plelemlq.cpp

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

#include "plelemlq.h"
#include "global.h"
#include "globmat.h"
#include "genfile.h"
#include "adaptivity.h"
#include "node.h"
#include "element.h"
#include "intpoints.h"
#include "loadcase.h"
#include "gadaptivity.h"
#include <stdlib.h>
#include <math.h>



planeelemlq::planeelemlq (void)
{
  long i,j;
  
  //  number nodes on element
  nne=4;
  //  number of DOFs on element
  ndofe=8;
  //  number of strain/stress components
  tncomp=3;
  //  number of functions approximated
  napfun=2;
  //  order of numerical integration of mass matrix
  intordmm=2;
  //  number of edges on element
  ned=4;
  //  number of nodes on one edge
  nned=2;
  //  order of numerical integration on element edges (boundaries)
  intordb=2;
  
  //  number of blocks (parts of geometric matrix)
  nb=2;
  
  //  number of strain/stress components
  ncomp = new long [nb];
  ncomp[0]=2;
  ncomp[1]=1;
  
  //  cumulative number of components approximated
  cncomp = new long [nb];
  cncomp[0]=0;
  cncomp[1]=2;

  //  number of integration points
  //  order of numerical integration of stiffness matrix
  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]=4;  nip[0][1]=0;
  nip[1][0]=0;  nip[1][1]=1;
  
  //  total number of integration points
  tnip=0;
  for (i=0;i<nb;i++){
    for (j=0;j<nb;j++){
      tnip+=nip[i][j];
    }
  }
  
  intordsm[0][0]=2;  intordsm[0][1]=0;
  intordsm[1][0]=0;  intordsm[1][1]=1;
  
}

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


void planeelemlq::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 - coordinates on element
   @param nodval - nodal values
   
   JK
*/
double planeelemlq::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 assembles coordinates of integration points
   
   @param eid - element id
   @param ipp - integration point pointer
   @param ri - row index
   @param ci - column index
   @param ipcoord - array containing coordinates of integration points
   
   JK, 8.5.2002
*/
void planeelemlq::ipcoord (long eid,long ipp,long ri,long ci,vector &coord)
{
  long i,j,ii;
  double xi,eta;
  vector x(nne),y(nne),w(intordsm[ri][ci]),gp(intordsm[ri][ci]);

  gauss_points (gp.a,w.a,intordsm[ri][ci]);
  Mt->give_node_coord2d (x,y,eid);
  ii=Mt->elements[eid].ipp[ri][ci];

  for (i=0;i<intordsm[ri][ci];i++){
    xi=gp[i];
    for (j=0;j<intordsm[ri][ci];j++){
      eta=gp[j];
      if (ii==ipp){
	coord[0]=approx (xi,eta,x);
	coord[1]=approx (xi,eta,y);
	coord[2]=0.0;
      }
      ii++;
    }
  }
}

/**
   function assembles coordinates of integration points in block [ri][ci]
   
   @param eid - element id
   @param ri - row index
   @param ci - column index
   @param ipcoord - array containing coordinates of integration points
   
   JK, 8.5.2002
*/
void planeelemlq::ipcoordblock (long eid,long ri,long ci,double **coord)
{
  long i,j,k;
  double xi,eta;
  vector x(nne),y(nne),w(intordsm[ri][ci]),gp(intordsm[ri][ci]);
  
  gauss_points (gp.a,w.a,intordsm[ri][ci]);
  Mt->give_node_coord2d (x,y,eid);
  
  k=0;
  for (i=0;i<intordsm[ri][ci];i++){
    xi=gp[i];
    for (j=0;j<intordsm[ri][ci];j++){
      eta=gp[j];
      
      coord[k][0]=approx (xi,eta,x);
      coord[k][1]=approx (xi,eta,y);
      coord[k++][2]=0.0;
    }
  }
}

/**
   function assembles %matrix of base (approximation, shape) functions
   
   @param n - array containing %matrix
   @param xi, eta - natural coordinates
   
   JK, 9.7.2001
*/
void planeelemlq::bf_matrix (matrix &n,double xi,double eta)
{
  long i,j,k;
  vector bf(nne);
  
  bf_lin_4_2d (bf.a,xi,eta);
  
  fillm (0.0,n);

  j=0;  k=1;
  for (i=0;i<nne;i++){
    n[0][j]=bf[i];
    n[1][k]=bf[i];
    j+=2;  k+=2;
  }
}



/**
   function assembles strain-displacement (geometric) %matrix
   
   @param gm - geometric %matrix
   @param x,y - array containing node coordinates
   @param xi,eta - natural coordinates
   @param jac - Jacobian
   
   JK, 9.7.2001
*/
void planeelemlq::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_lin_4_2d (dx.a,eta);
  dy_bf_lin_4_2d (dy.a,xi);
  
  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];
    gm[2][i2]=dx[i];
    i1+=2;  i2+=2;
  }

}

/**
   function assembles blocks of strain-displacement (geometric) %matrix
   
   @param gm - geometric %matrix
   @param ri - row index (number of required block)
   @param x,y - array containing node coordinates
   @param xi,eta - natural coordinates
   @param jac - Jacobian
   
   JK, 9.7.2001
*/
void planeelemlq::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_lin_4_2d (dx.a,eta);
  dy_bf_lin_4_2d (dy.a,xi);
  
  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];
      gm[1][i2]=dy[i];
      i1+=2;  i2+=2;
    }
  }
  if (ri==1){
    i1=0;  i2=1;
    for (i=0;i<nne;i++){
      gm[0][i1]=dy[i];
      gm[0][i2]=dx[i];
      i1+=2;  i2+=2;
    }
  }
}

/**
   function assembles auxiliary vectors B for evaluation of stiffness %matrix
   in geometrically nonlinear problems
   
   @param x,y - array containing node coordinates
   @param xi,eta - natural coordinates
   @param jac - Jacobian
   @param b11,b12,b21,b22 - vectors of derivatives of shape functions
   
   JK, 21.9.2005
*/
void planeelemlq::bvectors (vector &x,vector &y,double xi,double eta,double &jac,
			    vector &b11,vector &b12,vector &b21,vector &b22)
{
  vector dx(nne),dy(nne);
  
  dx_bf_lin_4_2d (dx.a,eta);
  dy_bf_lin_4_2d (dy.a,xi);
  
  derivatives_2d (dx,dy,jac,x,y,xi,eta);
  
  fillv (0.0,b11);
  fillv (0.0,b12);
  fillv (0.0,b21);
  fillv (0.0,b22);

  //  du/dx
  b11[0]=dx[0];  b11[2]=dx[1];  b11[4]=dx[2];  b11[6]=dx[3];
  //  du/dy
  b12[0]=dy[0];  b12[2]=dy[1];  b12[4]=dy[2];  b12[6]=dy[3];
  //  dv/dx
  b21[1]=dx[0];  b21[3]=dx[1];  b21[5]=dx[2];  b21[7]=dx[3];
  //  dv/dy
  b22[1]=dy[0];  b22[3]=dy[1];  b22[5]=dy[2];  b22[7]=dy[3];
}

/**
   function computes strain-displacement %matrix for geometrically nonlinear problems
   
   @param gm - strain-displacement %matrix
   @param r - array of nodal displacements
   @param x,y - array containing node coordinates
   @param xi,eta - natural coordinates
   @param jac - Jacobian

   JK, 21.9.2005
*/
void planeelemlq::gngeom_matrix (matrix &gm,vector &r,vector &x,vector &y,double xi,double eta,double &jac)
{
  long i;
  vector b11(ndofe),b12(ndofe),b21(ndofe),b22(ndofe),av(ndofe);
  matrix am(ndofe,ndofe);
  
  fillm (0.0,gm);
  
  bvectors (x,y,xi,eta,jac,b11,b12,b21,b22);
  
  // *******
  //  E_11
  // *******
  
  //  B11 dr
  for (i=0;i<ndofe;i++){
    gm[0][i]+=b11[i];
  }
  
  //  r B11 B11 dr
  vxv (b11,b11,am);
  vxm (r,am,av);
  for (i=0;i<ndofe;i++){
    gm[0][i]+=av[i];
  }
  
  //  r B21 B21 dr
  vxv (b21,b21,am);
  vxm (r,am,av);
  for (i=0;i<ndofe;i++){
    gm[0][i]+=av[i];
  }

  
  // *******
  //  E_22
  // *******
  
  //  B22 dr
  for (i=0;i<ndofe;i++){
    gm[1][i]+=b22[i];
  }
  
  //  r B22 B22 dr
  vxv (b22,b22,am);
  vxm (r,am,av);
  for (i=0;i<ndofe;i++){
    gm[1][i]+=av[i];
  }
  
  //  r B12 B12 dr
  vxv (b12,b12,am);
  vxm (r,am,av);
  for (i=0;i<ndofe;i++){
    gm[1][i]+=av[i];
  }
  

  // **************
  //  E_12 = E_21
  // **************
  
  //  (B12 + B21) dr
  for (i=0;i<ndofe;i++){
    gm[2][i]+=b12[i]+b21[i];
  }
  
  //  r B11 B12 dr
  vxv (b11,b12,am);
  vxm (r,am,av);
  for (i=0;i<ndofe;i++){
    gm[2][i]+=av[i];
  }
  
  //  r B12 B11 dr
  vxv (b12,b11,am);
  vxm (r,am,av);
  for (i=0;i<ndofe;i++){
    gm[2][i]+=av[i];
  }
  
  //  r B22 B21 dr
  vxv (b22,b21,am);
  vxm (r,am,av);
  for (i=0;i<ndofe;i++){
    gm[2][i]+=av[i];
  }
  
  //  r B21 B22 dr
  vxv (b21,b22,am);
  vxm (r,am,av);
  for (i=0;i<ndofe;i++){
    gm[2][i]+=av[i];
  }
  


}


/**
   function computes gradient %matrix for geometrically nonlinear problems
   
   @param grm - gradient %matrix
   @param x,y - array containing node coordinates
   @param xi,eta - natural coordinates
   @param jac - Jacobian

   JK, 21.9.2005
*/
void planeelemlq::gnl_grmatrix (matrix &grm,vector &x,vector &y,double xi,double eta,double &jac)
{
  long i;
  vector b11(ndofe),b12(ndofe),b21(ndofe),b22(ndofe);
  
  bvectors (x,y,xi,eta,jac,b11,b12,b21,b22);
  
  for (i=0;i<ndofe;i++){
    grm[0][i]=b11[i];
    grm[1][i]=b12[i];
    grm[2][i]=b21[i];
    grm[3][i]=b22[i];
  }
}





/**
   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
   
   JK
*/
void planeelemlq::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 from local nodal coordinate
   system to the global coordinate system x_g = T x_l
   
   @param nodes - array containing node numbers
   @param tmat - transformation %matrix
   
   JK, 9.7.2001
*/
void planeelemlq::transf_matrix (ivector &nod,matrix &tmat)
{
  long i,n,m;

  fillm (0.0,tmat);

  n=nod.n;
  m=tmat.m;
  for (i=0;i<m;i++){
    tmat[i][i]=1.0;
  }
  
  for (i=0;i<n;i++){
    if (Mt->nodes[nod[i]].transf>0){
      tmat[i*2][i*2]   = Mt->nodes[nod[i]].e1[0];    tmat[i*2][i*2+1]   = Mt->nodes[nod[i]].e2[0];
      tmat[i*2+1][i*2] = Mt->nodes[nod[i]].e1[1];    tmat[i*2+1][i*2+1] = Mt->nodes[nod[i]].e2[1];
    }
  }
}





/**
   function computes stiffness %matrix of plane rectangular
   finite element with bilinear approximation functions
   
   function computes stiffness %matrix for geometrically linear problems
   
   @param eid - number of element
   @param ri,ci - row and column indices
   @param sm - stiffness %matrix
   @param x,y - vectors of nodal coordinates
   
   JK, 10.7.2001
*/
void planeelemlq::gl_stiffness_matrix (long eid,long ri,long ci,matrix &sm,vector &x,vector &y)
{
  long i,j,ii,jj,ipp;
  double xi,eta,jac,thick;
  ivector nodes(nne);
  vector w,gp,t(nne);
  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;

      allocv (intordsm[ii][jj],w);
      allocv (intordsm[ii][jj],gp);

      allocm (ncomp[jj],ndofe,gmc);
      allocm (ncomp[ii],ncomp[jj],dd);

      gauss_points (gp.a,w.a,intordsm[ii][jj]);

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

      for (i=0;i<intordsm[ii][jj];i++){
	xi=gp[i];
	for (j=0;j<intordsm[ii][jj];j++){
	  eta=gp[j];

	  //  blocks of geometric matrices
	  geom_matrix_block (gmr,ii,x,y,xi,eta,jac);
	  geom_matrix_block (gmc,jj,x,y,xi,eta,jac);

	  //  matrix of stiffness of the material
	  Mm->matstiff (d,ipp);

	  //
	  dmatblock (ii,jj,d,dd);

	  //  thickness in integration point
	  thick = approx (xi,eta,t);

	  jac*=thick*w[i]*w[j];
	  
	  jac=fabs(jac);

	  //  contribution to the stiffness matrix of the element
	  bdbjac (sm,gmr,dd,gmc,jac);
	  
	  ipp++;
	}
      }
      
      destrm (dd);  destrm (gmc);  destrv (gp);  destrv (w);
    }
    destrm (gmr);
  }
  
}

/**
   function computes stiffness %matrix of quadrilateral finite element
   
   function computes stiffness %matrix for geometrically nonlinear problems
   
   @param lcid - load case id
   @param eid - element id
   @param ri,ci - row and column indices
   @param sm - stiffness %matrix
   @param x,y - vectors of nodal coordinates
   
   JK, 21.9.2005
*/
void planeelemlq::gnl_stiffness_matrix (long lcid,long eid,long ri,long ci,matrix &sm,vector &x,vector &y)
{
  long i,j,ipp;
  double xi,eta,jac,jac2,thick;
  ivector cn(ndofe),nodes(nne);