plelemsubqt.cpp

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

#include "plelemsubqt.h"
#include "global.h"
#include "globmat.h"
#include "genfile.h"
#include "adaptivity.h"
#include "node.h"
#include "element.h"
#include "intpoints.h"
#include "plelemlt.h"
#include "plelemlq.h"
#include "plelemqq.h"
#include <stdlib.h>
#include <math.h>



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

  nne=6;  ndofe=12;  tncomp=3;  napfun=2;
  intordmm=6;  ned=3;  nned=3;  intordb = 3;

  nb=2;

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

  cncomp = new long [nb];
  cncomp[0]=0;
  cncomp[1]=2;

  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;  nip[0][1]=0;
  nip[1][0]=0;  nip[1][1]=3;
  
  intordsm[0][0]=3;  intordsm[0][1]=0;
  intordsm[1][0]=0;  intordsm[1][1]=3;

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

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

  }
  delete [] nip;
  
}

void planeelemsubqt::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 - natural coordinates
   @param nodval - nodal values
*/
double planeelemsubqt::approx (double xi,double eta,vector &nodval)
{
  double f;
  vector bf(nne);
  
  bf_quad_3_2d (bf.a,xi,eta);
  scprd (bf,nodval,f);
  return f;
}

/**
   function returns matrix of base function

   17.8.2001
*/
void planeelemsubqt::bf_matrix (matrix &n,double xi,double eta)
{
  long i,i1,i2;
  vector bf(nne);
  
  bf_quad_3_2d (bf.a,xi,eta);
  fillm (0.0,n);
  
  i1=0;  i2=1;
  for (i=0;i<nne;i++){
    n[0][i1]=bf[i];  i1+=2;
    n[1][i2]=bf[i];  i2+=2;
  }
}

/**
   function assembles geometric matrix
   
   @param gm - geometric matrix
   @param x,y - node coordinates
   @param xi,eta - natural coordinates
   
*/
void planeelemsubqt::geom_matrix (matrix &gm,vector &x,vector &y,double xi,double eta)
{
  long i,i1,i2;
  double jac;
  vector dx(nne),dy(nne);

  dx_bf_quad_3_2d (dx.a,xi,eta);
  dy_bf_quad_3_2d (dy.a,xi,eta);

  derivatives_2d (dx,dy,jac,x,y,xi,eta);

  fillm (0.0,gm);

  i1=0;  i2=1;
  for (i=0;i<nne;i++){
    gm[0][i1]=dx[i];
    gm[1][i2]=dy[i];
    gm[2][i1]=dy[i];  i1+=2;
    gm[2][i2]=dx[i];  i2+=2;
  }
}

/**
   function assembles blocks of geometric matrix
   
   @param gm - geometric matrix
   @param x,y - node coordinates
   @param ri - row index
   @param xi,eta - natural coordinates
   
*/
void planeelemsubqt::geom_matrix_block (matrix &gm,double ri,vector &x,vector &y,double xi,double eta)
{
  long i,i1,i2;
  double jac;
  vector dx(nne),dy(nne);
  
  dx_bf_quad_3_2d (dx.a,xi,eta);
  dy_bf_quad_3_2d (dy.a,xi,eta);

  derivatives_2d (dx,dy,jac,x,y,xi,eta);

  fillm (0.0,gm);

  if (ri==0){
    i1=0;  i2=1;
    for (i=0;i<nne;i++){
      gm[0][i1]=dx[i];  i1+=2;
      gm[1][i2]=dy[i];  i2+=2;
    }
  }
  
  if (ri==1){
    i1=0;  i2=1;
    for (i=0;i<nne;i++){
      gm[0][i1]=dy[i];  i1+=2;
      gm[0][i2]=dx[i];  i2+=2;
    }
  }
}

void planeelemsubqt::dmatblock (long ri,long ci,matrix &d, matrix &dd)
{
  fillm (0.0,dd);
  
  if (ri==0 && ci==0){
    dd[0][0]=d[0][0];  dd[0][1]=d[0][1];
    dd[1][0]=d[1][0];  dd[1][1]=d[1][1];
  }
  if (ri==0 && ci==1){
    dd[0][0]=d[0][2];
    dd[1][0]=d[1][2];
  }
  if (ri==1 && ci==0){
    dd[0][0]=d[2][0];  dd[0][1]=d[2][1];
  }
  if (ri==1 && ci==1){
    dd[0][0]=d[2][2];
  }
}

/**
   transformation matrix x_g = T x_l

   17.8.2001
*/
void planeelemsubqt::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*2][i*2]   = Mt->nodes[nodes[i]].e1[0];  tmat[i*2][i*2+1]   = Mt->nodes[nodes[i]].e2[0];
      tmat[i*2+1][i*2] = Mt->nodes[nodes[i]].e1[1];  tmat[i*2+1][i*2+1] = Mt->nodes[nodes[i]].e2[1];
    }
  }
}

/**
   function computes stiffness matrix of plane stress triangular
   finite element with quadratic approximation functions

   @param eid - number of element
   @param sm - stiffness matrix

   25.8.2001
*/
void planeelemsubqt::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 t(nne),gp1,gp2,w;
  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;
      
      allocm (ncomp[jj],ndofe,gmc);
      allocm (ncomp[ii],ncomp[jj],dd);
      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]);
      ipp=Mt->elements[eid].ipp[ri+ii][ci+jj];
      
      for (i=0;i<intordsm[ii][jj];i++){
	// geometric matrix
	geom_matrix_block (gmr,ii,x,y,gp1[i],gp2[i]);
	geom_matrix_block (gmc,jj,x,y,gp1[i],gp2[i]);
	
	//  stiffness matrix of material
	Mm->matstiff (d,ipp);  ipp++;
	dmatblock (ii,jj,d,dd);
	
	thick = approx (gp1[i],gp2[i],t);
	
	//  det is equal to double area of the element
	jac=w[i]*thick*det;
    
	//  contribution to the stiffness matrix of the element
	bdbjac (sm,gmr,dd,gmc,jac);
      }
      destrm (dd);  destrm (gmc);  destrv (gp1);  destrv (gp2);  destrv (w);
    }
    destrm (gmr);
  }
  
}

void planeelemsubqt::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 plane stress triangular
   finite element with quadratic approximation functions

   @param eid - number of element
   @param mm - mass matrix

   25.8.2001
*/
void planeelemsubqt::mass_matrix (long eid,matrix &mm,vector &x,vector &y)
{
  long i;
  double jac,det,thick,rho;
  ivector nodes(nne);
  vector w(intordmm),gp1(intordmm),gp2(intordmm),t(nne),dens(nne);
  matrix n(napfun,ndofe);
  
  Mt->give_elemnodes (eid,nodes);
  Mc->give_thickness (eid,nodes,t);
  Mc->give_density (eid,nodes,dens);

  //  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]);
  
  gauss_points_tr (gp1.a,gp2.a,w.a,intordmm);
  
  fillm (0.0,mm);
  
  for (i=0;i<intordmm;i++){
    bf_matrix (n,gp1[i],gp2[i]);
    
    thick = approx (gp1[i],gp2[i],t);
    rho = approx (gp1[i],gp2[i],dens);
    
    jac=w[i]*thick*rho*det;
    
    nnj (mm.a,n.a,jac,n.m,n.n);
  }
  
}

void planeelemsubqt::res_mass_matrix (long eid,matrix &mm)
{
  vector x(nne),y(nne);
  Mt->give_node_coord2d (x,y,eid);
  mass_matrix (eid,mm,x,y);
}


void planeelemsubqt::load_matrix (long eid,matrix &lm)
  //  function computes load matrix of the plane stress triangular
  //  finite element with quadratic approximation functions
  //  load vector is obtained after premultiplying load matrix
  //  by nodal load values
  //  
  //  eid - number of element
  //  lm - load matrix
  //
  //  25.8.2001
{
  long i;
  double jac,det,thick;
  ivector nodes(nne);
  vector x(nne),y(nne),w(intordmm),gp1(intordmm),gp2(intordmm),t(nne);
  matrix n(napfun,ndofe);
  
  Mt->give_elemnodes (eid,nodes);
  Mt->give_node_coord2d (x,y,eid);
  Mc->give_thickness (eid,nodes,t);

  gauss_points_tr (gp1.a,gp2.a,w.a,intordmm);

  //  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,lm);
  
  for (i=0;i<intordmm;i++){
    bf_matrix (n,gp1[i],gp2[i]);
    
    thick = approx (gp1[i],gp2[i],t);
    
    jac=w[i]*thick*det;
    
    nnj (lm.a,n.a,jac,n.m,n.n);
  }
  
}


void planeelemsubqt::res_mainip_strains (long lcid,long eid)
{
  vector x(nne),y(nne);
  Mt->give_node_coord2d (x,y,eid);
  mainip_strains (lcid,eid,0,0,x,y);
}


/**
   function computes strains in main 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 planeelemsubqt::mainip_strains (long lcid,long eid,long ri,long ci,vector &x,vector &y)
{
  long i,ii,ipp;
  vector r(ndofe),gp1,gp2,w,eps,aux;
  ivector nodes(nne),cn(ndofe);
  matrix gm,tmat;

  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);
  }

  
  for (ii=0;ii<nb;ii++){
    allocv (intordsm[ii][ii],gp1);
    allocv (intordsm[ii][ii],gp2);
    allocv (intordsm[ii][ii],w);
    allocv (ncomp[ii],eps);
    allocm (ncomp[ii],ndofe,gm);
    
    gauss_points_tr (gp1.a,gp2.a,w.a,intordsm[ii][ii]);
    
    ipp=Mt->elements[eid].ipp[ri+ii][ci+ii];
    for (i=0;i<intordsm[ii][ii];i++){
      geom_matrix_block (gm,ii,x,y,gp1[i],gp2[i]);
      mxv (gm,r,eps);
      
      Mm->storestrain (lcid,ipp,cncomp[ii],ncomp[ii],eps);
      ipp++;
    }
    destrm (gm);  destrv (eps);  destrv (w);  destrv (gp1);  destrv (gp2);
  }
  
}

/**
   function computes strains in nodes of element
   
   @param lcid - load case id
   @param eid - element id
   
   10.5.2002
*/
void planeelemsubqt::nod_strains (long lcid,long eid,long ri,long ci)
{
  long i,ii,ipp;
  double *lsm,*lhs,*rhs;
  vector nxi(nne),neta(nne),r(ndofe),gp1,gp2,w,eps,aux,natcoord(2);
  ivector nodes(nne);

  lsm = new double [9];

  nodecoord (nxi,neta);
  Mt->give_elemnodes (eid,nodes);

  for (ii=0;ii<nb;ii++){
    allocv (intordsm[ii][ii],gp1);
    allocv (intordsm[ii][ii],gp2);
    allocv (intordsm[ii][ii],w);
    allocv (ncomp[ii],eps);
    lhs = new double [ncomp[ii]*3];
    rhs = new double [ncomp[ii]*3];
    gauss_points_tr (gp1.a,gp2.a,w.a,intordsm[ii][ii]);
    
    nullv (lsm,9);
    nullv (rhs,ncomp[ii]*3);
    
    ipp=Mt->elements[eid].ipp[ri+ii][ci+ii];
    for (i=0;i<intordsm[ii][ii];i++){
      Mm->givestrain (lcid,ipp,cncomp[ii],ncomp[ii],eps);
      
      natcoord[0]=gp1[i];  natcoord[1]=gp2[i];
      matassem_lsm (lsm,natcoord);
      rhsassem_lsm (rhs,natcoord,eps);
      
      ipp++;
    }
    
    solve_lsm (lsm,lhs,rhs,Mp->zero,3,ncomp[ii]);
    Mt->strain_nodal_values (nodes,nxi,neta,nxi,lhs,2,cncomp[ii],ncomp[ii],lcid);

    delete [] lhs;  delete [] rhs;
    destrv (eps);  destrv (w);  destrv (gp1);  destrv (gp2);
  }
  
  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 planeelemsubqt::elem_strains (double **stra,long lcid,long eid,long ri,long ci)
{
  long i,ii,ipp;
  double xi,eta,*lsm,*lhs,*rhs;
  vector nxi(nne),neta(nne),gp1,gp2,w,eps,aux,natcoord(2);
  ivector nodes(nne);

  lsm = new double [9];
  
  nodecoord (nxi,neta);
  Mt->give_elemnodes (eid,nodes);
  
  for (ii=0;ii<nb;ii++){
    allocv (intordsm[ii][ii],gp1);
    allocv (intordsm[ii][ii],gp2);
    allocv (intordsm[ii][ii],w);
    allocv (ncomp[ii],eps);
    lhs = new double [ncomp[ii]*3];
    rhs = new double [ncomp[ii]*3];
    gauss_points_tr (gp1.a,gp2.a,w.a,intordsm[ii][ii]);
    
    nullv (lsm,9);
    nullv (rhs,ncomp[ii]*3);
    
    ipp=Mt->elements[eid].ipp[ri+ii][ci+ii];
    for (i=0;i<intordsm[ii][ii];i++){
      xi=gp1[i];
      eta=gp2[i];
      
      Mm->givestrain (lcid,ipp,cncomp[ii],ncomp[ii],eps);
      
      natcoord[0]=xi;  natcoord[1]=eta;
      matassem_lsm (lsm,natcoord);
      rhsassem_lsm (rhs,natcoord,eps);

      ipp++;
    }
    
    solve_lsm (lsm,lhs,rhs,Mp->zero,3,ncomp[ii]);
    nodal_values (stra,nxi,neta,nxi,lhs,2,cncomp[ii],ncomp[ii]);

    delete [] lhs;  delete [] rhs;
    destrv (eps);  destrv (w);  destrv (gp1);  destrv (gp2);
  }
  
  delete [] lsm;
}


/**
   function computes strains in arbitrary point on element
   
   @param lcid - load case id
   @param eid - element id
   @param xi,eta - natural coordinates
   @param fi,li - first and last indices
   @param eps - array containing strains
   
   11.5.2002
*/
void planeelemsubqt::appstrain (long lcid,long eid,double xi,double eta,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]=approx (xi,eta,nodval);
    k++;
  }
  
  destrv (nodes);  destrv (nodval);
}

/**
   function computes strains in all integration points
   
   @param lcid - load case id
   @param eid - element id
   @param ri,ci - row and column indices
   
   10.5.2002
*/
void planeelemsubqt::allip_strains (double **stra,long lcid,long eid,long ri,long ci)
{
  long i,ii,jj,ipp;
  //double xi,eta;
  vector eps(tncomp),gp1,gp2,w;
  
  for (ii=0;ii<nb;ii++){
    for (jj=0;jj<nb;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]);
      ipp=Mt->elements[eid].ipp[ri+ii][ci+jj];
      
      for (i=0;i<intordsm[ii][jj];i++){
	if (Mp->strainaver==0)
	  //appval (xi,eta,0,tncomp,eps,stra);
	  appval (gp1[i],gp2[i],0,tncomp,eps,stra);
	if (Mp->strainaver==1)
	  appstrain (lcid,eid,gp1[i],gp2[i],0,tncomp,eps);

	Mm->storestrain (lcid,ipp,eps);
	ipp++;
      }
      destrv (w);  destrv (gp2);  destrv (gp1);
    }
  }
}

void planeelemsubqt::strains (long lcid,long eid,long ri,long ci)
{
  long i,naep,ncp,sid;
  double **stra;
  vector coord,eps;