soilplateq.cpp

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

#include "soilplateq.h"
#include "q4plate.h"
#include "global.h"
#include "globmat.h"
#include "genfile.h"
#include "node.h"
#include "element.h"
#include <stdlib.h>
#include <math.h>

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

  nne=4;  ndofe=12;  tncomp=5;  napfun=2; ned=4;  nned=2;  
  intordmm=3; intordb=2; ssst=plate;
  nb=2; 
  
  ncomp = new long [nb];
  ncomp[0]=3;
  ncomp[1]=2;
  
  cncomp = new long [nb];
  cncomp[0]=0;
  cncomp[1]=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]=9;  nip[0][1]=0;
  nip[1][0]=0;  nip[1][1]=4;
  
  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]=2;
}

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

  delete [] cncomp;
  delete [] ncomp;
}

void soilplateq::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 xi,eta - coordinates on element
   @param nodval - nodal values
*/
double soilplateq::approx (double xi,double eta,vector &nodval)
{
  double f;
  vector bf(nne);
  
  bf_lin_4_2d (bf.a,xi,eta);
  
  scprd (bf,nodval,f);
  
  return f;
}

/**
   function assembles matrix of transformation for Q4plate
   20.3.2002
*/
void soilplateq::atd_matrix (matrix &atd,vector &x,vector &y)
{
  double sx,sy;
  matrix p(16,16),p1(16,16),ct(4,2);
  vector dl(4);
  long i,j,i1,i2,i3,i4,ii;

  dl[0]=sqrt((x[1]-x[0])*(x[1]-x[0])+(y[1]-y[0])*(y[1]-y[0]));
  dl[1]=sqrt((x[2]-x[1])*(x[2]-x[1])+(y[2]-y[1])*(y[2]-y[1]));
  dl[2]=sqrt((x[3]-x[2])*(x[3]-x[2])+(y[3]-y[2])*(y[3]-y[2]));
  dl[3]=sqrt((x[0]-x[3])*(x[0]-x[3])+(y[0]-y[3])*(y[0]-y[3]));
  // matrix vector of sides {cos,sin} 
  ct[0][0]=(x[1]-x[0])/dl[0];
  ct[0][1]=(y[1]-y[0])/dl[0];
  ct[1][0]=(x[2]-x[1])/dl[1];
  ct[1][1]=(y[2]-y[1])/dl[1];
  ct[2][0]=(x[3]-x[2])/dl[2];
  ct[2][1]=(y[3]-y[2])/dl[2];
  ct[3][0]=(x[0]-x[3])/dl[3];
  ct[3][1]=(y[0]-y[3])/dl[3];
  fillm (0.0,p);
  fillm (0.0,atd);

  for (i=0;i<nne;i++){
    i1=3*i;
    i2=i1+1;
    i3=i1+2;
    i4=12+i;
    p[i1][0]=1.;
    p[i1][1]=x[i];
    p[i1][2]=y[i];
    p[i1][3]=x[i]*y[i];
    p[i1][4]=x[i]*x[i];
    p[i1][5]=y[i]*y[i];
    p[i1][6]=x[i]*x[i]*y[i];
    p[i1][7]=y[i]*y[i]*x[i];
    p[i1][8]=x[i]*x[i]*x[i];
    p[i1][9]=y[i]*y[i]*y[i];
    p[i1][10]=x[i]*x[i]*x[i]*y[i];
    p[i1][11]=y[i]*y[i]*y[i]*x[i];
    p[i2][5]=y[i]*2.;
    p[i2][6]=x[i]*x[i];
    p[i2][7]=y[i]*x[i]*2.;
    p[i2][9]=y[i]*y[i]*3.;
    p[i2][10]=x[i]*x[i]*x[i];
    p[i2][11]=y[i]*y[i]*x[i]*3.;
    p[i2][14]=1.;
    p[i2][15]=x[i];
    p[i3][4]=-x[i]*2.;
    p[i3][6]=-x[i]*y[i]*2.;
    p[i3][7]=-y[i]*y[i];
    p[i3][8]=-x[i]*x[i]*3.;
    p[i3][10]=-x[i]*x[i]*y[i]*3.;
    p[i3][11]=-y[i]*y[i]*y[i];
    p[i3][12]=-1.;
    p[i3][13]=-y[i];

    ii=i+1;

    if (ii > 3) ii=ii-4;
    
    sy=(y[i]+y[ii])/2.;
    sx=(x[i]+x[ii])/2.;
    p[i4][1]= ct[i][0];
    p[i4][2]= ct[i][1];
    p[i4][3]= sy*ct[i][0]+sx*ct[i][1];
    p[i4][12]=-ct[i][0];
    p[i4][13]=-sy*ct[i][0];
    p[i4][14]=-ct[i][1];
    p[i4][15]=-sx*ct[i][1];
  }

  double *ee;
  ee = new double [16*16];
  for (i=0;i<16;i++){
    for (j=0;j<16;j++){
      ee[i*16+j]=0.0;
    }
    ee[i*16+i]=1.0;
  }
  
  gemp (p.a,p1.a,ee,16,16,Mp->zero,1);
  delete [] ee;
  
  for (i=0;i<p1.n;i++){
    atd[i][0] =p1[i][0]  -p1[i][12]/dl[0]+p1[i][15]/dl[3];
    atd[i][1] =p1[i][1]  -p1[i][12]*ct[0][1]/2.-p1[i][15]*ct[3][1]/2.;
    atd[i][2] =p1[i][2]  +p1[i][12]*ct[0][0]/2.+p1[i][15]*ct[3][0]/2.;
    atd[i][3] =p1[i][3]  -p1[i][13]/dl[1]+p1[i][12]/dl[0];
    atd[i][4] =p1[i][4]  -p1[i][13]*ct[1][1]/2.-p1[i][12]*ct[0][1]/2.;
    atd[i][5] =p1[i][5]  +p1[i][13]*ct[1][0]/2.+p1[i][12]*ct[0][0]/2.;
    atd[i][6] =p1[i][6]  -p1[i][14]/dl[2]+p1[i][13]/dl[1];
    atd[i][7] =p1[i][7]  -p1[i][14]*ct[2][1]/2.-p1[i][13]*ct[1][1]/2.;
    atd[i][8] =p1[i][8]  +p1[i][14]*ct[2][0]/2.+p1[i][13]*ct[1][0]/2.;
    atd[i][9] =p1[i][9]  -p1[i][15]/dl[3]+p1[i][14]/dl[2];
    atd[i][10]=p1[i][10] -p1[i][15]*ct[3][1]/2.-p1[i][14]*ct[2][1]/2.;
    atd[i][11]=p1[i][11] +p1[i][15]*ct[3][0]/2.+p1[i][14]*ct[2][0]/2.;
  }
  
}
/**
   function extracts components of the soil
   part of stiffness matrix of the material to the matrix ds
   20.3.2002
*/
void soilplateq::dbmat (matrix &db,double c1, double c2, long ri, long ci)
{

  if (ri==0 && ci==0){
  db[0][0] = c1;   db[0][1] = 0.0;  db[0][2] = 0.0;
  db[1][0] = 0.0;  db[1][1] = c2;   db[1][2] = 0.0;
  db[2][0] = 0.0;  db[2][1] = 0.0;  db[2][2] = c2;
  }
  if (ri==1 && ci==1){
    db[0][0] = c2*5.0/6.0;		db[0][1] = 0.0;
    db[1][0] = 0.0;             db[1][1] = c2*5.0/6.0;
  }
}
void soilplateq::transfmat (ivector &nodes,matrix &tmat)
{
  long i,n,m;
  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+1][i*3+1]=Mt->nodes[nodes[i]].e1[0];  tmat[i*3+1][i*3+2]=Mt->nodes[nodes[i]].e2[0];
      tmat[i*3+2][i*3+1]=Mt->nodes[nodes[i]].e1[1];  tmat[i*3+2][i*3+2]=Mt->nodes[nodes[i]].e2[1];
    }
  }
}

void soilplateq::appval (double xi,double eta,long fi,long nc,vector &eps,double **val)
{
  long i,j,k;
  vector nodval;
  
  k=0;
  allocv (nne,nodval);
  for (i=fi;i<fi+nc;i++){
    for (j=0;j<nne;j++){
      nodval[j]=val[j][i];
    }
    eps[k]=approx (xi,eta,nodval);
    k++;
  }
  
  destrv (nodval);
}
  
void soilplateq::nodecoord (vector &xi,vector &eta)
{
  xi[0] = 1.0;  eta[0] = 1.0;
  xi[1] =-1.0;  eta[1] = 1.0;
  xi[2] =-1.0;  eta[2] =-1.0;
  xi[3] = 1.0;  eta[3] =-1.0;
}


void soilplateq::geom_matrix (matrix &gm,matrix &atd,vector &x,vector &y, vector &l)
{
  int i;
  double sx,sy;

// quadrilateral   w, dw/dx. dw/dy
  sx=(x[0]*(1+l[0])*(1+l[1])+x[1]*(1-l[0])*(1+l[1])+x[2]*(1-l[0])*(1-l[1])+x[3]*(1+l[0])*(1-l[1]))/4.;
  sy=(y[0]*(1+l[0])*(1+l[1])+y[1]*(1-l[0])*(1+l[1])+y[2]*(1-l[0])*(1-l[1])+y[3]*(1+l[0])*(1-l[1]))/4.;

  for (i=0;i<gm.n;i++){
    gm[0][i]=atd[0][i]+sx*atd[1][i]+sy*atd[2][i]+sx*sy*atd[3][i]+sx*sx*atd[4][i]+sy*sy*atd[5][i]+
      sx*sx*sy*atd[6][i]+sy*sy*sx*atd[7][i]+sx*sx*sx*atd[8][i]+sy*sy*sy*atd[9][i]+sx*sx*sx*sy*atd[10][i]+sx*sy*sy*sy*atd[11][i];
    gm[1][i]=atd[1][i]+sy*atd[3][i]+2.*sx*atd[4][i]+2.*sx*sy*atd[6][i]+sy*sy*atd[7][i]+3.*sx*sx*atd[8][i]+3.*sx*sx*sy*atd[10][i]+sy*sy*sy*atd[11][i];
//	gm[1][i]=0.0;
	gm[2][i]=atd[2][i]+sx*atd[3][i]+2.*sy*atd[5][i]+sx*sx*atd[6][i]+2.*sy*sx*atd[7][i]+3.*sy*sy*atd[9][i]+sx*sx*sx*atd[10][i]+3.*sx*sy*sy*atd[11][i];
//	gm[2][i]=0.0;
  }
}
void soilplateq::geom_matrix_shear (matrix &gm,matrix &atd,vector &x,vector &y,vector &l)
{
  long i;
  double sx,sy;
  
  // first point is in I Q
  sx=(x[0]*(1+l[0])*(1+l[1])+x[1]*(1-l[0])*(1+l[1])+x[2]*(1-l[0])*(1-l[1])+x[3]*(1+l[0])*(1-l[1]))/4.;
  sy=(y[0]*(1+l[0])*(1+l[1])+y[1]*(1-l[0])*(1+l[1])+y[2]*(1-l[0])*(1-l[1])+y[3]*(1+l[0])*(1-l[1]))/4.;
  
  for (i=0;i<atd.n;i++){
    gm[0][i]=atd[1][i]+sy*atd[3][i]-atd[12][i]-sy*atd[13][i];
    gm[1][i]=atd[2][i]+sx*atd[3][i]-atd[14][i]-sx*atd[15][i];
  }
}

void soilplateq::res_stiffness_matrix (long eid,matrix &sm)
{
  vector x(nne),y(nne);
  Mt->give_node_coord2d (x,y,eid);
  stiffness_matrix (eid,0,0,sm,x,y);
}

	  
void soilplateq::stiffness_matrix (long eid,long ri, long ci, matrix &sm,vector &x, vector &y)
{
  long ii,jj,i,j,ipp;
  double jac,a,a0,a1;
  ivector nodes(nne);
  vector w,gp,l(2);
  matrix gm,cc,atd(16,12),d(3,3);
//     jakobian
  Mt->give_elemnodes (eid,nodes);
  
// translation to center it is necesary for w which in local coord. and no in relation
  a=(x[0]+x[1]+x[2]+x[3])/4.;
  x[0]=x[0]-a;
  x[1]=x[1]-a;
  x[2]=x[2]-a;
  x[3]=x[3]-a;
  a=(y[0]+y[1]+y[2]+y[3])/4.;
  y[0]=y[0]-a;
  y[1]=y[1]-a;
  y[2]=y[2]-a;
  y[3]=y[3]-a;

  
  //     jakobian
  a = (x[2]-x[0])*(y[3]-y[1])-(y[2]-y[0])*(x[3]-x[1]);
  a0=-(x[3]-x[2])*(y[1]-y[0])+(y[3]-y[2])*(x[1]-x[0]);
  a1=-(x[2]-x[1])*(y[3]-y[0])+(y[2]-y[1])*(x[3]-x[0]);
  
  atd_matrix (atd,x,y);
  fillm (0.0,sm);
  
  ipp=Mt->elements[eid].ipp[ri][ci];
  Mm->matstiff (d,ipp);
 
  for (ii=0;ii<nb;ii++){
    for (jj=0;jj<nb;jj++){
      if (intordsm[ii][jj]==0)  continue;
      allocv (intordsm[ii][jj],w); allocv (intordsm[ii][jj],gp);
      allocm (ncomp[jj],ndofe,gm);
      allocm (ncomp[ii],ncomp[jj],cc);

      ipp=Mt->elements[eid].ipp[ri+ii][ci+jj];
      gauss_points (gp.a,w.a,intordsm[ii][jj]);

	  for (i=0;i<intordsm[ii][jj];i++){
		 l[0]=gp[i];  
		for (j=0;j<intordsm[ii][jj];j++){
		  l[1]=gp[j];
		  jac=(a+a0*l[0]+a1*l[1])/8.*w[i]*w[j];

		  if(ii==0) geom_matrix (gm,atd,x,y,l);
		  else if(ii==1) geom_matrix_shear (gm,atd,x,y,l);
          dbmat (cc, d[0][0],d[1][1],ii,jj);
          bdbjac (sm,gm,cc,gm,jac);
		  ipp++;
		}
	  }
      destrm (cc);  destrm (gm);  destrv (gp);  destrv (w);
	}
 
  }


/*
  for (i=0;i<intordsm[0][0];i++){
	for (j=0;j<intordsm[0][0];j++){
	  l[0]=gp[i];  l[1]=gp[j];
	  jac=(a+a0*l[0]+a1*l[1])/8.*w[i]*w[j];
	  geom_matrix (gm,atd,x,y,l);
      Mm->matstiff (cc,ipp);
//      imat=Mm->ip[ipp].idm[Mm->ip[ipp].gemid()];
      bdbjac (sm,gm,cc,gm,jac);
	  ipp++;  
	}
  }
  destrm (cc); destrm (gm);  destrv (gp);  destrv (w);
*/

//  fprintf (Out,"\n\n kontrola matice tuhosti");
//  for (i=0;i<ndofe;i++){fprintf (Out,"\n");
//    for (j=0;j<ndofe;j++){fprintf (Out," %le",sm[i][j]);}
//  }
//    fprintf (Out,"\n\n diagonalni prvky, %ld,\n",eid);
//    for (i=0;i<ndofe;i++){fprintf (Out," %le",sm[i][i]);}

}


void soilplateq::res_mainip_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
  long transf = Mt->locsystems (nodes);
  if (transf>0){