plelemrotlq.cpp

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

#include "plelemrotlq.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>



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

  nne=4;  ndofe=12;  tncomp=3;  napfun=3;
  intordmm=2;  ned=4;  nned=2;
  
  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];
  }
  
  intordsm[0][0]=3;  intordsm[0][1]=0;
  intordsm[1][0]=0;  intordsm[1][1]=3;
  
  nip[0][0]=9;  nip[0][1]=0;
  nip[1][0]=0;  nip[1][1]=9;
  
  tnip=0;
  for (i=0;i<nb;i++){
    for (j=0;j<nb;j++){
      tnip+=nip[i][j];
    }
  }

}

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

void planeelemrotlq::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 prepares auxiliary data for element with rotational degrees of freedom
   
   @param x,y - vectors of node coordinates
   @param l - vector of lengths
   @param nx,ny - vectors of normal vectors components

   8.12.2001
*/
void planeelemrotlq::auxdata (vector &x,vector &y,vector &l,vector &nx,vector &ny)
{
  double sx,sy;
  sx=x[1]-x[0];  sy=y[1]-y[0];
  l[0]=sqrt(sx*sx+sy*sy);
  nx[0]=sy/l[0];  ny[0]=sx*(-1.0)/l[0];
  
  sx=x[2]-x[1];  sy=y[2]-y[1];
  l[1]=sqrt(sx*sx+sy*sy);
  nx[1]=sy/l[1];  ny[1]=sx*(-1.0)/l[1];

  sx=x[3]-x[2];  sy=y[3]-y[2];
  l[2]=sqrt(sx*sx+sy*sy);
  nx[2]=sy/l[2];  ny[2]=sx*(-1.0)/l[2];

  sx=x[0]-x[3];  sy=y[0]-y[3];
  l[3]=sqrt(sx*sx+sy*sy);
  nx[3]=sy/l[3];  ny[3]=sx*(-1.0)/l[3];
}

/**
   function approximates function defined by nodal values
   
   @param xi,eta - coordinates on element
   @param nodval - nodal values
*/
double planeelemrotlq::approx (double xi,double eta,vector &nodval)
{
  double f;
  vector bf(nne);
  
  bf_lin_4_2d (bf.a,xi,eta);
  scprd (bf,nodval,f);
  return f;
}

/**
   function returns matrix of base function
   9.7.2001
*/
void planeelemrotlq::bf_matrix (matrix &n,double xi,double eta,vector &l,vector &nx,vector &ny)
{
  long i,j,k,m,ii,jj;
  vector bf(nne);
  
  fillm (0.0,n);

  bf_rot_4_2d (bf.a,xi,eta,nx.a,ny.a,l.a);
  
  j=0;  k=1;  m=2;  ii=4;  jj=8;
  for (i=0;i<nne;i++){
    n[0][j]=bf[i];
    n[0][m]=bf[ii];
    n[1][k]=bf[i];
    n[1][m]=bf[jj];
    j+=3;  k+=3;  m+=3;  ii++;  jj++;
  }
}

void planeelemrotlq::geom_matrix (matrix &gm,vector &x,vector &y,double xi,double eta,
				  vector &l,vector &nx,vector &ny,double &jac)
{
  long i,i1,i2,i3,ii,jj;
  vector dx(3*nne),dy(3*nne);
  
  dx_bf_rot_4_2d (dx.a,xi,eta,nx.a,ny.a,l.a);
  dy_bf_rot_4_2d (dy.a,xi,eta,nx.a,ny.a,l.a);
  
  derivatives_2d (dx,dy,jac,x,y,xi,eta);
  
  fillm (0.0,gm);
  
  i1=0;  i2=1;  i3=2;  ii=4;  jj=8;

  for (i=0;i<nne;i++){
    gm[0][i1]=dx[i];
    gm[0][i3]=dx[ii];
    gm[1][i2]=dy[i];
    gm[1][i3]=dy[jj];
    gm[2][i1]=dy[i];
    gm[2][i2]=dx[i];
    gm[2][i3]=dy[ii]+dx[jj];
    i1+=3;  i2+=3;  i3+=3;  ii++;  jj++;
  }

  /*
  gm[0][0]=dx[0];
  gm[0][2]=dx[4];
  gm[0][3]=dx[1];
  gm[0][5]=dx[5];
  gm[0][6]=dx[2];
  gm[0][8]=dx[6];
  gm[0][9]=dx[3];
  gm[0][11]=dx[7];

  gm[1][1]=dy[0];
  gm[1][2]=dy[8];
  gm[1][4]=dy[1];
  gm[1][5]=dy[9];
  gm[1][7]=dy[2];
  gm[1][8]=dy[10];
  gm[1][10]=dy[3];
  gm[1][11]=dy[11];
  
  gm[2][0]=dy[0];
  gm[2][1]=dx[0];
  gm[2][2]=dy[4]+dx[8];
  gm[2][3]=dy[1];
  gm[2][4]=dx[1];
  gm[2][5]=dy[5]+dx[9];
  gm[2][6]=dy[2];
  gm[2][7]=dx[2];
  gm[2][8]=dy[6]+dx[10];
  gm[2][9]=dy[3];
  gm[2][10]=dx[3];
  gm[2][11]=dy[7]+dx[11];
  */
}

void planeelemrotlq::geom_matrix_block (matrix &gm,long ri,vector &x,vector &y,double xi,double eta,
					vector &l,vector &nx,vector &ny,double &jac)
{
  long i,i1,i2,i3,ii,jj;
  vector dx(3*nne),dy(3*nne);
  
  dx_bf_rot_4_2d (dx.a,xi,eta,nx.a,ny.a,l.a);
  dy_bf_rot_4_2d (dy.a,xi,eta,nx.a,ny.a,l.a);
  
  derivatives_2d (dx,dy,jac,x,y,xi,eta);
  
  fillm (0.0,gm);
  
  if (ri==0){
    i1=0;  i2=1;  i3=2;  ii=4;  jj=8;

    for (i=0;i<nne;i++){
      gm[0][i1]=dx[i];
      gm[0][i3]=dx[ii];
      gm[1][i2]=dy[i];
      gm[1][i3]=dy[jj];
      i1+=3;  i2+=3;  i3+=3;  ii++;  jj++;
    }

    /*
    gm[0][0]=dx[0];
    gm[0][2]=dx[4];
    gm[0][3]=dx[1];
    gm[0][5]=dx[5];
    gm[0][6]=dx[2];
    gm[0][8]=dx[6];
    gm[0][9]=dx[3];
    gm[0][11]=dx[7];

    gm[1][1]=dy[0];
    gm[1][2]=dy[8];
    gm[1][4]=dy[1];
    gm[1][5]=dy[9];
    gm[1][7]=dy[2];
    gm[1][8]=dy[10];
    gm[1][10]=dy[3];
    gm[1][11]=dy[11];
    */
  }
  if (ri==1){
    i1=0;  i2=1;  i3=2;  ii=4;  jj=8;

    for (i=0;i<nne;i++){
      gm[0][i1]=dy[i];
      gm[0][i2]=dx[i];
      gm[0][i3]=dy[ii]+dx[jj];
      i1+=3;  i2+=3;  i3+=3;  ii++;  jj++;
    }

    /*
    gm[0][0]=dy[0];
    gm[0][1]=dx[0];
    gm[0][2]=dy[4]+dx[8];

    gm[0][3]=dy[1];
    gm[0][4]=dx[1];
    gm[0][5]=dy[5]+dx[9];

    gm[0][6]=dy[2];
    gm[0][7]=dx[2];
    gm[0][8]=dy[6]+dx[10];

    gm[0][9]=dy[3];
    gm[0][10]=dx[3];
    gm[0][11]=dy[7]+dx[11];
    */
  }
  
}

void planeelemrotlq::addgeommat (matrix &gm,vector &x,vector &y,double xi,double eta,
				 vector &l,vector &nx,vector &ny,double &jac)
{
  long i,i1,i2,i3,ii,jj;
  vector bf(ndofe),dx(ndofe),dy(ndofe);
  
  bf_rot_4_2d (bf.a,xi,eta,nx.a,ny.a,l.a);
  dx_bf_rot_4_2d (dx.a,xi,eta,nx.a,ny.a,l.a);
  dy_bf_rot_4_2d (dy.a,xi,eta,nx.a,ny.a,l.a);
  
  derivatives_2d (dx,dy,jac,x,y,xi,eta);
  
  fillm (0.0,gm);
  
  i1=0;  i2=1;  i3=2;  ii=4;  jj=8;

  for (i=0;i<nne;i++){
    gm[0][i1]=0.0-dy[i]/2.0;
    gm[0][i2]=dx[i]/2.0;
    gm[0][i3]=dx[jj]/2.0-dy[ii]/2.0-bf[i];
    i1+=3;  i2+=3;  i3+=3;  ii++;  jj++;
  }

  /*
  gm[0][0]=0.0-dy[0]/2.0;
  gm[0][1]=dx[0]/2.0;
  gm[0][2]=dx[8]/2.0-dy[4]/2.0-bf[0];

  gm[0][3]=0.0-dy[1]/2.0;
  gm[0][4]=dx[1]/2.0;
  gm[0][5]=dx[9]/2.0-dy[5]/2.0-bf[1];

  gm[0][6]=0.0-dy[2]/2.0;
  gm[0][7]=dx[2]/2.0;
  gm[0][8]=dx[10]/2.0-dy[6]/2.0-bf[2];

  gm[0][9]=0.0-dy[3]/2.0;
  gm[0][10]=dx[3]/2.0;
  gm[0][11]=dx[11]/2.0-dy[7]/2.0-bf[3];
  */
}


void planeelemrotlq::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
*/
void planeelemrotlq::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*3][i*3]   = Mt->nodes[nodes[i]].e1[0];    tmat[i*3][i*3+1]   = Mt->nodes[nodes[i]].e2[0];  tmat[i*3][i*3+2]   = 0.0;
      tmat[i*3+1][i*3] = Mt->nodes[nodes[i]].e1[1];    tmat[i*3+1][i*3+1] = Mt->nodes[nodes[i]].e2[1];  tmat[i*3+1][i*3+2] = 0.0;
      tmat[i*3+2][i*3] = 0.0;                          tmat[i*3+2][i*3+1] = 0.0;                        tmat[i*3+2][i*3+2] = 1.0;
    }
  }
}

/**
   function computes stiffness matrix of plane stress quadrilateral
   finite element with rotational degrees of freedom with
   bilinear approximation functions

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

   8.12.2001
*/
void planeelemrotlq::stiffness_matrix (long eid,long ri,long ci,matrix &sm,vector &x,vector &y)
{
  long i,j,ii,jj,ipp;
  double xi,eta,ww1,ww2,jac,thick;
  ivector nodes(nne);
  vector l(nne),nx(nne),ny(nne),w,gp,t(nne);
  matrix gmr,gmc,dd,d(tncomp,tncomp);
  
  Mt->give_elemnodes (eid,nodes);
  Mc->give_thickness (eid,nodes,t);
  auxdata (x,y,l,nx,ny);
  
  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;
      
      allocv (intordsm[ii][jj],w);
      allocv (intordsm[ii][jj],gp);
      
      allocm (ncomp[jj],ndofe,gmc);
      allocm (ncomp[ii],ncomp[jj],dd);
      
      ipp=Mt->elements[eid].ipp[ii][jj];
      gauss_points (gp.a,w.a,intordsm[ii][jj]);
      
      
      for (i=0;i<intordsm[ii][jj];i++){
	xi=gp[i];  ww1=w[i];
	for (j=0;j<intordsm[ii][jj];j++){
	  eta=gp[j];  ww2=w[j];
	  
	  //  geometrical matrix
	  geom_matrix_block (gmr,ii,x,y,xi,eta,l,nx,ny,jac);
	  geom_matrix_block (gmc,jj,x,y,xi,eta,l,nx,ny,jac);
	  
	  //  matrix of stiffness of the material
	  Mm->matstiff (d,ipp);
	  dmatblock (ii,jj,d,dd);
	  
	  thick = approx (xi,eta,t);
	  
	  jac*=thick*ww1*ww2;
	  
	  //  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 (gp);  destrv (w);
    }
    destrm (gmr);
  }
  

  allocv (1,w);
  allocv (1,gp);
  gauss_points (gp.a,w.a,1);
  allocm (1,ndofe,gmr);
  allocm (ndofe,ndofe,gmc);
  for (i=0;i<1;i++){
    for (j=0;j<1;j++){
      xi=gp[i];  eta=gp[j];
      
      addgeommat (gmr,x,y,xi,eta,l,nx,ny,jac);
      mtxm (gmr,gmr,gmc);
      thick = approx (xi,eta,t);
      cmulm (thick*jac*w[i]*w[j],gmc);
      addm (sm,gmc,sm);
    }
  }

  /*
  allocv (2,w);
  allocv (2,gp);
  gauss_points (gp.a,w.a,2);
  allocm (1,ndofe,gmr);
  allocm (ndofe,ndofe,gmc);
  for (i=0;i<2;i++){
    for (j=0;j<2;j++){
      xi=gp[i];  eta=gp[j];
      
      addgeommat (gmr,x,y,xi,eta,l,nx,ny,jac);
      mtxm (gmr,gmr,gmc);
      thick = approx (xi,eta,t);
      cmulm (thick*jac*w[i]*w[j],gmc);
      addm (sm,gmc,sm);
    }
  }
  */

  destrm (gmc);  destrm (gmr);
  destrv (gp);  destrv (w);

}

void planeelemrotlq::res_stiffness_matrix (long eid,matrix &sm)
{
  long transf;
  ivector nodes(nne);