barel2d.cpp

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

#include <math.h>
#include "barel2d.h"
#include "global.h"
#include "globmat.h"
#include "genfile.h"
#include "element.h"
#include "node.h"
#include "intpoints.h"
#include "loadcase.h"



barel2d::barel2d (void)
{
  long i;
  
  //  number nodes on element
  nne=2;
  //  number of DOFs on element
  ndofe=4;
  //  number of strain/stress components
  tncomp=1;
  //  number of functions approximated
  napfun=2;
  ssst = bar;
  
  //  number of blocks (parts of geometric matrix)
  nb=1;
  
  //  number of strain/stress components
  ncomp = new long [nb];
  ncomp[0]=1;
  
  //  cumulative number of components approximated
  cncomp = new long [nb];
  cncomp[0]=0;
  
  //  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]=1;

  //  total number of integration points
  tnip=0;
  for (i=0;i<nb;i++){
    tnip+=nip[i][i];
  }
  
  intordsm[0][0]=1;
}

barel2d::~barel2d (void)
{
  long i;
  
  for (i=0;i<nb;i++){
    delete [] nip[i];
    delete [] intordsm[i];
  }
  delete [] nip;
  delete [] intordsm;

  delete [] cncomp;
  delete [] ncomp;
}

void barel2d::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 assembles strain-displacement (geometric) %matrix
   geometric %matrix is in global coordinate system

   @param gm - geometric %matrix
   @param s,c - sin and cos
   @param l - length of the bar
   
   JK, 10.8.2001
*/
void barel2d::geom_matrix (matrix &gm,double s,double c,double l)
{
  gm[0][0]=c/l*(-1.0);
  gm[0][1]=s/l*(-1.0);
  gm[0][2]=c/l;
  gm[0][3]=s/l;
}

/**
   function assembles strain-displacement (geometric) %matrix
   geometric %matrix is in local element coordinate system
   
   @param gm - geometric %matrix
   @param x - node coordinates
   @param jac - Jacobian
   
   JK, 10.8.2001
*/
void barel2d::geom_matrix (matrix &gm,vector &x,double &jac)
{
  double xi=0.0,n[2];
  vector dx(2);
  
  dx_bf_lin_1d (n);
  derivatives_1d (dx,jac,x,xi);
  
  gm[0][0]= dx[0];
  gm[0][2]= dx[1];
}



/**
   function approximates function defined by nodal values

   @param xi - natural coordinate
   @param nodval - nodal values
   
   JK
*/
double barel2d::approx (double xi,vector &nodval)
{
  double f;
  vector bf(nne);

  bf_lin_1d (bf.a,xi);

  scprd (bf,nodval,f);

  return f;
}



/**
   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, 3.2.2002
*/
void barel2d::transf_matrix (ivector &nodes,matrix &tmat)
{
  long i;
  fillm (0.0,tmat);
  
  for (i=0;i<tmat.m;i++){
    tmat[i][i]=1.0;
  }
  
  for (i=0;i<nodes.n;i++){
    if (Mt->nodes[nodes[i]].transf>0){
      tmat[i*2+0][i*2]=Mt->nodes[nodes[i]].e1[0];   tmat[i*2+0][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];
    }
  }

}


//void barel2d::bar_transf_matrix (vector &x, matrix &tmat,vector &gx,vector &gy)
void barel2d::tran_mat (vector &x, matrix &tmat,vector &gx,vector &gy)
{
  long i,j;
  vector gv(2*gx.n),lv(2*gx.n);
  
  j=0;
  for (i=0;i<gx.n;i++){
    gv[j]=gx[i];  j++;
    gv[j]=gy[i];  j++;
  }
  
  //globloctransf (gv,lv,tmat);
  glvectortransf (gv,lv,tmat);

  
  for (i=0;i<gx.n;i++){
    x[i]=lv[i*2];
  }
}

/**
   function computes stiffness %matrix of twodimensional bar element
   
   @param eid - element id
   @param ri,ci - row and column indices
   @param sm - stiffness %matrix

   JK, 10.8.2001
*/
void barel2d::stiffness_matrix (long eid,long ri,long ci,matrix &sm)
{
  long ipid,transf;
  double c,s,l,a,jac;
  ivector nodes (nne);
  vector x(nne),y(nne);
  matrix gm(tncomp,ndofe),d(tncomp,tncomp),tmat (ndofe,ndofe);

  fillm (0.0,sm);
  
  //  node cooridnates
  Mt->give_node_coord2d (x,y,eid);
  
  //  length of the element
  l=sqrt ((x[1]-x[0])*(x[1]-x[0])+(y[1]-y[0])*(y[1]-y[0]));
  if (l<Mp->zero){
    fprintf (stderr,"\n\n zero length of the %ld truss element",eid);
    fprintf (stderr,"\n in function barel2d::stiffness_matrix (barel2d.cpp).\n");
  }
  
  s=(y[1]-y[0])/l;
  c=(x[1]-x[0])/l;
  
  //  geometric matrix
  geom_matrix (gm,s,c,l);
  //  number of first integration point on element
  ipid=Mt->elements[eid].ipp[ri][ci];
  //  stiffness matrix of material
  Mm->matstiff (d,ipid);
  //  area of bar cross-section
  Mc->give_area (eid,a);

  jac=a*l;
  //  B^T D B
  bdbj (sm.a,gm.a,d.a,jac,gm.m,gm.n);
  

  //  transformation of stiffness matrix from global coordinate system
  //  to the local nodal systems
  Mt->give_elemnodes (eid,nodes);
  transf = Mt->locsystems (nodes);
  if (transf>0){
    transf_matrix (nodes,tmat);
    glmatrixtransf (sm,tmat);
  }
  
}


/**
   function computes stiffness %matrix of twodimensional bar element
   
   @param eid - element id
   @param sm - stiffness %matrix
   
   JK, 10.8.2001
*/
void barel2d::res_stiffness_matrix (long eid,matrix &sm)
{
  stiffness_matrix (eid,0,0,sm);
}

/**
   function computes mass %matrix of twodimensional bar element
   
   @param eid - element id
   @param mm - mass %matrix

   JK, 10.8.2001
*/
void barel2d::mass_matrix (long eid,matrix &mm)
{
  double l,a,rho;
  vector x(nne),y(nne);
  
  fillm (0.0,mm);

  Mt->give_node_coord2d (x,y,eid);

  //  length of the element
  l=sqrt ((x[1]-x[0])*(x[1]-x[0])+(y[1]-y[0])*(y[1]-y[0]));
  if (l<Mp->zero){
    fprintf (stderr,"\n\n zero length of the %ld truss element",eid);
    fprintf (stderr,"\n in function barel2d::mass_matrix (file %s, line %d).\n",__FILE__,__LINE__);
  }
  
  //  area of bar cross-section
  Mc->give_area (eid,a);
  //  density of the material
  Mc->give_densitye (eid,rho);
  
  mm[0][0]=a*rho*l*1.0/3.0;
  mm[0][1]=0.0;
  mm[0][2]=a*rho*l*1.0/6.0;
  mm[0][3]=0.0;

  mm[1][0]=0.0;
  mm[1][1]=a*rho*l*1.0/3.0;
  mm[1][2]=0.0;
  mm[1][3]=a*rho*l*1.0/6.0;

  mm[2][0]=a*rho*l*1.0/6.0;
  mm[2][1]=0.0;
  mm[2][2]=a*rho*l*1.0/3.0;
  mm[2][3]=0.0;

  mm[3][0]=0.0;
  mm[3][1]=a*rho*l*1.0/6.0;
  mm[3][2]=0.0;
  mm[3][3]=a*rho*l*1.0/3.0;
}




void barel2d::giveloccoord(vector &x, vector &y,vector &lx)
{
  double l;

  lx[0] = 0.0;
  l = sqr(x[1] - x[0]) + sqr(y[1] - y[0]);
  l = sqrt(l);
  lx[1] = l;
}






/**
   function computes strain at integration points
   
   @param lcid - load case id
   @param eid - element id
   
   JK
*/
void barel2d::res_ip_strains (long lcid,long eid)
{
  long transf;
  vector x(nne),r(ndofe),aux(ndofe);
  ivector cn(ndofe),nodes(nne);
  matrix tmat(ndofe,ndofe);
  
  //  code numbers
  Mt->give_code_numbers (eid,cn.a);
  //  displacements at element nodes
  eldispl (lcid,eid,r.a,cn.a,ndofe);
  
  //  transformation of displacement vector
  //  (in the case of nodal coordinate systems)
  Mt->give_elemnodes (eid,nodes);
  transf = Mt->locsystems (nodes);
  if (transf>0){
    transf_matrix (nodes,tmat);
    lgvectortransf (aux,r,tmat);
    copyv (aux,r);
  }
  
  ip_strains (lcid,eid,0,0,r);
  
}

/**
   function computes strains at integration point

   @param lcid - load case id
   @param eid - element id
   @param ri - row index
   @param ci - column index
   @param r - nodal displacements
   
   10.5.2002
*/
void barel2d::ip_strains (long lcid,long eid,long ri,long ci,vector &r)
{
  long ipid;
  double s,c,l;
  vector x(nne),y(nne),eps(tncomp);
  matrix gm(tncomp,ndofe);

  //  node cooridnates
  Mt->give_node_coord2d (x,y,eid);
  
  //  length of the element
  l=sqrt ((x[1]-x[0])*(x[1]-x[0])+(y[1]-y[0])*(y[1]-y[0]));
  if (l<Mp->zero){
    fprintf (stderr,"\n\n zero length of the %ld truss element",eid);
    fprintf (stderr,"\n in function barel2d::ip_strains (barel2d.cpp).\n");
  }
  
  s=(y[1]-y[0])/l;
  c=(x[1]-x[0])/l;

  //  geometrix matrix
  geom_matrix (gm,s,c,l);
  //  strain computation
  mxv (gm,r,eps);
  //  strain storage
  ipid=Mt->elements[eid].ipp[ri][ci];
  Mm->storestrain (lcid,ipid,eps);
}


/**
   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 barel2d::nod_strains_ip (long lcid,long eid,long ri,long ci)
{
  long i,j,ipid;
  ivector ipnum(nne),nod(nne);
  vector eps(tncomp);
  
  //  numbers of integration points closest to nodes
  //  (function is from the file GEFEL/ordering.cpp)
  ipid=Mt->elements[eid].ipp[ri][ci];
  nodip_bar (ipid,intordsm[0][0],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 at strain points
   
   @param lcid - load case id
   @param eid - element id
   @param ri,ci - row and column indices
   
   JK
*/
void barel2d::strains (long lcid,long eid,long ri,long ci)
{
  long i,naep,ncp,sid;
  vector coord,eps;

  switch (Mm->stra.tape[eid]){
  case nowhere:{
    break;
  }
  case intpts:{
    //allip_strains (lcid,eid,ri,ci);
    break;
  }
  case enodes:{
    nod_strains_ip (lcid,eid,ri,ci);
    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 (1,coord);
    for (i=0;i<naep;i++){
      Mm->stra.give_aepcoord (sid,i,coord);

      if (Mp->strainaver==0)
	//appval (coord[0],0,ncp,eps,stra);
      if (Mp->strainaver==1)
	//appstrain (lcid,eid,coord[0],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 barelq2d::strains (file %s, line %d).\n",__FILE__,__LINE__);
  }
  }

}