plelemqt.cpp

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

#include "plelemqt.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 "plelemsubqt.h"
#include "plelemlq.h"
#include "plelemqq.h"
#include "loadcase.h"
#include "gadaptivity.h"
#include <stdlib.h>
#include <math.h>


planeelemqt::planeelemqt (void)
{
  long i,j;
  
  //  number nodes on element
  nne=6;
  //  number of DOFs on element
  ndofe=12;
  //  number of strain/stress components
  tncomp=3;
  //  number of functions approximated
  napfun=2;
  //  order of numerical integration of mass matrix
  intordmm=6;
  //  number of edges on element
  ned=3;
  //  number of nodes on one edge
  nned=3;
  //  order of numerical integration on element edges (boundaries)
  intordb=3;

  //  number of blocks (parts of geometric matrix)
  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;
  
  tnip=0;
  for (i=0;i<nb;i++){
    for (j=0;j<nb;j++){
      tnip+=nip[i][j];
    }
  }

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

}

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

void planeelemqt::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
   
   1.4.2002
*/
double planeelemqt::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 assembles %matrix of approximation function
   
   @param n - %matrix of approximation functions
   @param xi,eta - natural coordinates
   
   17.8.2001
*/
void planeelemqt::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
   @param jac - Jacobian
   
   1.4.2002
*/
void planeelemqt::geom_matrix (matrix &gm,vector &x,vector &y,double xi,double eta,double &jac)
{
  long i,i1,i2;
  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 geometric %matrix
   
   @param gm - geometric %matrix
   @param x,y - node coordinates
   @param xi,eta - natural coordinates
   @param jac - Jacobian
   
   1.4.2002
*/
void planeelemqt::geom_matrix_block (matrix &gm,long ri,vector &x,vector &y,double xi,double eta,double &jac)
{
  long i,i1,i2;
  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;
    }
  }
}

/**
   function assembles blocks of stiffness %matrix of material
   
   @param ri - row index
   @param ci - column index
   @param d - stiffness %matrix of material
   @param dd - required block of stiffness %matrix of material
*/
void planeelemqt::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];
  }
}

/**
   function assembles transformation %matrix x_g = T x_l
   
   17.8.2001
*/
void planeelemqt::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 triangular
   finite element with quadratic approximation functions

   @param eid - element id
   @param sm - stiffness %matrix

   25.8.2001
*/
void planeelemqt::stiffness_matrix (long eid,long ri,long ci,matrix &sm,vector &x,vector &y)
{
  long i,ii,jj,ipp;
  double jac,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);

  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],jac);
	geom_matrix_block (gmc,jj,x,y,gp1[i],gp2[i],jac);
	
	//  stiffness matrix of material
	Mm->matstiff (d,ipp);
	dmatblock (ii,jj,d,dd);
	
	//  thickness
	thick = approx (gp1[i],gp2[i],t);
	
	jac*=w[i]*thick;
	
	//fprintf (stdout,"\n jakobian  %lf",jac);
	
	//  contribution to the stiffness matrix of the element
	//bdbj (sm.a,gm.a,d.a,jac,gm.m,gm.n);
	bdbjac (sm,gmr,dd,gmc,jac);
	
	ipp++;
      }
      destrm (dd);  destrm (gmc);  destrv (gp1);  destrv (gp2);  destrv (w);
    }
    destrm (gmr);
  }

}

void planeelemqt::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);
  }
}

/**
   function computes mass %matrix of triangular
   finite element with quadratic approximation functions

   @param eid - element id
   @param mm - mass %matrix

   25.8.2001
*/
void planeelemqt::mass_matrix (long eid,matrix &mm)
{
  long i;
  double jac,thick,rho;
  ivector nodes(nne);
  vector x(nne),y(nne),w(intordmm),gp1(intordmm),gp2(intordmm),t(nne),dens(nne);
  matrix n(napfun,ndofe);

  Mt->give_elemnodes (eid,nodes);
  Mt->give_node_coord2d (x,y,eid);
  Mc->give_thickness (eid,nodes,t);
  Mc->give_density (eid,nodes,dens);

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

  fillm (0.0,mm);

  for (i=0;i<intordmm;i++){
    //  matrix of approximation functions
    bf_matrix (n,gp1[i],gp2[i]);

    //  thickness
    thick = approx (gp1[i],gp2[i],t);

    //  density
    rho = approx (gp1[i],gp2[i],dens);

    //  Jacobian
    jac_2d (jac,x,y,gp1[i],gp2[i]);

    jac*=w[i]*thick*rho;

    //  N^T.N multiplication
    nnj (mm.a,n.a,jac,n.m,n.n);
  }

}

/**
   function computes load %matrix of triangular
   finite element with quadratic approximation functions
   load %vector is obtained after premultiplying load %matrix
   by nodal load values

   @param eid - number of element
   @param lm - load %matrix

   25.8.2001
*/
void planeelemqt::load_matrix (long eid,matrix &lm)
{
  long i;
  double jac,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);

  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_2d (jac,x,y,gp1[i],gp2[i]);
    
    jac*=w[i]*thick;
    
    nnj (lm.a,n.a,jac,n.m,n.n);
  }
  
}






void planeelemqt::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 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 planeelemqt::mainip_strains (long lcid,long eid,long ri,long ci,vector &x,vector &y,vector &r)
{
  long i,ii,ipp;
  double jac;
  vector gp1,gp2,w,eps;
  matrix gm;