axisymlt.cpp

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

#include "axisymlt.h"
#include "global.h"
#include "globmat.h"
#include "genfile.h"
#include "element.h"
#include "node.h"
#include "loadcase.h"
#include "intpoints.h"
#include <stdlib.h>

axisymlt::axisymlt (void)
{
  long i,j;
  
  nne=3;  ndofe=6;  tncomp=4;  napfun=2;
  ned=3;  nned=2;  intordmm=3;  intordb=2;  ssst=axisymm;

  //nb=3;
  nb=1;

  ncomp = new long [nb];
  ncomp[0]=4;
  
  /*
  ncomp[0]=2;
  ncomp[1]=1;
  ncomp[2]=1;
  */
  
  cncomp = new long [nb];
  cncomp[0]=0;
  
  /*
  cncomp[0]=0;
  cncomp[1]=2;
  cncomp[2]=3;
  */

  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;  nip[0][1]=1;  nip[0][2]=0;
  nip[1][0]=1;  nip[1][1]=1;  nip[1][2]=0;
  nip[2][0]=0;  nip[2][1]=0;  nip[2][2]=1;

  intordsm[0][0]=1;  intordsm[0][1]=1;  intordsm[0][2]=0;
  intordsm[1][0]=1;  intordsm[1][1]=1;  intordsm[1][2]=0;
  intordsm[2][0]=0;  intordsm[2][1]=0;  intordsm[2][2]=1;
*/
/*
  nip[0][0]=1;  nip[0][1]=3;  nip[0][2]=0;
  nip[1][0]=3;  nip[1][1]=3;  nip[1][2]=0;
  nip[2][0]=0;  nip[2][1]=0;  nip[2][2]=1;

  intordsm[0][0]=1;  intordsm[0][1]=3;  intordsm[0][2]=0;
  intordsm[1][0]=3;  intordsm[1][1]=3;  intordsm[1][2]=0;
  intordsm[2][0]=0;  intordsm[2][1]=0;  intordsm[2][2]=1;
*/
  
  /*
  nip[0][0]=3;  nip[0][1]=3;  nip[0][2]=0;
  nip[1][0]=3;  nip[1][1]=3;  nip[1][2]=0;
  nip[2][0]=0;  nip[2][1]=0;  nip[2][2]=3;

  intordsm[0][0]=3;  intordsm[0][1]=3;  intordsm[0][2]=0;
  intordsm[1][0]=3;  intordsm[1][1]=3;  intordsm[1][2]=0;
  intordsm[2][0]=0;  intordsm[2][1]=0;  intordsm[2][2]=3;
  */
  
  nip[0][0]=3;
  intordsm[0][0]=3;
  
  tnip=0;
  for (i=0;i<nb;i++){
    for (j=0;j<nb;j++){
      tnip+=nip[i][j];
    }
  }
  
}

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

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

void axisymlt::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 areacoord - vector containing area coordinates
   @param nodval - nodal values

*/
double axisymlt::approx (vector &areacoord,vector &nodval)
{
  double f;
  scprd (areacoord,nodval,f);
  return f;
}

/**
   function approximates function defined by nodal values

   @param xi,eta - natural coordinates
   @param nodval - nodal values

*/
double axisymlt::approx_nat (double xi,double eta,vector &nodval)
{
  double f;
  vector areacoord(3);
  areacoord[0]=xi;
  areacoord[1]=eta;
  areacoord[2]=1.0-areacoord[0]-areacoord[1];
  scprd (areacoord,nodval,f);
  return f;
}

/**
   function returns matrix of approximation functions
   
   @param n - matrix of approximation functions
   @param areacoord - array containing area coordinates

   29.3.2002
*/
void axisymlt::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 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 areacoord - area coordinates
   @param x,y - node coordinates
   
   29.3.2002
*/
void axisymlt::geom_matrix (matrix &gm,vector &areacoord,vector &x,vector &y)
{
  double det,r;
  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]);
  //  radius
  r = approx (areacoord,x);
  
  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]=areacoord[0]/r;
  gm[2][2]=areacoord[1]/r;
  gm[2][4]=areacoord[2]/r;

  gm[3][0]=c[0];
  gm[3][1]=b[0];
  gm[3][2]=c[1];
  gm[3][3]=b[1];
  gm[3][4]=c[2];
  gm[3][5]=b[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 areacoord - area coordinates
   @param x,y - node coordinates
   
   29.3.2002
*/
void axisymlt::geom_matrix_block (matrix &gm,long ri,vector &areacoord,vector &x,vector &y)
{
  double det,r;
  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]);
  //  radius
  r = approx (areacoord,x);
  
  plsb (b.a,y.a,det);
  plsc (c.a,x.a,det);

  fillm (0.0,gm);
  
  if (ri==0){
    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];
  }
  if (ri==1){  
    gm[0][0]=areacoord[0]/r;
    gm[0][2]=areacoord[1]/r;
    gm[0][4]=areacoord[2]/r;
  }
  if (ri==2){
    gm[0][0]=c[0];
    gm[0][1]=b[0];
    gm[0][2]=c[1];
    gm[0][3]=b[1];
    gm[0][4]=c[2];
    gm[0][5]=b[2];
  }
}

/**
   function extracts blocks from stiffness matrix of the material
   
   @param ri,ci - row and column indices
   @param d - stiffness matrix of material
   @param dd - required block from stiffness matrix of material
   
   10.5.2002
*/
void axisymlt::dmatblock (long ri,long ci,matrix &d, matrix &dd)
{
  fillm (0.0,dd);
  
  if (ri==0 && ci==0){
    dd[0][0]=d[0][0];  dd[0][1]=d[0][1];
    dd[1][0]=d[1][0];  dd[1][1]=d[1][1];
  }
  if (ri==0 && ci==1){
    dd[0][0]=d[0][2];
    dd[1][0]=d[1][2];
  }
  if (ri==0 && ci==2){
    dd[0][0]=d[0][3];
    dd[1][0]=d[1][3];
  }
  
  if (ri==1 && ci==0){
    dd[0][0]=d[2][0];  dd[0][1]=d[2][1];
  }
  if (ri==1 && ci==1){
    dd[0][0]=d[2][2];
  }
  if (ri==1 && ci==2){
    dd[0][0]=d[2][3];
  }
  
  if (ri==2 && ci==0){
    dd[0][0]=d[3][0];  dd[0][1]=d[3][1];
  }
  if (ri==2 && ci==1){
    dd[0][0]=d[3][2];
  }
  if (ri==2 && ci==2){
    dd[0][0]=d[3][3];
  }
}


/**
   nutno otestovat! pak je mozne smazat tuto hlasku
   
   transformation matrix x_g = T x_l

   17.8.2001
*/
void axisymlt::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 triangular axisymmetric
   finite element with linear approximation functions
   
   @param eid - number of element
   @param ri,ci - row and column indices
   @param sm - stiffness matrix
   
   17.8.2001
*/
void axisymlt::stiffness_matrix (long eid,long ri,long ci,matrix &sm)
{
  long i,ii,jj,ipp,transf;
  double jac,det,r;
  ivector nodes(nne);
  vector gp1,gp2,w,x(nne),y(nne),areacoord(3);
  matrix gm(tncomp,ndofe),gmr,gmc,dd,d(tncomp,tncomp);
  
  Mt->give_elemnodes (eid,nodes);
  Mt->give_node_coord2d (x,y,eid);
  
  //  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,sm);
  

  for (ii=0;ii<nb;ii++){
    //allocm (ncomp[ii],ndofe,gmr);
    for (jj=0;jj<nb;jj++){
      if (intordsm[ii][jj]==0)  continue;

      allocv (intordsm[ii][jj],w);
      allocv (intordsm[ii][jj],gp1);
      allocv (intordsm[ii][jj],gp2);
      
      //allocm (ncomp[jj],ndofe,gmc);
      //allocm (ncomp[ii],ncomp[jj],dd);
      
      gauss_points_tr (gp1.a,gp2.a,w.a,intordsm[ii][jj]);
      
      ipp=Mt->elements[eid].ipp[ri+ii][ci+jj];
      
      for (i=0;i<intordsm[ii][jj];i++){
	areacoord[0]=gp1[i];
	areacoord[1]=gp2[i];
	areacoord[2]=1.0-areacoord[0]-areacoord[1];
	
	//  geometric matrix
	geom_matrix (gm,areacoord,x,y);
	//geom_matrix_block (gmr,ii,areacoord,x,y);
	//geom_matrix_block (gmc,jj,areacoord,x,y);
	
	//  matrix of stiffness of the material
	Mm->matstiff (d,ipp);
	//dmatblock (ii,jj,d,dd);
	
	r = approx (areacoord,x);
	jac=w[i]*r*det;
	
	//  contribution to the stiffness matrix of the element
	//bdbjac (sm,gmr,dd,gmc,jac);
	bdbjac (sm,gm,d,gm,jac);
	
	ipp++;
      }
      
      //destrm (dd);  destrm (gmc);
      destrv (gp2);  destrv (gp1);  destrv (w);
    }
    //destrm (gmr);
  }
  
  //  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 axisymlt::res_stiffness_matrix (long eid,matrix &sm)
{
  stiffness_matrix (eid,0,0,sm);
}


/**
   function computes mass matrix of the triangular axisymmetric
   finite element with linear approximation functions
   
   @param eid - number of element
   @param mm - mass matrix

   29.3.2002
*/
void axisymlt::mass_matrix (long eid,matrix &mm)
{
  long i;
  double jac,det,rho,r;
  ivector nodes(nne);
  vector x(nne),y(nne),w(intordmm),gp1(intordmm),gp2(intordmm),dens(nne);
  matrix n(napfun,ndofe);
  
  Mt->give_elemnodes (eid,nodes);
  Mt->give_node_coord2d (x,y,eid);
  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]);