barelq3d.cpp

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

#include <math.h>
#include "barelq3d.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"



barelq3d::barelq3d (void)
{
  long i;

  nne=3;  ndofe=9;  tncomp=1;  napfun=1;
  tnip=3;
  ssst = bar;

  nb=1;

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

  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]=3;

  intordsm[0][0]=3;
  
  zero=Mp->zero;
}

barelq3d::~barelq3d (void)
{
  long i;

  for (i=0;i<nb;i++){
    delete [] nip[i];
    delete [] intordsm[i];
  }
  delete [] nip;
  delete [] intordsm;

  delete [] cncomp;
  delete [] ncomp;
}

void barelq3d::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 barelq3d::dirvect (vector &s,vector &x,vector &y,vector &z)
{
  double d;
  
  s[0]=x[1]-x[0];
  s[1]=y[1]-y[0];
  s[2]=z[1]-z[0];
  
  d=sqrt(s[0]*s[0]+s[1]*s[1]+s[2]*s[2]);
  
  if (d<zero){
    fprintf (stderr,"\n\n zero norm of direction vector in function dirvect (file %s, line %d).\n",__FILE__,__LINE__);
  }
  
  s[0]/=d;
  s[1]/=d;
  s[2]/=d;
}

/**
   function approximates function defined by nodal values

   @param xi,eta - coordinates on element
   @param nodval - nodal values
   
   JK, 28.9.2005
*/
double barelq3d::approx (double xi,vector &nodval)
{
  double f;
  vector bf(nne);

  bf_quad_1d (bf.a,xi);

  scprd (bf,nodval,f);

  return f;
}

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

   @param gm - strain-displacement (geometric) %matrix
   @param x - direction %vector
   @param s - direction %vector
   @param xi - natural coordinate
   @param jac - Jacobian

   JK, 28.9.2005
*/
void barelq3d::geom_matrix (matrix &gm, vector &x,vector &s,double xi,double &jac)
{
  vector dx(nne);
  
  dx_bf_quad_1d (dx.a,xi);
  derivatives_1d (dx, jac, x, xi);
  
  fillm (0.0, gm);
  
  gm[0][0]= dx[0]*s[0];
  gm[0][1]= dx[0]*s[1];
  gm[0][2]= dx[0]*s[2];
  gm[0][3]= dx[1]*s[0];
  gm[0][4]= dx[1]*s[1];
  gm[0][5]= dx[1]*s[2];
  gm[0][6]= dx[2]*s[0];
  gm[0][7]= dx[2]*s[1];
  gm[0][8]= dx[2]*s[2];
}

/**
   function computes local coordinates
   coordinates of nodes after transformatikon of the bar to the x axis
   
   @param x,y,z - vectors of nodal coordinates
   @param lx - %vector of the x coordinates after transformation
   
   JK, 28.9.2005
*/
void barelq3d::giveloccoord(vector &x,vector &y,vector &z,vector &lx)
{
  double l;
  
  lx[0] = 0.0;
  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]));
  lx[1] = l;
  l = sqrt((x[2]-x[0])*(x[2]-x[0]) + (y[2]-y[0])*(y[2]-y[0]) + (z[2]-z[0])*(z[2]-z[0]));
  lx[2] = l;
}





void barelq3d::give_glob_loc_tmat(vector &x, vector &y, matrix &tmat)
{
  double c, s, l;

  fillm(0.0, tmat);
  l = sqrt(sqr(x[1]-x[0]) + sqr(y[1]-y[0]));
  c = (x[1] - x[0]) / l;
  s = (y[1] - y[0]) / l;
  tmat[0][0] = tmat[2][2] = tmat[4][4] =  c;
  tmat[0][1] = tmat[2][3] = tmat[4][5] =  s;
  tmat[1][0] = tmat[3][2] = tmat[5][4] = -s;
  tmat[1][1] = tmat[3][3] = tmat[5][5] =  c;
}

void barelq3d::give_loc_glob_tmat(vector &x, vector &y, matrix &tmat)
{
  double c, s, l;

  fillm(0.0, tmat);
  l = sqrt(sqr(x[1]-x[0]) + sqr(y[1]-y[0]));
  c = (x[1] - x[0]) / l;
  s = (y[1] - y[0]) / l;
  tmat[0][0] = tmat[2][2] = tmat[4][4] =  c;
  tmat[0][1] = tmat[2][3] = tmat[4][5] = -s;
  tmat[1][0] = tmat[3][2] = tmat[5][4] =  s;
  tmat[1][1] = tmat[3][3] = tmat[5][5] =  c;
}

/**
   transformation matrix x_g = T x_l
*/
void barelq3d::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][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 one element
   
   @param eid - element id
   @param ri,ci - row and column indices
   @param sm - stiffness %matrix
   @param lx - %vector of x coodinates of nodes after bar transformation to the x axis
   @param s - direction %vector
   
   JK, 28.9.2005
*/
void barelq3d::stiffness_matrix (long eid,long ri,long ci,matrix &sm,vector &lx,vector &s)
{
  long i,ipp;
  double a,xi,jac;
  vector w,gp,t(nne);
  matrix gm(tncomp,ndofe),d(tncomp,tncomp);
  
  //  setting of stiffness matrix
  fillm (0.0,sm);
  //  area of cross section
  Mc->give_area (eid,a);
  
  allocv (intordsm[0][0],w);
  allocv (intordsm[0][0],gp);
  gauss_points (gp.a,w.a,intordsm[0][0]);
  
  //  integration point id
  ipp=Mt->elements[eid].ipp[ri][ci];
  
  for (i=0;i<intordsm[0][0];i++){
    xi=gp[i];
    
    //  strain-displacement matrix
    geom_matrix (gm,lx,s,xi,jac);
    //  matrix of stiffness of the material
    Mm->matstiff (d,ipp);
    jac*=a*w[i];
    //  contribution to the stiffness matrix of the element
    bdbjac (sm,gm,d,gm,jac);
    
    ipp++;
  }
  
}

/**
   function computes stiffness %matrix of 3D bar element
   with quadratic shape functions
   
   @param eid - element id
   @param sm - stiffness %matrix
   
   JK, 28.9.2005
*/
void barelq3d::res_stiffness_matrix (long eid,matrix &sm)
{
  long transf;
  ivector nodes(nne);
  vector gx(nne),gy(nne),gz(nne),x(nne),s(nne);
  matrix tmat (ndofe,ndofe);
  
  //  nodal coordinates in global system
  Mt->give_node_coord3d (gx,gy,gz,eid);
  
  //  computation of x coodinates in local system attached to the bar
  giveloccoord (gx,gy,gz,x);
  //  computation of direction vector
  dirvect (s,gx,gy,gz);
  
  //  stiffness matrix
  stiffness_matrix (eid,0,0,sm,x,s);
  
  //  nodes on element
  Mt->give_elemnodes (eid,nodes);
  //  transformation of stiffness matrix
  transf = Mt->locsystems (nodes);
  if (transf>0){
    transf_matrix (nodes,tmat);
    glmatrixtransf (sm,tmat);
  }
}



void barelq3d::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 (%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 barelq3d::res_mainip_strains (long lcid,long eid)
{
  vector aux,gx(nne),gy(nne),gz(nne),x(nne),s(3),r(ndofe);
  ivector cn(ndofe),nodes(nne);
  matrix tmat;
  
  //  coordinates of nodes in global system
  Mt->give_node_coord3d (gx,gy,gz,eid);
  //  coordinates of nodes in local system
  giveloccoord (gx,gy,gz,x);
  //  direction vector
  dirvect (s,gx,gy,gz);
  //  nodes of element
  Mt->give_elemnodes (eid,nodes);
  //  code numbers
  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);
  }
  
  //  computation of strains
  mainip_strains (lcid,eid,0,0,x,s,r);
}

/**
   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 lx - %vector of x-coordinates in local system
   @param s - direction %vector
   @param r - %vector of nodal displacements
   
   JK, 29.9.2005
*/
void barelq3d::mainip_strains (long lcid,long eid,long ri,long ci,vector &lx,vector &s,vector &r)
{
  long i,ii,ipp;
  double xi,jac;
  vector gp,w,eps;
  matrix gm;

  for (ii=0;ii<nb;ii++){
    if (intordsm[ii][ii]==0)  continue;

    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]);
    
    //  integration point id
    ipp=Mt->elements[eid].ipp[ri+ii][ci+ii];
    
    for (i=0;i<intordsm[ii][ii];i++){
      xi=gp[i];
      
      //  strain-displacement matrix
      geom_matrix (gm,lx,s,xi,jac);
      mxv (gm,r,eps);

      Mm->storestrain (lcid,ipp,cncomp[ii],ncomp[ii],eps);
      ipp++;
    }

    destrm (gm);  destrv (eps);  destrv (w);  destrv (gp);
  }

}

/**
   function computes strains at nodes of element

   @param lcid - load case id
   @param eid - element id
   @param ri,ci - row and column indices
   
   JK, 29.9.2005
*/
void barelq3d::nod_strains_ip (long lcid,long eid,long ri,long ci)
{
  long i,j;
  ivector ipnum(nne),nod(nne);
  vector eps(tncomp);
  
  //  numbers of integration points closest to nodes
  nodipnum (eid,ri,ci,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 nodal strains directly
   
   @param lcid - load case id
   @param eid - element id
   @param stra - array for strain components
   
   JK, 29.9.2005
*/
void barelq3d::nod_strains_comp (long lcid,long eid,double **stra)
{
  long i,j;
  double jac;
  ivector cn(ndofe),nodes(nne);
  vector gx(nne),gy(nne),gz(nne),x(nne),s(3),nxi(nne),r(ndofe),eps(tncomp),aux;
  matrix tmat,gm(tncomp,ndofe);
  
  //  node coordinates
  Mt->give_node_coord3d (gx,gy,gz,eid);
  //  x-coordinates in local system
  giveloccoord (gx,gy,gz,x);
  //  computation of direction vector
  dirvect (s,gx,gy,gz);
  //  node numbers
  Mt->give_elemnodes (eid,nodes);
  //  code numbers of the 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);
  }
  
  //  natural coordinates of element nodes
  nodecoord (nxi);
  
  //  loop over nodes
  for (i=0;i<nne;i++){
    //  strain-displacement (geometric) matrix
    geom_matrix (gm,x,s,nxi[i],jac);
    //  strain computation
    mxv (gm,r,eps);
    
    for (j=0;j<eps.n;j++){
      stra[i][j]=eps[j];
    }
  }

}

/**
   function computes all strain components at all integration points
   
   @param lcid - load case id
   @param eid - element id
   
   JK, 29.9.2005
*/
void barelq3d::res_allip_strains (long lcid,long eid)
{
  //  all strain components at all integration points
  allip_strains (lcid,eid,0,0);
}

/**
   function assembles all values at all integration points
   
   @param lcid - load case id
   @param eid - element id
   @param ri,ci - row and column indices
   
   JK, 29.9.2005
*/
void barelq3d::allip_strains (long lcid,long eid,long ri,long ci)
{
  //  blocks of strain components at integration points
  res_mainip_strains (lcid,eid);
}


/**
   function computes strains at strain points
   
   @param lcid - load case id
   @param eid - element id
   @param ri,ci - row and column indices
   
   JK, 29.9.2005
*/
void barelq3d::strains (long lcid,long eid,long ri,long ci)
{
  long i;
  double **stra;
  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 barelq3d::strains (file %s, line %d).\n",__FILE__,__LINE__);
  }
  }

  if (Mp->strainaver==0){
    for (i=0;i<nne;i++){
      delete [] stra[i];
    }
    delete [] stra;
  }
}