/***********************************************************************
* 
*               *****   ***    ***
*                  *   *   *  *   *
*                 *     ***    ***
*                *     *   *  *   *
*               *****   ***    ***
*
* A FREE Finite Elements Analysis Program in ANSI C for the UNIX OS.
*
* Composed and edited and copyright by 
* Professor Dr.-Ing. Frank Rieg, University of Bayreuth, Germany
*
* eMail: 
* frank.rieg@uni-bayreuth.de
* dr.frank.rieg@t-online.de
* 
* V10.0  December 12, 2001
*
* Z88 should compile and run under any UNIX OS and Motif 2.0.
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2, or (at your option)
* any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; see the file COPYING.  If not, write to
* the Free Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA.
***********************************************************************/ 
/***********************************************************************
* diese Compilerunit umfasst: spla88 - Elementsteifigkeitsroutine
*                             ssb88  - Berechnung der Matrizen bbi & bsv
* 6-Knoten Serendipity Reissner- Mindlin- Platte, dreieckig
* 12.6.2002 Rieg
***********************************************************************/

/***********************************************************************
* Fuer UNIX
***********************************************************************/
#ifdef FR_UNIX
#include <z88f.h>
#endif

/***********************************************************************
* Fuer Windows 95
***********************************************************************/
#ifdef FR_WIN95
#include <z88f.h>
#endif

/***********************************************************************
*  Functions
***********************************************************************/
int ssb88(FR_DOUBLE *det,FR_DOUBLE *r,FR_DOUBLE *s);

/***********************************************************************
* hier beginnt Function spla88
***********************************************************************/
int spla88(void)
{
extern FR_DOUBLEAY se;

extern FR_DOUBLE xk[],yk[];
extern FR_DOUBLE bbi[],bsv[],xx[],dbi[],dsv[],be[],hi[];

extern FR_DOUBLE emode,rnuee,qparae,riyye;

extern FR_INT4 intore,ipflag;

FR_DOUBLE dbbi[10],dbsv[5];

FR_DOUBLE facbi,facsv,r,s,det,wt,stiffbi,stiffsv,rmok,skf;

FR_INT4 ne= 18,i,igauss,j,k,l;

int iret;
  
/*----------------------------------------------------------------------
* Gauss-Legendre Stuetzstellen fuer r
*---------------------------------------------------------------------*/
static FR_DOUBLE rg[40]= 
{ 
0.,0.,0.,0.,0.,0.,0.,   /* Elemente 0 - 6 leer              */
0.1666666666667,        /* intore = 3, 1.Ele Start bei i=7  */
0.6666666666667,
0.1666666666667,
0.,0.,0.,0.,0.,         /* Elemente 10-14 leer              */
0.1012865073235,        /* intore = 7, 1.Ele Start bei i=15 */  
0.7974269853531,
0.1012865073235,
0.4701420641051,
0.4701420641051,
0.0597158717898,
0.3333333333333,
0.,0.,0.,0.,0.,         /* Elemente 22-26 leer              */
0.0651301029022,        /* intore =13, 1.Ele Start bei i=27 */
0.8697397941956,
0.0651301029022,
0.3128654960049,
0.6384441885698,
0.0486903154253,
0.6384441885698,
0.3128654960049,
0.0486903154253,
0.2603459660790,
0.4793080678419,
0.2603459660790,
0.3333333333333
};

/*----------------------------------------------------------------------
* Gauss-Legendre Stuetzstellen fuer s
*---------------------------------------------------------------------*/
static FR_DOUBLE sg[40]= 
{ 
0.,0.,0.,0.,0.,0.,0.,   /* Elemente 0 - 6 leer              */
0.1666666666667,        /* intore = 3, 1.Ele Start bei i=7  */
0.1666666666667,
0.6666666666667,
0.,0.,0.,0.,0.,         /* Elemente 10-14 leer              */
0.1012865073235,        /* intore = 7, 1.Ele Start bei i=15 */
0.1012865073235,
0.7974269853531,
0.0597158717898,
0.4701420641051,
0.4701420641051,
0.3333333333333,
0.,0.,0.,0.,0.,         /* Elemente 22-26 leer              */
0.0651301029022,        /* intore =13, 1.Ele Start bei i=27 */
0.0651301029022,
0.8697397941956,
0.0486903154253,
0.3128654960049,
0.6384441885698,
0.0486903154253,
0.6384441885698,
0.3128654960049,
0.2603459660790,
0.2603459660790,
0.4793080678419,
0.3333333333333
};

/*----------------------------------------------------------------------
* Gauss-Legendre Integrationsgewichte
*---------------------------------------------------------------------*/
static FR_DOUBLE wg[40]= 
{ 
0.,0.,0.,0.,0.,0.,0.,   /* Elemente 0 - 6 leer              */
0.3333333333333,        /* intore = 3, 1.Ele Start bei i=7  */
0.3333333333333,
0.3333333333333,
0.,0.,0.,0.,0.,         /* Elemente 10-14 leer              */
0.1259391805448,        /* intore = 7, 1.Ele Start bei i=15 */
0.1259391805448,
0.1259391805448,
0.1323941527885,
0.1323941527885,
0.1323941527885,
0.225,
0.,0.,0.,0.,0.,         /* Elemente 22-26 leer              */
0.0533472356088,        /* intore =13, 1.Ele Start bei i=27 */
0.0533472356088,
0.0533472356088,
0.0771137608903,
0.0771137608903,
0.0771137608903,
0.0771137608903,
0.0771137608903,
0.0771137608903,
0.1756152574332,
0.1756152574332,
0.1756152574332,
-0.1495700444677
};

/*----------------------------------------------------------------------
* intore anpassen, damit Mischen mit apla88 via z88g moeglich ist
*---------------------------------------------------------------------*/
if(intore == 1 || intore == 2) intore = 3;
if(intore == 4)                intore = 7;

/*----------------------------------------------------------------------
* xk und yk umspeichern
*---------------------------------------------------------------------*/
for(i = 1;i <= 6;i++)
  {
  xx[i]  = xk[i];
  xx[6+i]= yk[i];
  }

/*----------------------------------------------------------------------
* Elastizitaetsmatrix aufstellen: Platten-Biegung
*---------------------------------------------------------------------*/
facbi = emode*qparae*qparae*qparae/(12.*(1. - rnuee*rnuee));
dbi[1]= facbi;
dbi[2]= facbi * rnuee;
dbi[3]= 0.;
dbi[4]= dbi[2];
dbi[5]= dbi[1];
dbi[6]= 0.;
dbi[7]= 0.;
dbi[8]= 0.;
dbi[9]= facbi * .5 * (1. - rnuee);
        
/*----------------------------------------------------------------------
* Elastizitaetsmatrix aufstellen: transversale Schubverzerrung
*---------------------------------------------------------------------*/
if(ipflag == 1)  rmok= 1.;     /* Reissner- Mindlin */
if(ipflag == 2)  rmok= 0.01;   /* Schubeinfluss daempfen */

skf= 5./6.;                    /* Schubkorrekturfaktor */

facsv= rmok*emode*skf*qparae/(2*(1. + rnuee));
dsv[1]= facsv;
dsv[2]= 0.;
dsv[3]= 0.;
dsv[4]= facsv;

/*----------------------------------------------------------------------
* Elementsteifigkeitsmatrix aufstellen
*---------------------------------------------------------------------*/
for(i = 1;i <= ne*ne;i++)
  se[i]= 0.;

for(i = 1;i <= ne;i++)
  be[i]= 0.;

for(igauss = 1;igauss <= intore;igauss++)
  {
  r= rg[igauss+2*intore];
  s= sg[igauss+2*intore];

/*======================================================================
* Matrix b der partiellen Ableitungen & Jacobi Determinante holen
*=====================================================================*/
  iret= ssb88(&det,&r,&s);
  if(iret != 0) return(iret);
    
  wt= wg[igauss+2*intore]*0.5 * det; /* Gaussg. halbieren */

/*======================================================================
* Element- Lastvektor be
*=====================================================================*/
  for(j = 1;j <= ne;j++)
    {
    be[j]+= hi[j]*wt*riyye;
    }
 
/*======================================================================
* Start Steifigkeitsmatrix
*=====================================================================*/
  for(j = 1;j <= ne;j++)
    {
 
/*======================================================================
* Biegeverzerrung: DBBI= B*C fuer Biegung
*=====================================================================*/
    for(k = 1;k <= 3;k++)
      {
      dbbi[k]= 0.;
      for(l = 1;l <= 3;l++)
        {
        dbbi[k]+= dbi[(k-1)*3 + l] * bbi[(l-1)*ne + j];
        }
      }

/*======================================================================
* Schubverzerrung: DBSV= B*C fuer Schub
*=====================================================================*/
    for(k = 1;k <= 2;k++)
      {
      dbsv[k]= 0.;
      for(l = 1;l <= 2;l++)
        {
        dbsv[k]+= dsv[(k-1)*2 + l] * bsv[(l-1)*ne + j];
        }
      }

/*======================================================================
* Steifigkeitsmatrix: Die jeweiligen DB's * B und aufsummieren
*=====================================================================*/
    for(i = j;i <= ne;i++)
      {
      stiffbi= 0.;
      stiffsv= 0.;
        
      for(l = 1;l <= 3;l++)
        stiffbi+= bbi[(l-1)*ne + i] * dbbi[l];

      for(l = 1;l <= 2;l++)
        stiffsv+= bsv[(l-1)*ne + i] * dbsv[l];

      se[i+ne*(j-1)]= se[i+ne*(j-1)] + (stiffbi+stiffsv) * wt;
      }
    }
  }

/*======================================================================
* die andere Haelfte der Steifigkeitsmatrix
*=====================================================================*/
for(j = 1;j <= ne;j++)
  {  
  for(i = j;i <= ne;i++)
    {
    se[j+ne*(i-1)]= se[i+ne*(j-1)];
    }
  }

return(0);
}

/***********************************************************************
* hier beginnt Function ssb88
***********************************************************************/
int ssb88(FR_DOUBLE *det,FR_DOUBLE *r,FR_DOUBLE *s)
{
/*---------------------------------------------------------------------
* xx geht rein, unveraendert (ex)
* bbi und bsv gehen raus, neu (ex)
* det geht raus, neu
* r,s gehen rein, unveraendert
*--------------------------------------------------------------------*/

extern FR_DOUBLE h[];
extern FR_DOUBLE bbi[],bsv[],xx[],p[],hi[];

FR_DOUBLE xj[5], xji[5];          /* ist 2x2 +1 */

FR_DOUBLE rr2,ss2,r4,r3,s4,s3,rs4,dum;
        
FR_INT4 i,j,k,k3;
         
/*----------------------------------------------------------------------
* Klammern der Formfunktionen belegen
*---------------------------------------------------------------------*/
rr2= 2. * (*r) * (*r);
ss2= 2. * (*s) * (*s);
r4 = 4. * (*r);
r3 = 3. * (*r);
s4 = 4. * (*s);
s3 = 3. * (*s);
rs4= 4. * (*r) * (*s);

/*----------------------------------------------------------------------
* Formfunktionen
*---------------------------------------------------------------------*/
h[1]= rr2 + ss2 + rs4 - r3 - s3 + 1.;
h[2]= rr2 - (*r);
h[3]= ss2 - (*s);
h[4]= r4 - 2*rr2 - rs4;
h[5]= rs4;
h[6]= s4 - 2*ss2 - rs4;

/*----------------------------------------------------------------------
* Partielle Ableitung der Formfunktionen nach r
*---------------------------------------------------------------------*/
p[1]= r4 + s4 - 3.;
p[2]= r4 - 1.;
p[3]= 0.;
p[4]= 4. - 8*(*r) -s4;
p[5]= s4;
p[6]= -s4;

/*----------------------------------------------------------------------
* Partielle Ableitung der Formfunktionen nach s
*---------------------------------------------------------------------*/
p[7] = s4 + r4 - 3.;
p[8] = 0.;
p[9] = s4 - 1.;
p[10]= -r4;
p[11]= r4;
p[12]= 4. - r4 - 8*(*s);

/*----------------------------------------------------------------------
* Jacobi-Matrix am Punkt (r,s) entwickeln
*---------------------------------------------------------------------*/
for(i = 1;i <= 2;i++)
  {
  for(j = 1;j <= 2;j++)
    {
    dum= 0.;
    for(k = 1;k <= 6;k++)
      {
      dum+= p[(i-1)*6 + k] * xx[(j-1)*6 + k];
      }
    xj[(i-1)*2 + j]= dum;
    }
  }

/*----------------------------------------------------------------------
* Jacobi-Determinante am Punkt (r,s) entwickeln
*---------------------------------------------------------------------*/
(*det)= xj[1] * xj[4] - xj[3] * xj[2];

if((*det) < 0.00000001)
  return(AL_JACNEG);

/*----------------------------------------------------------------------
* Berechnung der inversen Jacobi-Matrix
*---------------------------------------------------------------------*/
dum= 1./(*det);

xji[1]= xj[4]    * dum;
xji[2]= (-xj[2]) * dum;
xji[3]= (-xj[3]) * dum;
xji[4]= xj[1]    * dum;

/*----------------------------------------------------------------------
* Entwickeln der Matrix bbi fuer Biegung
*---------------------------------------------------------------------*/
for(i = 1;i <= 3*18;i++)
  bbi[i]= 0.;

k3= 0;

for(k = 1;k <= 6;k++)
  {
  k3+= 3;

  for(i = 1;i <= 2;i++)
    {
    bbi[   k3  ]+= xji[  i] * p[(i-1)*6+k];
    bbi[18+k3-1]-= xji[2+i] * p[(i-1)*6+k];
    }
  bbi[36+k3  ]= -bbi[18+k3-1];
  bbi[36+k3-1]= -bbi[   k3  ];
  }

/*----------------------------------------------------------------------
* Entwickeln der Matrix bsv fuer Schub
*---------------------------------------------------------------------*/
for(i = 1;i <= 2*18;i++)
  bsv[i]= 0.;

k3= 0;

for(k = 1;k <= 6;k++)
  {
  k3+= 3;

  for(i = 1;i <= 2;i++)
    {
    bsv[   k3-2]+= xji[2+i] * p[(i-1)*6+k];
    bsv[18+k3-2]+= xji[  i] * p[(i-1)*6+k];
    }
  bsv[   k3-1]= -h[k];
  bsv[18+k3  ]=  h[k];
  }

/*----------------------------------------------------------------------
* Entwickeln der Formfunktionen fuer den Lastvektor be
*---------------------------------------------------------------------*/
for(i = 1;i <= 18;i++)
  hi[i]= 0.;

k3= 1;

for(k = 1;k <= 6;k++)
  {
  hi[k3]= h[k];  
  k3+= 3;
  }

return(0);
}