plelemrotlt.cpp

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

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

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

  nne=3;  ndofe=9;  tncomp=3;  napfun=3;
  intordmm=3;  ned=3;  nned=2;
  
  nb=2;
  
  ncomp = new long [nb];
  ncomp[0]=2;
  ncomp[1]=1;
  
  cncomp = new long [nb];
  cncomp[0]=0;
  cncomp[1]=2;

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

  intordsm[0][0]=3;  intordsm[0][1]=0;
  intordsm[1][0]=0;  intordsm[1][1]=3;

}

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

void planeelemrotlt::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
   
   6.1.2002
*/
double planeelemrotlt::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
   
   1.4.2002
*/
double planeelemrotlt::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 base function
   
   6.1.2002
*/
void planeelemrotlt::bf_matrix (matrix &n,vector &l,vector &b,vector &c)
{
  vector bf(9);
  
  fillm (0.0,n);

  bf_rot_3_2d (bf.a,l.a,b.a,c.a);
  
  n[0][0]=bf[0];
  n[0][2]=bf[3];
  n[0][3]=bf[1];
  n[0][5]=bf[4];
  n[0][6]=bf[2];
  n[0][8]=bf[5];

  n[1][1]=bf[0];
  n[1][2]=bf[6];
  n[1][4]=bf[1];
  n[1][5]=bf[7];
  n[1][7]=bf[2];
  n[1][8]=bf[8];
}

void planeelemrotlt::geom_matrix (matrix &gm,vector &x,vector &y,vector &areacoord)
{
  double area,det;
  vector b(3),c(3),dx(9),dy(9);
  
  //  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]);
  area=det/2.0;
  plsb (b.a,y.a,det);
  plsc (c.a,x.a,det);

  dx_bf_rot_3_2d (dx.a,areacoord.a,b.a,c.a);
  dy_bf_rot_3_2d (dy.a,areacoord.a,b.a,c.a);

  fillm (0.0,gm);
  
  gm[0][0]=dx[0];
  gm[0][2]=dx[3];
  gm[0][3]=dx[1];
  gm[0][5]=dx[4];
  gm[0][6]=dx[2];
  gm[0][8]=dx[5];

  gm[1][1]=dy[0];
  gm[1][2]=dy[6];
  gm[1][4]=dy[1];
  gm[1][5]=dy[7];
  gm[1][7]=dy[2];
  gm[1][8]=dy[8];
  
  gm[2][0]=dy[0];
  gm[2][1]=dx[0];
  gm[2][2]=dy[3]+dx[6];
  gm[2][3]=dy[1];
  gm[2][4]=dx[1];
  gm[2][5]=dy[4]+dx[7];
  gm[2][6]=dy[2];
  gm[2][7]=dx[2];
  gm[2][8]=dy[5]+dx[8];
  
}

void planeelemrotlt::geom_matrix_block (matrix &gm,long ri,vector &x,vector &y,vector &areacoord)
{
  double area,det;
  vector b(3),c(3),dx(9),dy(9);
  
  //  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]);
  area=det/2.0;
  plsb (b.a,y.a,det);
  plsc (c.a,x.a,det);
  
  dx_bf_rot_3_2d (dx.a,areacoord.a,b.a,c.a);
  dy_bf_rot_3_2d (dy.a,areacoord.a,b.a,c.a);

  fillm (0.0,gm);
  
  if (ri==0){
    gm[0][0]=dx[0];
    gm[0][2]=dx[3];
    gm[0][3]=dx[1];
    gm[0][5]=dx[4];
    gm[0][6]=dx[2];
    gm[0][8]=dx[5];
    
    gm[1][1]=dy[0];
    gm[1][2]=dy[6];
    gm[1][4]=dy[1];
    gm[1][5]=dy[7];
    gm[1][7]=dy[2];
    gm[1][8]=dy[8];
  }
  
  if (ri==1){
    gm[0][0]=dy[0];
    gm[0][1]=dx[0];
    gm[0][2]=dy[3]+dx[6];
    gm[0][3]=dy[1];
    gm[0][4]=dx[1];
    gm[0][5]=dy[4]+dx[7];
    gm[0][6]=dy[2];
    gm[0][7]=dx[2];
    gm[0][8]=dy[5]+dx[8];
  }
}

void planeelemrotlt::addgeommat (matrix &gm,vector &x,vector &y,vector &areacoord,double &jac)
{
  long i,i1,i2,i3,ii,jj;
  double det,area;
  vector b(3),c(3),bf(ndofe),dx(ndofe),dy(ndofe);
  
  //  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]);
  jac = det;
  area=det/2.0;
  plsb (b.a,y.a,det);
  plsc (c.a,x.a,det);
  
  bf_rot_3_2d (bf.a,areacoord.a,b.a,c.a);
  dx_bf_rot_3_2d (dx.a,areacoord.a,b.a,c.a);
  dy_bf_rot_3_2d (dy.a,areacoord.a,b.a,c.a);
  
  fillm (0.0,gm);
  
  i1=0;  i2=1;  i3=2;  ii=3;  jj=6;
  
  for (i=0;i<nne;i++){
    gm[0][i1]=0.0-dy[i]/2.0;
    gm[0][i2]=dx[i]/2.0;
    gm[0][i3]=dx[jj]/2.0-dy[ii]/2.0-bf[i];
    i1+=3;  i2+=3;  i3+=3;  ii++;  jj++;
  }

}

void planeelemrotlt::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==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];
  }
}

/**
   transformation matrix x_g = T x_l
*/
void planeelemrotlt::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*3][i*3]   = Mt->nodes[nodes[i]].e1[0];   tmat[i*3][i*3+1]   = Mt->nodes[nodes[i]].e2[0];  tmat[i*3][i*3+2]   = 0.0;
      tmat[i*3+1][i*3] = Mt->nodes[nodes[i]].e1[1];   tmat[i*3+1][i*3+1] = Mt->nodes[nodes[i]].e2[1];  tmat[i*3+1][i*3+2] = 0.0;
      tmat[i*3+2][i*3] = 0.0;                         tmat[i*3+2][i*3+1] = 0.0;                        tmat[i*3+2][i*3+2] = 1.0;
    }
  }
}

/**
   function computes stiffness matrix of plane stress quadrilateral
   finite element with rotational degrees of freedom with
   bilinear approximation functions
   
   @param eid - number of element
   @param sm - stiffness matrix

   8.12.2001
*/
void planeelemrotlt::stiffness_matrix (long eid,long ri,long ci,matrix &sm,vector &x,vector &y)
{
  long i,ii,jj,ipp;
  double jac,det,thick;
  ivector nodes(nne);
  vector areacoord(3),t(nne),gp1,gp2,w;
  matrix gmr,gmc,dd,d(tncomp,tncomp);
  
  Mt->give_elemnodes (eid,nodes);
  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]);

  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;
      
      allocm (ncomp[jj],ndofe,gmc);
      allocm (ncomp[ii],ncomp[jj],dd);
      
      allocv (nip[ii][jj],gp1);
      allocv (nip[ii][jj],gp2);
      allocv (nip[ii][jj],w);
      
      
      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-gp1[i]-gp2[i];
        
        // geometric matrix
        geom_matrix_block (gmr,ii,x,y,areacoord);
        geom_matrix_block (gmc,jj,x,y,areacoord);
        
        
        //geom_matrix (gmr,x,y,areacoord);
        //geom_matrix (gmc,x,y,areacoord);
          
        
        //  stiffness matrix of material
        Mm->matstiff (d,ipp);
        dmatblock (ii,jj,d,dd);
        
        thick = approx (areacoord,t);
        
        jac=thick*det*w[i];
        
        //  contribution to the stiffness matrix of the element
        //bdbj (sm.a,gm.a,d.a,jac,gm.m,gm.n);
        bdbjac (sm,gmr,dd,gmc,jac);

        ipp++;
      }

      destrv (w);
      destrv (gp1);
      destrv (gp2);
      destrm (gmc);
      destrm (dd);
    }
    destrm (gmr);
  }
  
  allocv (1,w);
  allocv (1,gp1);
  allocv (1,gp2);

  gauss_points_tr (gp1.a,gp2.a,w.a,1);
  areacoord[0]=gp1[0];
  areacoord[1]=gp2[0];
  areacoord[2]=1.0-gp1[0]-gp2[0];
  
  allocm (1,ndofe,gmr);
  allocm (ndofe,ndofe,gmc);
  
  addgeommat (gmr,x,y,areacoord,jac);
  mtxm (gmr,gmr,gmc);
  thick = approx (areacoord,t);
  cmulm (thick*jac*w[0],gmc);
  addm (sm,gmc,sm);
  
  destrm (gmc);  destrm (gmr);
  destrv (gp1);  destrv (gp2);  destrv (w);
  
  
  
}

void planeelemrotlt::res_stiffness_matrix (long eid,matrix &sm)
{
  long transf;
  vector x(nne),y(nne);
  ivector nodes(nne);
  Mt->give_node_coord2d (x,y,eid);
  Mt->give_elemnodes (eid,nodes);

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

  //  transformation of stiffness matrix
  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 quadrilateral
   finite element with rotationale degrees of freedom wtih
   bilinear approximation functions
   
   @param eid - number of element
   @param mm - mass matrix
   
   8.12.2001
*/
void planeelemrotlt::mass_matrix (long eid,matrix &mm,vector &x,vector &y)
{
  long i;
  double jac,area,thick,rho;
  ivector nodes(nne);
  vector b(3),c(3),areacoord(3),w(intordmm),gp1(intordmm),gp2(intordmm),t(nne),dens(nne);
  matrix n(napfun,ndofe);
  
  Mt->give_elemnodes (eid,nodes);
  Mt->give_node_coord2d (x,y,eid);
  Mc->give_thickness (eid,nodes,t);
  Mc->give_density (eid,nodes,dens);

  //  det is equal to double area of the element
  area = ((x[1]-x[0])*(y[2]-y[0])-(x[2]-x[0])*(y[1]-y[0]))/2.0;
  
  b_coeff (b.a,y.a);
  c_coeff (c.a,x.a);

  gauss_points_tr (gp1.a,gp2.a,w.a,intordmm);
  
  fillm (0.0,mm);
  
  for (i=0;i<intordmm;i++){
    
    areacoord[0]=gp1[i];
    areacoord[1]=gp2[i];
    areacoord[2]=1.0-gp1[i]-gp2[i];
    
    bf_matrix (n,areacoord,b,c);
    
    thick = approx (areacoord,t);
    rho = approx (areacoord,dens);
    
    jac=w[i]*thick*rho*area*2.0;
    
    nnj (mm.a,n.a,jac,n.m,n.n);
  }
  
}

void planeelemrotlt::res_mass_matrix (long eid,matrix &mm)
{
  vector x(nne),y(nne);
  Mt->give_node_coord2d (x,y,eid);
  mass_matrix (eid,mm,x,y);
}


/**
   function computes load matrix of the plane stress rectangular
   finite element with bilinear approximation functions
   load vector is obtained after premultiplying load matrix
   by nodal load values

   @param eid - number of element
   @param lm - load matrix

   25.7.2001
*/
void planeelemrotlt::load_matrix (long eid,matrix &lm)
{