plelemlt.cpp

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

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



planeelemlt::planeelemlt (void)
{
  long i,j;

  //  number nodes on element
  nne=3;
  //  number of DOFs on element
  ndofe=6;
  //  number of strain/stress components
  tncomp=3;
  //  number of functions approximated
  napfun=2;
  //  order of numerical integration of mass matrix
  intordmm=3;
  //  number of edges on element
  ned=3;
  //  number of nodes on one edge
  nned=2;
  //  order of numerical integration on element edges (boundaries)
  intordb=2;
  
  //  number of blocks (parts of geometric matrix)
  nb=1;

  //  number of strain/stress components
  ncomp = new long [nb];
  ncomp[0]=3;

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

  intordsm[0][0]=1;
}

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

void planeelemlt::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
   area coordinates are used
   
   @param areacoord - vector containing area coordinates
   @param nodval - nodal values
   
   JK
*/
double planeelemlt::approx (vector &areacoord,vector &nodval)
{
  double f;
  scprd (areacoord,nodval,f);
  return f;
}

/**
   function approximates function defined by nodal values
   natural coordinates are used
   
   @param xi,eta - natural coordinates
   @param nodval - nodal values
   
   JK
*/
double planeelemlt::approx_nat (double xi,double eta,vector &nodval)
{
  double f;
  vector areacoord(3);

  //  conversion of natural coordinates to area coordinates
  areacoord[0]=xi;
  areacoord[1]=eta;
  areacoord[2]=1.0-areacoord[0]-areacoord[1];

  scprd (areacoord,nodval,f);
  return f;
}

/**
   function returns %matrix of base function

   @param n - %matrix of approximation functions
   @param xi,eta - natural coordinates
   
   JK, 17.8.2001
*/
void planeelemlt::bf_matrix (matrix &n,double xi,double eta)
{
  vector bf(nne);

  bf_lin_3_2d (bf.a,xi,eta);

  fillm (0.0,n);

  n[0][0]=bf[0];
  n[0][2]=bf[1];
  n[0][4]=bf[2];
  
  n[1][1]=bf[0];
  n[1][3]=bf[1];
  n[1][5]=bf[2];
}

/**
   function assembles strain-displacement (geometric) %matrix
   
   @param gm - geometric %matrix
   @param x,y - node coordinates
   
   JK, 17.8.2001
*/
void planeelemlt::geom_matrix (matrix &gm,vector &x,vector &y)
{
  double det;
  vector b(3),c(3);
  
  //  det is equal to double area of the element
  det = (x[1]-x[0])*(y[2]-y[0])-(x[2]-x[0])*(y[1]-y[0]);
  plsb (b.a,y.a,det);
  plsc (c.a,x.a,det);
  
  fillm (0.0,gm);

  gm[0][0]=b[0];
  gm[0][2]=b[1];
  gm[0][4]=b[2];
  
  gm[1][1]=c[0];
  gm[1][3]=c[1];
  gm[1][5]=c[2];
  
  gm[2][0]=c[0];
  gm[2][1]=b[0];
  gm[2][2]=c[1];
  gm[2][3]=b[1];
  gm[2][4]=c[2];
  gm[2][5]=b[2];
}

/**
   function assembles transformation %matrix from local nodal coordinate
   system to the global coordinate system x_g = T x_l
   
   @param inodes - array containing node numbers
   @param tmat - transfomation %matrix
   
   JK, 17.8.2001
*/
void planeelemlt::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 plane stress triangular
   finite element with linear approximation functions

   @param eid - element id
   @param ri,ci - row and column indices
   @param sm - stiffness %matrix
   @param x,y - node coordinates
   
   JK, 17.8.2001
*/
void planeelemlt::stiffness_matrix (long eid,long ri,long ci,matrix &sm,vector &x,vector &y)
{
  long ipp;
  double xi,eta,jac,det,thick;
  ivector nodes(nne);
  vector t(nne);
  matrix gm(tncomp,ndofe),d(tncomp,tncomp);

  //  element nodes
  Mt->give_elemnodes (eid,nodes);
  //  thickness of the element
  Mc->give_thickness (eid,nodes,t);

  //  det is equal to double area of the element
  det = (x[1]-x[0])*(y[2]-y[0])-(x[2]-x[0])*(y[1]-y[0]);
  
  xi=1.0/3.0;
  eta=1.0/3.0;

  fillm (0.0,sm);

  ipp=Mt->elements[eid].ipp[ri][ci];
  
  // geometric matrix
  geom_matrix (gm,x,y);
  
  //  stiffness matrix of material
  Mm->matstiff (d,ipp);
  
  thick = approx_nat (xi,eta,t);
  
  //  det is equal to double area of the element
  jac=thick*det/2.0;
  
  //  contribution to the stiffness matrix of the element
  bdbj (sm.a,gm.a,d.a,jac,gm.m,gm.n);

}

/**
   function computes stiffness %matrix of plane stress triangular
   finite element with linear approximation functions

   @param eid - element id
   @param sm - stiffness %matrix
   
   JK, 17.8.2001
*/
void planeelemlt::res_stiffness_matrix (long eid,matrix &sm)
{
  long transf;
  ivector nodes(nne);
  vector x(nne),y(nne);

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

  stiffness_matrix (eid,0,0,sm,x,y);

  //  transformation of stiffness matrix
  //  (in the case of nodal coordinate systems)
  Mt->give_elemnodes (eid,nodes);
  transf = Mt->locsystems (nodes);
  if (transf>0){
    matrix tmat (ndofe,ndofe);
    transf_matrix (nodes,tmat);
    glmatrixtransf (sm,tmat);
  }
}

/**
   function computes mass %matrix of the plane stress triangular
   finite element with linear approximation functions
   
   @param eid - number of element
   @param mm - mass %matrix
   @param x,y - node coordinates
   
   JK, 17.6.2001
*/
void planeelemlt::mass_matrix (long eid,matrix &mm,vector &x,vector &y)
{
  long i;
  double jac,det,thick,rho;
  ivector nodes(nne);
  vector w(intordmm),gp1(intordmm),gp2(intordmm),t(nne),dens(nne);
  matrix n(napfun,ndofe);
  
  //  element nodes
  Mt->give_elemnodes (eid,nodes);
  //  thickness of the element
  Mc->give_thickness (eid,nodes,t);
  //  density of the material
  Mc->give_density (eid,nodes,dens);
  
  //  det is equal to double area of the element
  det = (x[1]-x[0])*(y[2]-y[0])-(x[2]-x[0])*(y[1]-y[0]);
  
  gauss_points_tr (gp1.a,gp2.a,w.a,intordmm);
  
  fillm (0.0,mm);
  
  for (i=0;i<intordmm;i++){
    bf_matrix (n,gp1[i],gp2[i]);
    
    thick = approx_nat (gp1[i],gp2[i],t);
    rho = approx_nat (gp1[i],gp2[i],dens);
    
    jac=w[i]*thick*rho*det;
    
    nnj (mm.a,n.a,jac,n.m,n.n);
  }
  
}

/**
   function computes mass %matrix of the plane stress triangular
   finite element with linear approximation functions
   
   @param eid - number of element
   @param mm - mass %matrix
   
   JK, 17.6.2001
*/
void planeelemlt::res_mass_matrix (long eid,matrix &mm)
{
  long transf;
  ivector nodes(nne);
  vector x(nne),y(nne);

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

  mass_matrix (eid,mm,x,y);

  //  transformation of mass matrix
  //  (in the case of nodal coordinate systems)
  Mt->give_elemnodes (eid,nodes);
  transf = Mt->locsystems (nodes);
  if (transf>0){
    matrix tmat (ndofe,ndofe);
    transf_matrix (nodes,tmat);
    glmatrixtransf (mm,tmat);
  }

}


/**
   function computes load %matrix of the plane stress triangular
   finite element with linear approximation functions
   load vector is obtained after premultiplying load %matrix
   by nodal load values
   
   @param eid - number of element
   @param lm - load %matrix
   @param x,y - node coordinates

   JK, 25.7.2001
*/
void planeelemlt::load_matrix (long eid,matrix &lm,vector &x,vector &y)
{
  long i;
  double jac,det,thick;
  ivector nodes(nne);
  vector w(intordmm),gp1(intordmm),gp2(intordmm),b(3),c(3),t(nne);
  matrix n(napfun,ndofe);
  
  Mt->give_elemnodes (eid,nodes);
  Mc->give_thickness (eid,nodes,t);

  gauss_points_tr (gp1.a,gp2.a,w.a,intordmm);

  //  det is equal to double area of the element
  det = (x[1]-x[0])*(y[2]-y[0])-(x[2]-x[0])*(y[1]-y[0]);
  
  fillm (0.0,lm);
  
  for (i=0;i<intordmm;i++){
    bf_matrix (n,gp1[i],gp2[i]);
    
    thick = approx_nat (gp1[i],gp2[i],t);
    
    //  zkontrolovat deleni dvema
    jac=w[i]*thick*det;
    
    nnj (lm.a,n.a,jac,n.m,n.n);
  }
  
}

/**
   function computes load %matrix of the plane stress triangular
   finite element with linear approximation functions
   load vector is obtained after premultiplying load %matrix
   by nodal load values
   
   @param eid - number of element
   @param lm - load %matrix

   JK, 25.7.2001
*/
void planeelemlt::res_load_matrix (long eid,matrix &lm)
{
  long transf;
  ivector nodes(nne);
  vector x(nne),y(nne);
  
  Mt->give_node_coord2d (x,y,eid);

  load_matrix (eid,lm,x,y);

  //  transformation of load matrix
  //  (in the case of nodal coordinate systems)
  Mt->give_elemnodes (eid,nodes);
  transf = Mt->locsystems (nodes);
  if (transf>0){
    matrix tmat (ndofe,ndofe);
    transf_matrix (nodes,tmat);
    glmatrixtransf (lm,tmat);
  }

}

/**
   function computes strains at integration points
   
   @param lcid - load case id
   @param eid - element id
   
   JK
*/
void planeelemlt::res_ip_strains (long lcid,long eid)
{
  vector aux,x(nne),y(nne),r(ndofe);
  ivector cn(ndofe),nodes(nne);
  matrix tmat;

  Mt->give_node_coord2d (x,y,eid);
  Mt->give_elemnodes (eid,nodes);
  Mt->give_code_numbers (eid,cn.a);
  eldispl (lcid,eid,r.a,cn.a,ndofe);

  //  transformation of displacement vector
  //  (in the case of nodal coordinate systems)
  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);
  }

  ip_strains (lcid,eid,0,0,x,y,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 x,y - node coordinates
   @param r - nodal displacements
   
   JK, 10.5.2002
*/
void planeelemlt::ip_strains (long lcid,long eid,long ri,long ci,vector &x,vector &y,vector &r)
{
  long ipp;
  vector eps(tncomp);
  matrix gm(tncomp,ndofe);

  geom_matrix (gm,x,y);
  mxv (gm,r,eps);
  
  ipp=Mt->elements[eid].ipp[ri][ci];
  Mm->storestrain (lcid,ipp,cncomp[0],ncomp[0],eps);
}

/**
   function computes strains at nodes of element
   
   @param lcid - load case id
   @param eid - element id
   @param ri - row index
   @param ci - column index
   
   JK, 10.5.2002
*/
void planeelemlt::nod_strains (long lcid,long eid,long ri,long ci)
{
  long ipp;
  double *lsm,*lhs,*rhs;
  vector nxi(nne),neta(nne),eps,aux,natcoord(2);
  ivector nodes(nne);
  
  
  //  natural coordinates of element nodes
  //  (function is from the file GEFEL/ordering.cpp)
  nodcoord_planelt (nxi,neta);

  Mt->give_elemnodes (eid,nodes);
  
  allocv (ncomp[0],eps);
  lhs = new double [ncomp[0]*3];
  rhs = new double [ncomp[0]*3];
  lsm = new double [9];
  
  nullv (lsm,9);
  nullv (rhs,ncomp[0]*3);
  
  ipp=Mt->elements[eid].ipp[ri][ci];
  Mm->givestrain (lcid,ipp,cncomp[0],ncomp[0],eps);
  
  natcoord[0]=1.0/3.0;  natcoord[1]=1.0/3.0;
  matassem_lsm (lsm,natcoord);
  rhsassem_lsm (rhs,natcoord,eps);
  
  solve_lsm (lsm,lhs,rhs,Mp->zero,3,ncomp[0]);
  Mt->strain_nodal_values (nodes,nxi,neta,nxi,lhs,2,cncomp[0],ncomp[0],lcid);
  
  delete [] lsm;  delete [] lhs;  delete [] rhs;
  destrv (eps);  destrv (nodes);
}

/**
   function computes strains on element
   
   @param val - array containing strains on element
   @param lcid - load case id
   @param eid - element id
   
   15.7.2002
*/
void planeelemlt::elem_strains (double **stra,long lcid,long eid,long ri,long ci)
{
  long i,ii,ipp;
  double xi,eta,*lsm,*lhs,*rhs;
  vector nxi(nne),neta(nne),gp1,gp2,w,eps,aux,natcoord(2);

  lsm = new double [9];

  //  natural coordinates of element nodes
  //  (function is from the file GEFEL/ordering.cpp)
  nodcoord_planelt (nxi,neta);
  
  for (ii=0;ii<nb;ii++){
    allocv (intordsm[ii][ii],gp1);
    allocv (intordsm[ii][ii],gp2);
    allocv (intordsm[ii][ii],w);
    allocv (ncomp[ii],eps);
    lhs = new double [ncomp[ii]*3];
    rhs = new double [ncomp[ii]*3];
    gauss_points_tr (gp1.a,gp2.a,w.a,intordsm[ii][ii]);
    
    nullv (lsm,9);
    nullv (rhs,ncomp[ii]*3);
    
    ipp=Mt->elements[eid].ipp[ri+ii][ci+ii];
    for (i=0;i<intordsm[ii][ii];i++){
      xi=gp1[i];  eta=gp2[i];
      
      Mm->givestrain (lcid,ipp,cncomp[ii],ncomp[ii],eps);
      
      natcoord[0]=xi;  natcoord[1]=eta;
      matassem_lsm (lsm,natcoord);
      rhsassem_lsm (rhs,natcoord,eps);
      
      ipp++;
    }
    
    solve_lsm (lsm,lhs,rhs,Mp->zero,3,ncomp[ii]);
    nodal_values (stra,nxi,neta,nxi,lhs,2,cncomp[ii],ncomp[ii]);
    
    delete [] lhs;  delete [] rhs;
    destrv (eps);  destrv (w);  destrv (gp1);  destrv (gp2);
  }
  
  delete [] lsm;