axisymlq-nb3.cpp

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

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


axisymlq::axisymlq (void)
{
  long i,j;
  
  nne=4;  ndofe=8;  tncomp=4;  napfun=2;  ned=4;  nned=2;
  intordmm=3;  intordb=2;
  ssst=axisymm;
  nb=3;

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

  cncomp = new long [nb];
  cncomp[0]=0;
  cncomp[1]=2;
  cncomp[2]=3;
  
  
  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]=4;  nip[0][2]=0;
  nip[1][0]=4;  nip[1][1]=4;  nip[1][2]=0;
  nip[2][0]=0;  nip[2][1]=0;  nip[2][2]=1;
  
  intordsm[0][0]=2;  intordsm[0][1]=2;  intordsm[0][2]=0;
  intordsm[1][0]=2;  intordsm[1][1]=2;  intordsm[1][2]=0;
  intordsm[2][0]=0;  intordsm[2][1]=0;  intordsm[2][2]=1;

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

}

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

void axisymlq::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
   
*/
double axisymlq::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 approximation functions
   
   @param n - matrix of approximation functions
   @param xi,eta - natural coordinates
   
   9.7.2001
*/
void axisymlq::bf_matrix (matrix &n,double xi,double eta)
{
  long i,j,k;
  vector bf(nne);
  
  fillm (0.0,n);

  bf_lin_4_2d (bf.a,xi,eta);
  
  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 geometric matrix
   
   epsilon_x = du/dx
   epsilon_y = dv/dy
   epsilon_fi = u/r
   epsilon_xy = du/dy + dv/dx
   
   @param gm - geometric matrix
   @param ri - block index
   @param x,y - arrays of node coordinates
   @param xi,eta - natural coordinates
   @param jac - jacobian
   
   8.12.2001
*/
void axisymlq::geom_matrix (matrix &gm,vector &x,vector &y,double xi,double eta,double &jac)
{
  long i,i1,i2;
  double r;
  vector bf(nne),dx(nne),dy(nne);
  
  dx_bf_lin_4_2d (dx.a,eta);
  dy_bf_lin_4_2d (dy.a,xi);
  bf_lin_4_2d (bf.a,xi,eta);

  derivatives_2d (dx,dy,jac,x,y,xi,eta);
  
  r = approx (xi,eta,x);
  if (fabs(r)<Mp->zero){
    fprintf (stderr,"\n\n radius is equal %e in function axisymlq::geom_matrix_block (%s, line %d)",r,__FILE__,__LINE__);
  }
  
  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]=bf[i]/r;
    gm[3][i1]=dy[i];
    gm[3][i2]=dx[i];
    i1+=2;  i2+=2;
  }
}

/**
   function assembles part of geometric matrix
   
   epsilon_x = du/dx
   epsilon_y = dv/dy
   epsilon_fi = u/r
   epsilon_xy = du/dy + dv/dx
   
   @param gm - geometric matrix
   @param ri - block index
   @param x,y - arrays of node coordinates
   @param xi,eta - natural coordinates
   @param jac - jacobian
   
   8.12.2001
*/
void axisymlq::geom_matrix_block (matrix &gm,long ri,vector &x,vector &y,double xi,double eta,double &jac)
{
  long i,i1,i2;
  double r;
  vector bf(nne),dx(nne),dy(nne);
  
  dx_bf_lin_4_2d (dx.a,eta);
  dy_bf_lin_4_2d (dy.a,xi);
  bf_lin_4_2d (bf.a,xi,eta);

  derivatives_2d (dx,dy,jac,x,y,xi,eta);
  
  r = approx (xi,eta,x);
  if (fabs(r)<Mp->zero){
    fprintf (stderr,"\n\n radius is equal %e in function axisymlq::geom_matrix_block (%s, line %d)",r,__FILE__,__LINE__);
  }
  
  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;
    for (i=0;i<nne;i++){
      gm[0][i1]=bf[i]/r;
      i1+=2;
    }
  }
  if (ri==2){
    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 extracts blocks from stiffness matrix of the material
   
   @param ri,ci - row and column indices
   @param d - stiffness matrix of material
   @param dd - required block from stiffness matrix of material
   
   10.5.2002
*/
void axisymlq::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==0 && ci==2){
    dd[0][0]=d[0][3];
    dd[1][0]=d[1][3];
  }
  
  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];
  }
  if (ri==1 && ci==2){
    dd[0][0]=d[2][3];
  }
  
  if (ri==2 && ci==0){
    dd[0][0]=d[3][0];  dd[0][1]=d[3][1];
  }
  if (ri==2 && ci==1){
    dd[0][0]=d[3][2];
  }
  if (ri==2 && ci==2){
    dd[0][0]=d[3][3];
  }
}


/**
   nutno otestovat! pak je mozne smazat tuto hlasku
   
   transformation matrix x_g = T x_l
*/
void axisymlq::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 axisymmetric quadrilateral
   finite element with bilinear approximation functions
   
   @param eid - element id
   @param ri,ci - row and column indices
   @param sm - stiffness matrix

   8.12.2001
*/
void axisymlq::stiffness_matrix (long eid,long ri,long ci,matrix &sm)
{
  long i,j,ii,jj,ipp,transf;
  double xi,eta,jac,r;
  ivector nodes(nne);
  vector x(nne),y(nne),w,gp;
  matrix gmr,gmc,d(tncomp,tncomp),dd;
  
  Mt->give_elemnodes (eid,nodes);
  Mt->give_node_coord2d (x,y,eid);
  
  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];
	  
	  //  geometric matrix
	  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);
	  
	  r = approx (xi,eta,x);
	  jac*=w[i]*w[j]*r;
	  
	  //  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);
  }
  
  //  transformation of stiffness matrix
  transf = Mt->locsystems (nodes);
  if (transf>0){
    matrix tmat (ndofe,ndofe);
    transf_matrix (nodes,tmat);
    glmatrixtransf (sm,tmat);
  }
}

/**
   function computes resulting stiffness matrix of element
   
   @param eid - element id
   @param sm - stiffness matrix
   
   10.5.2002
*/
void axisymlq::res_stiffness_matrix (long eid,matrix &sm)
{
  stiffness_matrix (eid,0,0,sm);
}

/**
   function computes mass matrix of the rectangular axisymmetric
   finite element with bilinear approximation functions
   
   @param eid - number of element
   @param mm - mass matrix

   24.6.2001
*/
void axisymlq::mass_matrix (long eid,matrix &mm)
{
  long i,j;
  double jac,xi,eta,rho,r;
  ivector nodes(nne);
  vector x(nne),y(nne),w(intordmm),gp(intordmm),t(nne),dens(nne);
  matrix n(napfun,ndofe);
  
  Mt->give_elemnodes (eid,nodes);
  Mc->give_density (eid,nodes,dens);
  Mt->give_node_coord2d (x,y,eid);
  gauss_points (gp.a,w.a,intordmm);
  
  fillm (0.0,mm);

  for (i=0;i<intordmm;i++){
    xi=gp[i];
    for (j=0;j<intordmm;j++){
      eta=gp[j];
      jac_2d (jac,x,y,xi,eta);
      bf_matrix (n,xi,eta);
      
      rho = approx (xi,eta,dens);
      r = approx (xi,eta,x);
      jac*=w[i]*w[j]*rho*r;
      
      nnj (mm.a,n.a,jac,n.m,n.n);
    }
  }
  
}

void axisymlq::res_mainip_strains (long lcid,long eid)
{
  long i;
  vector x(nne),y(nne),r(ndofe),aux;
  ivector nodes(nne),cn(ndofe);
  matrix tmat;

  Mt->give_elemnodes (eid,nodes);
  Mt->give_node_coord2d (x,y,eid);
  Mt->give_code_numbers (eid,cn.a);
  eldispl (lcid,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);
    copyv (aux,r);
    destrv (aux);
    destrm (tmat);
  }
  
  for (i=0;i<nb;i++){
    mainip_strains (lcid,eid,0,0,i,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 axisymlq::mainip_strains (long lcid,long eid,long ri,long ci,long ii,vector &x,vector &y,vector &r)
{
  long i,j,ipp;
  double xi,eta,jac;
  vector gp,w,eps;
  matrix gm;
  
  allocv (intordsm[ii][ii],gp);
  allocv (intordsm[ii][ii],w);
  allocv (ncomp[ii],eps);
  allocm (ncomp[ii],ndofe,gm);
  
  gauss_points (gp.a,w.a,intordsm[ii][ii]);
  
  ipp=Mt->elements[eid].ipp[ri+ii][ci+ii];
  for (i=0;i<intordsm[ii][ii];i++){
    xi=gp[i];
    for (j=0;j<intordsm[ii][ii];j++){
      eta=gp[j];
      
      geom_matrix_block (gm,ii,x,y,xi,eta,jac);
      mxv (gm,r,eps);
      
      Mm->storestrain (lcid,ipp,cncomp[ii],eps);
      ipp++;
    }
  }
  
  destrm (gm);  destrv (eps);  destrv (w);  destrv (gp);
}

/**
   function computes strains in nodes of element
   
   @param lcid - load case id
   @param eid - element id
   
   10.5.2002
*/
void axisymlq::nod_strains (long lcid,long eid,long ri,long ci)
{
  long i,j,ii,ipp;
  double xi,eta,*lsm,*lhs,*rhs;
  vector x(nne),y(nne),nxi(nne),neta(nne),r(ndofe),gp,w,eps,aux,natcoord(2);
  ivector nodes(nne),cn(ndofe);
  matrix tmat;

  lsm = new double [9];