/*********************************************************************** * * ***** *** *** * * * * * * * * *** *** * * * * * * * ***** *** *** * * 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, 2002 * * 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: spur88 - Elementsteifigkeitsroutine * sb88 - Berechnung der Matrix b * diese Compilerunit enthaelt Routinen, die gedanklich an FORTRAN- * Quellen von H.J.Bathe, MIT, Cambridge, MA, USA angelehnt sind. * 23.3.2002 Rieg ***********************************************************************/ /*********************************************************************** * Fuer UNIX ***********************************************************************/ #ifdef FR_UNIX #include #endif /*********************************************************************** * Fuer Windows 95 ***********************************************************************/ #ifdef FR_WIN95 #include #endif /*********************************************************************** * Functions ***********************************************************************/ int sb88(FR_DOUBLE *det,FR_DOUBLE *r,FR_DOUBLE *s,FR_DOUBLE *t); /*********************************************************************** * hier beginnt Function spur88 ***********************************************************************/ int spur88(void) { extern FR_DOUBLEAY se; extern FR_DOUBLE xk[],yk[],zk[]; extern FR_DOUBLE b[],xx[],d[]; extern FR_DOUBLE emode,rnuee; extern FR_INT4 intore; FR_DOUBLE db[7]; FR_DOUBLE r,s,t,det,wt,stiff; FR_DOUBLE f0,f1,f2; FR_INT4 ne= 12,i,igauss,j,k,l; int iret; /*---------------------------------------------------------------------- * Gauss-Legendre Stuetzstellen *---------------------------------------------------------------------*/ static FR_DOUBLE rg[26]= { 0.,0.,0.,0.,0., /* Elemente 0 bis 4 leer */ 0.25, /* 1 Stuetzstelle, Start i=5 */ 0.,0.,0.,0.,0., /* Elemente 6 bis 16 leer */ 0.,0.,0.,0.,0.,0., 0.58541020, /* 4 Stuetzstellen, Start i=17 */ 0.13819660, 0.13819660, 0.13819660, 0.25, /* 5 Stuetzstellen, Start i=21 */ 0.5, 0.16666667, 0.16666667, 0.16666667 }; static FR_DOUBLE sg[26]= { 0.,0.,0.,0.,0., /* Elemente 0 bis 4 leer */ 0.25, /* 1 Stuetzstelle, Start i=5 */ 0.,0.,0.,0.,0., /* Elemente 6 bis 16 leer */ 0.,0.,0.,0.,0.,0., 0.13819660, /* 4 Stuetzstellen, Start i=17 */ 0.58541020, 0.13819660, 0.13819660, 0.25, /* 5 Stuetzstellen, Start i=21 */ 0.16666667, 0.5, 0.16666667, 0.16666667 }; static FR_DOUBLE tg[26]= { 0.,0.,0.,0.,0., /* Elemente 0 bis 4 leer */ 0.25, /* 1 Stuetzstelle, Start i=5 */ 0.,0.,0.,0.,0., /* Elemente 6 bis 16 leer */ 0.,0.,0.,0.,0.,0., 0.13819660, /* 4 Stuetzstellen, Start i=17 */ 0.13819660, 0.58541020, 0.13819660, 0.25, /* 5 Stuetzstellen, Start i=21 */ 0.16666667, 0.16666667, 0.5, 0.16666667 }; /*---------------------------------------------------------------------- * Gauss-Legendre Integrationsgewichte *---------------------------------------------------------------------*/ static FR_DOUBLE wg[26]= { 0.,0.,0.,0.,0., /* Elemente 0 bis 4 leer */ 1.0, /* 1 Stuetzstelle, Start i=5 */ 0.,0.,0.,0.,0., /* Elemente 6 bis 16 leer */ 0.,0.,0.,0.,0.,0., 0.25, /* 4 Stuetzstellen, Start i=17 */ 0.25, 0.25, 0.25, -0.8, /* 5 Stuetzstellen, Start i=21 */ 0.45, 0.45, 0.45, 0.45 }; /*---------------------------------------------------------------------- * xk und yk umspeichern *---------------------------------------------------------------------*/ for(i = 1;i <= 4;i++) { xx[i] = xk[i]; xx[4+i]= yk[i]; xx[8+i]= zk[i]; } /*---------------------------------------------------------------------- * Materialkonstanten *---------------------------------------------------------------------*/ f0= emode*(1.-rnuee) / ((1.+rnuee)*(1.-2.*rnuee)); f1= rnuee/(1.-rnuee) * f0; f2= (1.-2.*rnuee) / (2.*(1.-rnuee)) * f0; /*---------------------------------------------------------------------- * Elastizitaetsmatrix aufstellen *---------------------------------------------------------------------*/ for(i = 1;i <= 36;i++) d[i]= 0.; d[1] = f0; d[7] = f1; d[13]= f1; d[2] = f1; d[8] = f0; d[14]= f1; d[3] = f1; d[9] = f1; d[15]= f0; d[22]= f2; d[29]= f2; d[36]= f2; /*---------------------------------------------------------------------- * Elementsteifigkeitsmatrix aufstellen: 12 x 12 *---------------------------------------------------------------------*/ for(i = 1;i <= 144;i++) se[i]= 0.; for(igauss = 1;igauss <= intore;igauss++) { r= rg[igauss + intore*4]; s= sg[igauss + intore*4]; t= tg[igauss + intore*4]; /*====================================================================== * Matrix b der partiellen Ableitungen & Jacobi Determinante holen *=====================================================================*/ iret= sb88(&det,&r,&s,&t); if(iret != 0) return(iret); wt= wg[igauss + intore*4] * det * 0.1666666667; /* x 1/6 */ for(j = 1;j <= 12;j++) { for(k = 1;k <= 6;k++) { db[k]= 0.; for(l = 1;l <= 6;l++) { db[k]= db[k] + d[(k-1)*6 + l] * b[(l-1)*12 + j]; } } for(i = j;i <= 12;i++) { stiff= 0.; for(l = 1;l <= 6;l++) { stiff+= b[(l-1)*12 + i] * db[l]; } se[i+ne*(j-1)]= se[i+ne*(j-1)] + stiff * wt; } } } for(j = 1;j <= 12;j++) { for(i = j;i <= 12;i++) { se[j+ne*(i-1)]= se[i+ne*(j-1)]; } } return(0); } /*********************************************************************** * hier beginnt Function sb88 ***********************************************************************/ int sb88(FR_DOUBLE *det,FR_DOUBLE *r,FR_DOUBLE *s,FR_DOUBLE *t) { /*--------------------------------------------------------------------- * xx geht rein, unveraendert (ex) * b geht raus, neu (ex) * det geht raus, neu * r,s,t gehen rein, unveraendert *--------------------------------------------------------------------*/ extern FR_DOUBLE b[],xx[],p[]; FR_DOUBLE xj[10], xji[10]; /* ist 3x3 +1 */ FR_DOUBLE dum; FR_INT4 i,j,k,k3; /*---------------------------------------------------------------------- * Partielle Ableitung der Formfunktionen nach r *---------------------------------------------------------------------*/ p[1]= -1.; p[2]= 1.; p[3]= 0.; p[4]= 0.; /*---------------------------------------------------------------------- * Partielle Ableitung der Formfunktionen nach s *---------------------------------------------------------------------*/ p[5]= -1.; p[6]= 0.; p[7]= 1.; p[8]= 0.; /*---------------------------------------------------------------------- * Partielle Ableitung der Formfunktionen nach t *---------------------------------------------------------------------*/ p[ 9]= -1.; p[10]= 0.; p[11]= 0.; p[12]= 1.; /*---------------------------------------------------------------------- * Jacobi-Matrix am Punkt (r,s,t) entwickeln *---------------------------------------------------------------------*/ for(i = 1;i <= 3;i++) { for(j = 1;j <= 3;j++) { dum= 0.; for(k = 1;k <= 4;k++) { dum+= p[(i-1)*4 + k] * xx[(j-1)*4 + k]; } xj[(i-1)*3 + j]= dum; } } /*---------------------------------------------------------------------- * Jacobi-Determinante am Punkt (r,s,t) entwickeln *---------------------------------------------------------------------*/ (*det)= (xj[1] * xj[5] * xj[9]) - (xj[1] * xj[6] * xj[8]) + (xj[2] * xj[6] * xj[7]) - (xj[2] * xj[4] * xj[9]) + (xj[3] * xj[4] * xj[8]) - (xj[3] * xj[5] * xj[7]); if((*det) < 0.00000001) return(AL_JACNEG); /*---------------------------------------------------------------------- * Berechnung der inversen Jacobi-Matrix *---------------------------------------------------------------------*/ dum= 1./(*det); xji[1]= (xj[5] * xj[9] - xj[8] * xj[6])*dum; xji[2]= -(xj[2] * xj[9] - xj[8] * xj[3])*dum; xji[3]= (xj[2] * xj[6] - xj[5] * xj[3])*dum; xji[4]= -(xj[4] * xj[9] - xj[7] * xj[6])*dum; xji[5]= (xj[1] * xj[9] - xj[7] * xj[3])*dum; xji[6]= -(xj[1] * xj[6] - xj[4] * xj[3])*dum; xji[7]= (xj[4] * xj[8] - xj[7] * xj[5])*dum; xji[8]= -(xj[1] * xj[8] - xj[7] * xj[2])*dum; xji[9]= (xj[1] * xj[5] - xj[4] * xj[2])*dum; /*---------------------------------------------------------------------- * Entwickeln der Matrix b *---------------------------------------------------------------------*/ for(i = 1;i <= 72;i++) b[i]= 0.; k3= 0; for(k = 1;k <= 4;k++) { k3+= 3; for(i = 1;i <= 3;i++) { b[ k3-2]= b[ k3-2] + xji[ i] * p[(i-1)*4 + k]; b[12 + k3-1]= b[12 + k3-1] + xji[3 + i] * p[(i-1)*4 + k]; b[24 + k3 ]= b[24 + k3 ] + xji[6 + i] * p[(i-1)*4 + k]; } b[36 + k3-2]= b[12 + k3-1]; b[36 + k3-1]= b[ k3-2]; b[48 + k3-1]= b[24 + k3 ]; b[48 + k3 ]= b[12 + k3-1]; b[60 + k3-2]= b[24 + k3 ]; b[60 + k3 ]= b[ k3-2]; } return(0); }