barel3d.cpp

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

#include <math.h>
#include "barel3d.h"
#include "global.h"
#include "globmat.h"
#include "genfile.h"
#include "element.h"
#include "node.h"
#include "intpoints.h"
#include "loadcase.h"


/**
   JK, 27.9.2005
*/
barel3d::barel3d (void)
{
  long i;
  
  //  number nodes on element
  nne=2;
  //  number of DOFs on element
  ndofe=6;
  //  number of strain/stress components
  tncomp=1;
  //  number of functions approximated
  napfun=3;
  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;
}

barel3d::~barel3d (void)
{
  long i;
  
  for (i=0;i<nb;i++){
    delete [] nip[i];
    delete [] intordsm[i];
  }
  delete [] nip;
  delete [] intordsm;

  delete [] cncomp;
  delete [] ncomp;
  delete [] nip;
}

void barel3d::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 computes direction %vector
   
   @param s - direction %vector
   @param x,y,z - vectors of nodal coordinates
   
   JK, 28.9.2005
*/
void barel3d::dirvect (vector &s,double &l,vector &x,vector &y,vector &z)
{
  s[0]=x[1]-x[0];
  s[1]=y[1]-y[0];
  s[2]=z[1]-z[0];
  
  l=sqrt(s[0]*s[0]+s[1]*s[1]+s[2]*s[2]);
  
  if (l<Mp->zero){
    fprintf (stderr,"\n\n zero norm of direction vector in function dirvect (file %s, line %d).\n",__FILE__,__LINE__);
  }
  
  s[0]/=l;
  s[1]/=l;
  s[2]/=l;
}




/**
   function assembles strain-displacement (geometric) %matrix

   @param gm - strain-displacement (geometric) %matrix
   @param s - direction %vector

   JK, 27.9.2005
*/
void barel3d::geom_matrix (matrix &gm,vector &s,double l)
{
  gm[0][0]=s[0]/l*(-1.0);
  gm[0][1]=s[1]/l*(-1.0);
  gm[0][2]=s[2]/l*(-1.0);
  gm[0][3]=s[0]/l;
  gm[0][4]=s[1]/l;
  gm[0][5]=s[2]/l;
}


/**
   function approximates function defined by nodal values

   @param xi - coordinate on element
   @param nodval - nodal values
   
   JK, 27.9.2005
*/
double barel3d::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 barel3d::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 barel3d::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 threedimensonal element
   
   @param eid - element id
   @param ri,ci - row and column indices
   @param sm - stiffness %matrix

   JK, 27.9.2005
*/
void barel3d::stiffness_matrix (long eid,long ri,long ci,vector &s,matrix &sm)
{
  long ipp;
  double l,a,jac;
  vector x(nne),y(nne),z(nne);
  matrix gm(tncomp,ndofe),d(tncomp,tncomp);
  
  fillm (0.0,sm);
  
  // node coordinates
  Mt->give_node_coord3d (x,y,z,eid);
  
  //  length of the element
  l=sqrt ((x[1]-x[0])*(x[1]-x[0]) + (y[1]-y[0])*(y[1]-y[0]) + (z[1]-z[0])*(z[1]-z[0]));
  if (l<Mp->zero){
    fprintf (stderr,"\n\n zero length of the %ld truss element",eid);
    fprintf (stderr,"\n in function barel3d::stiffness_matrix (barel3d.cpp).\n");
  }
  
  
  //  strain-displacement matrix
  geom_matrix (gm,s,l);
  //  integration point id
  ipp=Mt->elements[eid].ipp[ri][ci];
  //  stiffness matrix of material
  Mm->matstiff (d,ipp);
  //  are of cross section
  Mc->give_area (eid,a);
  jac=a*l;

  bdbj (sm.a,gm.a,d.a,jac,gm.m,gm.n);
  
}

/**
   function computes stiffness %matrix
   
   @param eid - element id
   @param sm - stiffness %matrix
   
   JK, 27.9.2005
*/
void barel3d::res_stiffness_matrix (long eid,matrix &sm)
{
  long transf;
  double l;
  ivector nodes(nne);
  vector x(nne),y(nne),z(nne),s(3);
  matrix tmat (ndofe,ndofe);
  
  //  node coordinates
  Mt->give_node_coord3d (x,y,z,eid);
  
  //  direction vector
  dirvect (s,l,x,y,z);
  
  
  stiffness_matrix (eid,0,0,s,sm);


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


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

   JK, 27.9.2005
*/
void barel3d::mass_matrix (long eid,matrix &mm)
{
  double l,a,rho;
  vector x(nne),y(nne),z(nne);
  
  fillm (0.0,mm);

  Mt->give_node_coord3d (x,y,z,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 barel3d::mass_matrix (%s, line %d).\n",__FILE__,__LINE__);
  }
  Mc->give_area (eid,a);
  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 barel3d::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 strains at integration points
   
   @param lcid - load case id
   @param eid - element id
   @param ri,ci - row and column indices
   
   JK, 4.10.2005
*/
void barel3d::res_ip_strains (long lcid,long eid)
{
  long transf;
  double l;
  vector gx(nne),gy(nne),gz(nne),s(3),r(ndofe),aux(ndofe);
  ivector cn(ndofe),nodes(nne);
  matrix tmat(ndofe,ndofe);
  
  //  node coordinates
  Mt->give_node_coord3d (gx,gy,gz,eid);
  //  direction vector
  dirvect (s,l,gx,gy,gz);
  
  //  code numbers
  Mt->give_code_numbers (eid,cn.a);
  //  assembling of displacements defined on the element
  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){
    //  transformation matrix
    transf_matrix (nodes,tmat);
    lgvectortransf (aux,r,tmat);
    copyv (aux,r);
  }
  
  ip_strains (lcid,eid,0,0,s,r,l);
  
}

/**
   function computes strains at integration points of element

   @param lcid - load case id
   @param eid - element id
   @param ri - row index
   @param ci - column index
   @param s - direction %vector
   @param r - vector of nodal displacements
   
   JK, 3.10.2005
*/
void barel3d::ip_strains (long lcid,long eid,long ri,long ci,vector &s,vector &r,double l)
{
  long i,ipid;
  vector eps(tncomp);
  matrix gm(tncomp,ndofe);
  
  ipid=Mt->elements[eid].ipp[ri][ci];
  for (i=0;i<intordsm[0][0];i++){
    
    //  geometrix matrix
    geom_matrix (gm,s,l);
    //  strain computation
    mxv (gm,r,eps);
    
    //  strain storage
    Mm->storestrain (lcid,ipid,eps);
    ipid++;
  }
}

/**
   function computes strains in nodes of element

   @param lcid - load case id
   @param eid - element id
   @param ri,ci - row and column indices

   JK, 10.5.2002
*/
void barel3d::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 barel3d::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__);