid,eid,ri,ci);
    break;
  }
  case enodes:{
    break;
  }
  case userdefined:{
    //  number of auxiliary element points
    naep = Mm->stra.give_naep (eid);
    ncp = Mm->stra.give_ncomp (eid);
    sid = Mm->stra.give_sid (eid);
    allocv (ncp,eps);
    allocv (2,coord);
    for (i=0;i<naep;i++){
      Mm->stra.give_aepcoord (sid,i,coord);
      l[0]=coord[0];l[1]=coord[1];l[2]=1-coord[1]-coord[2];
      if (Mp->strainaver==0)
		appval (l,0,ncp,eps,stra);
      if (Mp->strainaver==1)
        appstrain (lcid,eid,l,0,ncp,eps);
      Mm->stra.storevalues(lcid,eid,i,eps);
    }
    destrv (eps);
    destrv (coord);
    break;
  }
  default:{
    fprintf (stderr,"\n\n unknown strain point is required in function planeelemlt::strains (%s, line %d).\n",__FILE__,__LINE__);
  }
  }
  if (Mp->strainaver==0){
    for (i=0;i<nne;i++){
      delete [] stra[i];
    }
    delete [] stra;
  }
}



/**
   function computes stresses DKT
*/
void dktelem::res_allip_stresses (long lcid,long eid)
{
  //  blocks of stress components at integration points
  mainip_stresses (lcid,eid,0,0);
}

void dktelem::mainip_stresses (long lcid,long eid,long ri,long ci)
{
  long i,ipp,ij;
  double thick;
  ivector nodes(nne);
  vector l(3),t(nne);
  vector eps(ncomp[0]),sig(ncomp[0]),auxsig(ncomp[0]),gp1(intordsm[0][0]),gp2(intordsm[0][0]),w(intordsm[0][0]);
  matrix d(5,5),dd(ncomp[0],ncomp[0]);
    
    Mt->give_elemnodes (eid,nodes);
    Mc->give_thickness (eid,nodes,t);
    gauss_points_tr (gp1.a,gp2.a,w.a,intordsm[0][0]);
    ipp=Mt->elements[eid].ipp[ri][ci];
    
  fprintf (Out,"\n\n stress");
  fprintf (Out,"\n\n prvek cislo %ld",eid);

  for (i=0;i<intordsm[0][0];i++){
      Mm->matstiff (d,ipp);
      l[0]=gp1[i]; l[1]=gp2[i];l[2]=1.0-l[0]-l[1];
      fillv (0.0,sig);
//	  if (Mp->strainaver==0)
	    Mm->givestrain (lcid,ipp,cncomp[0],ncomp[0],eps);
//	  if (Mp->strainaver==1)
//	    appstrain (lcid,eid,l,cncomp[0],ncomp[0],eps);
      thick = t[0]*l[0]+t[1]*l[1]+t[2]*l[2];
      dbmat (d,dd,thick);
	  mxv (dd,eps,auxsig);
	  addv (auxsig,sig,sig);
	  Mm->storestress (lcid,ipp,cncomp[0],ncomp[0],sig);
            fprintf (Out,"\n");
		  for (ij=0;ij<ncomp[0];ij++){ fprintf (Out,"%20.10e",sig[ij]);	}
     
      ipp++;
	}
		  
}

void dktelem::nod_stresses (long lcid,long eid,long ri,long ci)
{
  long i,ipp;
  double thick,*lsm,*lhs,*rhs;
  vector nxi(nne),neta(nne),r,natcoord(2),l(3),t(nne);
  vector eps(ncomp[0]),sig(ncomp[0]),auxsig(ncomp[0]),gp1(intordsm[0][0]),gp2(intordsm[0][0]),w(intordsm[0][0]);
  ivector nodes(nne);
  matrix gm,d(5,5),dd(ncomp[0],ncomp[0]);
  
  lsm = new double [9];

  Mt->give_elemnodes (eid,nodes);
  Mc->give_thickness (eid,nodes,t);
  
  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++){
      
      Mm->matstiff (d,ipp);
      l[0]=gp1[i]; l[1]=gp2[i];l[2]=1.0-l[0]-l[1];
      thick = t[0]*l[0]+t[1]*l[1]+t[2]*l[2];
      fillv (0.0,sig);
	  if (Mp->strainaver==0)
	    Mm->givestrain (lcid,ipp,cncomp[0],ncomp[0],eps);
	  if (Mp->strainaver==1)
	    appstrain (lcid,eid,l,cncomp[0],ncomp[0],eps);
      thick = t[0]*l[0]+t[1]*l[1]+t[2]*l[2];
      dbmat (d,dd,thick);
	  mxv (dd,eps,auxsig);
	  addv (auxsig,sig,sig);
      
      natcoord[0]=gp1[i];  natcoord[1]=gp2[i];
      matassem_lsm (lsm,natcoord);
      rhsassem_lsm (rhs,natcoord,sig);
      
      ipp++;

    }
    
    solve_lsm (lsm,lhs,rhs,Mp->zero,3,ncomp[0]);
    Mt->stress_nodal_values (nodes,nxi,neta,nxi,lhs,2,cncomp[0],ncomp[0],lcid);
    
    
    delete [] lhs;  delete [] rhs;
    delete [] lsm;
}

void dktelem::elem_stresses (double **stra,double **stre,long lcid,long eid,long ri,long ci)
{
  long i,ipp;
  double thick,*lsm,*lhs,*rhs;
  vector nxi(nne),neta(nne),r,natcoord(2),l(3),t(nne);
  vector eps(ncomp[0]),sig(ncomp[0]),auxsig(ncomp[0]),gp1(intordsm[0][0]),gp2(intordsm[0][0]),w(intordsm[0][0]);
  ivector nodes(nne);
  matrix gm,d(5,5),dd(ncomp[0],ncomp[0]);
  
  lsm = new double [9];

  Mt->give_elemnodes (eid,nodes);
  Mc->give_thickness (eid,nodes,t);
  
  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++){
      
      Mm->matstiff (d,ipp);
      l[0]=gp1[i]; l[1]=gp2[i];l[2]=1.0-l[0]-l[1];
      thick = t[0]*l[0]+t[1]*l[1]+t[2]*l[2];
      fillv (0.0,sig);
	  if (Mp->strainaver==0)
	    appval (l,cncomp[0],ncomp[0],eps,stra);
	  if (Mp->strainaver==1)
	    appstrain (lcid,eid,l,cncomp[0],ncomp[0],eps);
      thick = t[0]*l[0]+t[1]*l[1]+t[2]*l[2];
      dbmat (d,dd,thick);
	  mxv (dd,eps,auxsig);
	  addv (auxsig,sig,sig);
      
      natcoord[0]=gp1[i];  natcoord[1]=gp2[i];
      matassem_lsm (lsm,natcoord);
      rhsassem_lsm (rhs,natcoord,sig);
      
      ipp++;

    }
    
    solve_lsm (lsm,lhs,rhs,Mp->zero,3,ncomp[0]);
    Mt->stress_nodal_values (nodes,nxi,neta,nxi,lhs,2,cncomp[0],ncomp[0],lcid);
    
    
    delete [] lhs;  delete [] rhs;
  
    delete [] lsm;
}

void dktelem::appstress (long lcid,long eid,vector &l,long fi,long ncomp,vector &sig)
{
  long i,j,k;
  ivector nodes(nne);
  vector nodval(nne);
  
  if (ncomp != sig.n){
    fprintf (stderr,"\n\n wrong interval of indices in function stress (%s, line %d).\n",__FILE__,__LINE__);
    abort ();
  }

    
  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]].stress[lcid*tncomp+i];
    }
    sig[k] = nodval[0]*l[0]+nodval[1]*l[1]+nodval[2]*l[2];
    k++;
  }
  
}

void dktelem::allip_stresses (double **stre,long lcid,long eid,long ri,long ci)
{
  long i,ipp;
  vector sig(ncomp[0]),l(3),gp1(intordsm[0][0]),gp2(intordsm[0][0]),w(intordsm[0][0]);
  
  gauss_points_tr (gp1.a,gp2.a,w.a,intordsm[0][0]);
  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];
	  if (Mp->stressaver==0)
	    appval (l,cncomp[0],ncomp[0],sig,stre);
	  if (Mp->stressaver==1)
	    appstress (lcid,eid,l,0,tncomp,sig);
	Mm->storestress (lcid,ipp,sig);
	ipp++;
  }
}

void dktelem::stresses (long lcid,long eid,long ri, long ci)
{
  long i,naep,ncp,sid;
  double **stra,**stre;
  vector coord,sig,l(3);
  
  if (Mp->stressaver==0){
    stra = new double* [nne];
    stre = new double* [nne];
    for (i=0;i<nne;i++){
      stra[i] = new double [tncomp];
      stre[i] = new double [tncomp];
    }
    elem_strains (stra,lcid,eid,ri,ci);
    elem_stresses (stra,stre,lcid,eid,ri,ci);
  }
  
  switch (Mm->stre.tape[eid]){
  case nowhere:{
    break;
  }
  case intpts:{
    allip_stresses (stre,lcid,eid,ri,ci);
    break;
  }
  case enodes:{
    break;
  }
  case userdefined:{
    //  number of auxiliary element point
    naep = Mm->stre.give_naep (eid);
    ncp = Mm->stre.give_ncomp (eid);
    sid = Mm->stre.give_sid (eid);
    allocv (ncp,sig);
    allocv (2,coord);
    for (i=0;i<naep;i++){
      Mm->stre.give_aepcoord (sid,i,coord);
      l[0]=coord[0]; l[1]=coord[1];l[2]=1.0-coord[0]-coord[1];
      if (Mp->stressaver==0)
	appval (l,0,ncp,sig,stre);
      if (Mp->stressaver==1)
	appstress (lcid,eid,l,0,ncp,sig);
      Mm->stre.storevalues(lcid,eid,i,sig);
    }
    destrv (sig);
    destrv (coord);
    break;
  }
  default:{
    fprintf (stderr,"\n\n unknown stress point is required in function planeelemlq::stresses (%s, line %d).\n",__FILE__,__LINE__);
  }
  }
  if (Mp->stressaver==0){
    for (i=0;i<nne;i++){
      delete [] stra[i];
      delete [] stre[i];
    }
    delete [] stra;
    delete [] stre;
  }
  
}


/**
  function computes load vector from edge forces fz of the DKT
  15.3.2002
*/
void dktelem::nodeforces (long eid,long *le,double *nv,vector &nf)
{
  double cn0,sn0,cn1,sn1,cn2,sn2;
  ivector nodes(nne);
  vector x(nne),y(nne),dl(3);
  
  Mt->give_elemnodes (eid,nodes);
  Mt->give_node_coord2d (x,y,eid);

  if (le[0]==1){
    cn0= (y[1]-y[0])*dl[0]/60.;
    sn0=-(x[1]-x[0])*dl[0]/60.;
    nf[1]+=-(3.*nv[0]+2.*nv[3])*cn0;
    nf[2]+=-(3.*nv[0]+2.*nv[3])*sn0;
    nf[4]+= (2.*nv[0]+3.*nv[3])*cn0;
    nf[5]+= (2.*nv[0]+3.*nv[3])*sn0;
    nf[0]+=((2.-0.1)*nv[0] +(1.+0.1)*nv[3])*dl[0]/6.;
    nf[3]+=((1.-0.1)*nv[0] +(2.+0.1)*nv[3])*dl[0]/6.;
  }
  if (le[1]==1){
    cn1= (y[2]-y[1])*dl[1]/60.;
    sn1=-(x[2]-x[1])*dl[1]/60.;
    nf[4]+=-(3.*nv[1]+2.*nv[0])*cn1;
    nf[5]+=-(3.*nv[1]+2.*nv[0])*sn1;
    nf[7]+= (2.*nv[1]+3.*nv[0])*cn1;
    nf[8]+= (2.*nv[1]+3.*nv[0])*sn1;
    nf[3]+=((2.-0.1)*nv[3] +(1.+0.1)*nv[6])*dl[1]/6.;
    nf[6]+=((1.-0.1)*nv[3] +(2.+0.1)*nv[6])*dl[1]/6.;
  }
  if (le[2]==1){
    cn2= (y[0]-y[2])*dl[2]/60.;
    sn2=-(x[0]-x[2])*dl[2]/60.;
    nf[7]+=-(3.*nv[2]+2.*nv[1])*cn2;
    nf[8]+=-(3.*nv[2]+2.*nv[1])*sn2;
    nf[1]+= (2.*nv[2]+3.*nv[1])*cn2;
    nf[2]+= (2.*nv[2]+3.*nv[1])*sn2;
    nf[6]+=((2.-0.1)*nv[6] +(1.+0.1)*nv[9])*dl[2]/6.;
    nf[0]+=((1.-0.1)*nv[6] +(2.+0.1)*nv[9])*dl[2]/6.;
  }
}


/**
  function computes load vector from area forces fz of the DKT
  15.3.2002
*/
void dktelem::areaforces (long eid,double *nv,vector &nf)
{
   double pl,cn0,cn1,cn2,sn0,sn1,sn2;
   ivector nodes(nne);
   vector x(nne),y(nne);

   Mt->give_elemnodes (eid,nodes);
   Mt->give_node_coord2d (x,y,eid);
  
   pl = fabs(((x[1]-x[0])*(y[2]-y[0])-(x[2]-x[0])*(y[1]-y[0]))/2.);

   cn0= (y[1]-y[0])*pl/360.;
   cn1= (y[2]-y[1])*pl/360.;
   cn2= (y[0]-y[2])*pl/360.;
   sn0=-(x[1]-x[0])*pl/360.;
   sn1=-(x[2]-x[1])*pl/360.;
   sn2=-(x[0]-x[2])*pl/360.;
   nf[1]=-(7.*nv[0]+3.*nv[3]+5.*nv[6])*cn2+(7.*nv[0]+5.*nv[3]+3.*nv[6])*cn0;
   nf[2]=-(7.*nv[0]+3.*nv[3]+5.*nv[6])*sn2+(7.*nv[0]+5.*nv[3]+3.*nv[6])*sn0;
   nf[4]=-(5.*nv[0]+7.*nv[3]+3.*nv[6])*cn0+(3.*nv[0]+7.*nv[3]+5.*nv[6])*cn1;
   nf[5]=-(5.*nv[0]+7.*nv[3]+3.*nv[6])*sn0+(3.*nv[0]+7.*nv[3]+5.*nv[6])*sn1;
   nf[7]=-(3.*nv[0]+5.*nv[3]+7.*nv[6])*cn1+(5.*nv[0]+3.*nv[3]+7.*nv[6])*cn2;
   nf[8]=-(3.*nv[0]+5.*nv[3]+7.*nv[6])*sn1+(5.*nv[0]+3.*nv[3]+7.*nv[6])*sn2;
   nf[0]=(nv[0]/6. +nv[3]/12.+nv[6]/12.)*pl;
   nf[3]=(nv[0]/12.+nv[3]/6. +nv[6]/12.)*pl;
   nf[6]=(nv[0]/12.+nv[3]/12.+nv[6]/6. )*pl;


}




void dktelem::inicipval(long eid, long ri, long ci, matrix &nodval, inictype *ictn)
{
  long i, j, k, ipp;
  long ii, jj, nv = nodval.n;
  long nstra;
  double xi, eta;
//  double ipval;
  vector w, gp1, gp2, anv(nne);

  nstra = 0;
  for (j = 0; j < nv; j++) // for all initial values
  {
    for(i = 0; i < nne; i++) // for all nodes on element
      anv[i] = nodval[i][j];
    for (ii = 0; ii < nb; ii++)
    {
      for (jj = 0; jj < nb; jj++)
      {
        ipp=Mt->elements[eid].ipp[ri+ii][ci+jj];
        if (intordsm[ii][jj] == 0)
          continue;
        allocv (intordsm[ii][jj],gp1);
        allocv (intordsm[ii][jj],gp2);
        allocv (intordsm[ii][jj],w);
        gauss_points_tr (gp1.a, gp2.a, w.a, intordsm[ii][jj]);
        for (k = 0; k < intordsm[ii][jj]; k++)
        {
          xi=gp1[k];
          eta=gp2[k];
          //  value in integration point
//          ipval = approx_nat(xi, eta, anv);
          if ((ictn[i] & inistrain) && (j < Mm->ip[ipp].ncompstr))
          {
            //Mm->ip[ipp].strain[j] += ipval;
            ipp++;
            continue;
          }
          if ((ictn[i] & inistress) && (j < nstra + Mm->ip[ipp].ncompstr))
          {
            //Mm->ip[ipp].stress[j] += ipval;
            ipp++;
            continue;
          }
          if ((ictn[i] & iniother) && (j < nv))
          {
            //Mm->ip[ipp].other[j] += ipval;
            ipp++;
            continue;
          }
          ipp++;
        }
        destrv(gp1);  destrv (gp2);  destrv (w);
      }
    }
    if (ictn[i] & inistrain) nstra++;
  }
}