axisymqq.cpp

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

#include "axisymqq.h"
#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>


axisymqq::axisymqq (void)
{
  long i,j;
  
  nne=8;  ndofe=16;  tncomp=4;  napfun=2;  ned=4;  nned=3;
  intordmm=3;  intordb=2;
  ssst=axisymm;

  nb=1;
  
  ncomp = new long [nb];
  ncomp[0]=4;
  
  cncomp = new long [nb];
  cncomp[0]=0;
  
  
  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]=9;
  
  intordsm[0][0]=3;
  
  
  tnip=0;
  for (i=0;i<nb;i++){
    for (j=0;j<nb;j++){
      tnip+=nip[i][j];
    }
  }

}

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

void axisymqq::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 axisymqq::approx (double xi,double eta,vector &nodval)
{
  double f;
  vector bf(nne);
  
  bf_quad_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 axisymqq::bf_matrix (matrix &n,double xi,double eta)
{
  long i,j,k;
  vector bf(nne);
  
  fillm (0.0,n);

  bf_quad_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 axisymqq::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_quad_4_2d (dx.a,xi,eta);
  dy_bf_quad_4_2d (dy.a,xi,eta);
  bf_quad_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 axisymqq::geom_matrix_block (%s, line %d)",r,__FILE__,__LINE__);
    r=0.00001;
  }
  
  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 axisymqq::geom_matrix_block (matrix &gm,long ri,vector &x,vector &y,double xi,double eta,double &jac)
{
  if (nb==1){
    geom_matrix (gm,x,y,xi,eta,jac);
  }
  else{
    long i,i1,i2;
    double r;
    vector bf(nne),dx(nne),dy(nne);
    
    dx_bf_quad_4_2d (dx.a,xi,eta);
    dy_bf_quad_4_2d (dy.a,xi,eta);
    bf_quad_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 axisymqq::geom_matrix_block (%s, line %d)",r,__FILE__,__LINE__);
      r=0.00001;
    }
    
    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;
      }
    }
  }
}

/**
   nutno otestovat! pak je mozne smazat tuto hlasku
   
   transformation matrix x_g = T x_l
*/
void axisymqq::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 axisymqq::stiffness_matrix (long eid,long ri,long ci,matrix &sm)
{
  long i,j,ipp,transf;
  double xi,eta,jac,r;
  ivector nodes(nne);
  vector x(nne),y(nne),w,gp;
  matrix gm(tncomp,ndofe),d(tncomp,tncomp);
  
  Mt->give_elemnodes (eid,nodes);
  Mt->give_node_coord2d (x,y,eid);
  
  fillm (0.0,sm);
  
  
  allocv (intordsm[0][0],w);
  allocv (intordsm[0][0],gp);
  
  gauss_points (gp.a,w.a,intordsm[0][0]);
  
  ipp=Mt->elements[eid].ipp[ri][ci];
  
  for (i=0;i<intordsm[0][0];i++){
    xi=gp[i];
    for (j=0;j<intordsm[0][0];j++){
      eta=gp[j];
      
      //  geometric matrix
      geom_matrix (gm,x,y,xi,eta,jac);
      
      //  matrix of stiffness of the material
      Mm->matstiff (d,ipp);
      
      r = approx (xi,eta,x);
      jac*=w[i]*w[j]*r;
      
      //  contribution to the stiffness matrix of the element
      bdbjac (sm,gm,d,gm,jac);
      
      ipp++;
    }
  }
  destrv (gp);  destrv (w);
  
  //  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 axisymqq::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 axisymqq::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 axisymqq::res_mainip_strains (long lcid,long eid)
{
  mainip_strains (lcid,eid,0,0);
}

/**
   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 axisymqq::mainip_strains (long lcid,long eid,long ri,long ci)
{
  long i,j,ipp;
  double xi,eta,jac;
  vector x(nne),y(nne),r(ndofe),gp,w,eps(tncomp),aux;
  ivector nodes(nne),cn(ndofe);
  matrix gm(tncomp,ndofe),tmat;

  Mt->give_elemnodes (eid,nodes);
  Mt->give_node_coord2d (x,y,eid);
  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);
  }
  
  
  allocv (intordsm[0][0],gp);
  allocv (intordsm[0][0],w);
  
  gauss_points (gp.a,w.a,intordsm[0][0]);
  
  ipp=Mt->elements[eid].ipp[ri][ci];
  for (i=0;i<intordsm[0][0];i++){
    xi=gp[i];
    for (j=0;j<intordsm[0][0];j++){
      eta=gp[j];
      
      geom_matrix (gm,x,y,xi,eta,jac);
      mxv (gm,r,eps);
      
      Mm->storestrain (lcid,ipp,eps);
      ipp++;
    }
  }
  
  destrv (w);  destrv (gp);
  
}

/**
   function computes strains in nodes of element

   @param lcid - load case id
   @param eid - element id
   @param ri,ci - row and column indices
   
   10.5.2002
*/
void axisymqq::nod_strains_ip (long lcid,long eid)
{
  long i,j;
  ivector ipnum(nne),nod(nne);
  vector eps(tncomp);
  
  //  numbers of integration points closest to nodes
  nodipnum (eid,ipnum);
  
  //  node numbers of the element
  Mt->give_elemnodes (eid,nod);
  
  for (i=0;i<nne;i++){
    //  strains at the closest integration point
    Mm->givestrain (lcid,ipnum[i],eps);
    
    //  storage of strains to the node
    j=nod[i];
    Mt->nodes[j].storestrain (lcid,0,eps);
  }
  
}

/**
   function computes strains in nodes of element
   
   @param lcid - load case id
   @param eid - element id
   
   JK, 23.9.2004
*/
void axisymqq::nod_strains_comp (long lcid,long eid)
{
  long i,j;
  double jac;
  vector x(nne),y(nne),nxi(nne),neta(nne),r(ndofe),eps(tncomp),aux;
  ivector nodes(nne),cn(ndofe);
  matrix gm(tncomp,ndofe),tmat;
  
  //  natural coordinates of nodes of element
  nodecoord (nxi,neta);
  //  node numbers of element
  Mt->give_elemnodes (eid,nodes);
  //  coordinates of element nodes
  Mt->give_node_coord2d (x,y,eid);
  //  code numbers of element
  Mt->give_code_numbers (eid,cn.a);
  //  nodal displacements
  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 (i=0;i<nne;i++){
    //  block of geometric matrix
    geom_matrix (gm,x,y,nxi[i],neta[i],jac);
    //  strain computation
    mxv (gm,r,eps);
    
    //  storage of nodal strains
    j=nodes[i];
    Mt->nodes[j].storestrain (lcid,0,eps);
  }
  
}

/**
   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 axisymqq::res_allip_strains (long lcid,long eid)
{
  allip_strains (lcid,eid,0,0);
}
/**
   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 axisymqq::allip_strains (long lcid,long eid,long ri,long ci)
{
  //  blocks of strain components at integration points
  res_mainip_strains (lcid,eid);
}



void axisymqq::strains (long lcid,long eid,long ri,long ci)
{
  vector coord,eps;
  
  switch (Mm->stra.tape[eid]){
  case nowhere:{
    break;
  }
  case intpts:{
    //allip_strains (stra,lcid,eid,ri,ci);
    break;
  }
  case enodes:{
    nod_strains_ip (lcid,eid);
    break;
  }
  case userdefined:{
    /*
    //  number of auxiliary element points
    naep = Mm->stra.give_naep (eid);
    ncp = Mm->stra.give_ncomp (eid);
    sid = Mm->stra.give_sid (eid);
    allocv (ncp,eps);
    allocv (2,coord);
    for (i=0;i<naep;i++){
      Mm->stra.give_aepcoord (sid,i,coord);
      
      if (Mp->strainaver==0)
	appval (coord[0],coord[1],0,ncp,eps,stra);
      if (Mp->strainaver==1)
	appstrain (lcid,eid,coord[0],coord[1],0,ncp,eps);
      
      Mm->stra.storevalues(lcid,eid,i,eps);
    }
    destrv (eps);
    destrv (coord);
    */
    break;
  }
  default:{
    fprintf (stderr,"\n\n unknown strain point is required in function planeelemlq::strains (%s, line %d).\n",__FILE__,__LINE__);
  }
  }

}

/**
   function assembles natural coordinates of nodes of element
   
   @param xi - array containing natural coordinates xi
   @param eta - array containing natrual coordinates eta
   
   10.5.2002
*/
void axisymqq::nodecoord (vector &xi,vector &eta)
{
  xi[0] =  1.0;  eta[0] =  1.0;
  xi[1] = -1.0;  eta[1] =  1.0;
  xi[2] = -1.0;  eta[2] = -1.0;
  xi[3] =  1.0;  eta[3] = -1.0;
  xi[4] =  0.0;  eta[4] =  1.0;
  xi[5] = -1.0;  eta[5] =  0.0;
  xi[6] =  0.0;  eta[6] = -1.0;
  xi[7] =  1.0;  eta[7] =  0.0;
}

/**
   function returns numbers of integration point closest to element nodes
   
   @param eid - element id
   @param ri,ci - row and column indices
   @param ipnum - array of numbers
   
   JK, 25.9.2004
*/
void axisymqq::nodipnum (long eid,ivector &ipnum)
{
  long i,j;
  
  j=intordsm[0][0];
  i=Mt->elements[eid].ipp[0][0];
  
  /*
  ipnum[0]=i+j*(j-1)+j-1;
  ipnum[1]=i+j-1;
  ipnum[2]=i;
  ipnum[3]=i+j*(j-1);
  */
  
  ipnum[0]=i+8;
  ipnum[1]=i+2;
  ipnum[2]=i+0;
  ipnum[3]=i+6;
  ipnum[4]=i+5;
  ipnum[5]=i+1;
  ipnum[6]=i+3;
  ipnum[7]=i+7;
  
}

/**
   function computes strains in arbitrary point on element
   
   @param xi, eta - natural coordinates of the point
   @param eps - array containing strains
   @param val - array containing values on element
   
   11.5.2002
*/
void axisymqq::appval (double xi,double eta,long fi,long nc,vector &eps,double **val)
{
  long i,j,k;
  vector nodval;
  
  k=0;
  allocv (nne,nodval);
  for (i=fi;i<fi+nc;i++){
    for (j=0;j<nne;j++){
      nodval[j]=val[j][i];
    }
    eps[k]=approx (xi,eta,nodval);
    k++;
  }
  
  destrv (nodval);
}

/**
   function computes stresses at integration points