/*********************************************************************** * * ***** *** *** * * * * * * * * *** *** * * * * * * * ***** *** *** * * 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: slqu88 - Elementsteifigkeitsroutine * sl88 - Berechnung der Matrix b * diese Compilerunit enthaelt Routinen, die gedanklich an FORTRAN- * Quellen von H.J.Bathe, MIT, Cambridge, MA, USA angelehnt sind. * 3.1.2004 Rieg ***********************************************************************/ /*********************************************************************** * Fuer UNIX ***********************************************************************/ #ifdef FR_UNIX #include #include /* fprintf */ #include /* FR_SQRT */ #endif /*********************************************************************** * Fuer Windows 95 ***********************************************************************/ #ifdef FR_WIN95 #include #include /* fprintf */ #include /* FR_SQRT */ #endif /*********************************************************************** * Functions ***********************************************************************/ int sl88(FR_DOUBLE *r,FR_DOUBLE *s,FR_DOUBLE *t); FR_DOUBLE hexgh(FR_DOUBLE sig[]); /*********************************************************************** * hier beginnt Function slqu88 ***********************************************************************/ int slqu88(void) { extern FILE *fo3,*fo5; extern FR_DOUBLEAY smw; extern FR_DOUBLEAY gmw; extern FR_INT4AY jsm; extern FR_INT4AY koi; extern FR_INT4AY koffs; extern FR_DOUBLE ul[]; extern FR_DOUBLE h[]; extern FR_DOUBLE xk[],yk[],zk[]; extern FR_DOUBLE b[],xx[],d[]; extern FR_DOUBLE emode,rnuee; extern FR_INT4 nint,isflag,kc; FR_DOUBLE eps[7],sig[7],rv[9]; FR_DOUBLE r,s,t,xs,ys,zs,sigv,ax,ay,az,rmin; FR_DOUBLE f0,f1,f2; FR_INT4 jp[9]; FR_INT4 i,lx,ly,lz,j,k,jk; int iret; /*---------------------------------------------------------------------- * Gauss-Legendre Stuetzstellen, variabel *---------------------------------------------------------------------*/ static FR_DOUBLE xg[17]= { 0., 0., -.5773502691896, -.7745966692415, -.8611363115941, 0., +.5773502691896, 0., -.3399810435849, 0., 0., +.7745966692415, +.3399810435849, 0., 0., 0., +.8611363115941 }; /*---------------------------------------------------------------------- * Gauss-Legendre Stuetzstellen, fix fuer 2 x 2 x 2 *---------------------------------------------------------------------*/ static FR_DOUBLE xgo[9]= {0., +.5773502691896, -.5773502691896, -.5773502691896, +.5773502691896, +.5773502691896, -.5773502691896, -.5773502691896, +.5773502691896 }; static FR_DOUBLE ygo[9]= {0., +.5773502691896, +.5773502691896, -.5773502691896, -.5773502691896, +.5773502691896, +.5773502691896, -.5773502691896, -.5773502691896 }; static FR_DOUBLE zgo[9]= {0., +.5773502691896, +.5773502691896, +.5773502691896, +.5773502691896, -.5773502691896, -.5773502691896, -.5773502691896, -.5773502691896 }; /*---------------------------------------------------------------------- * natuerliche Koordinaten der Eckknoten *---------------------------------------------------------------------*/ static FR_DOUBLE rkr[9]= { 0., 1.,-1.,-1., 1., 1.,-1.,-1., 1. }; static FR_DOUBLE rks[9]= { 0., 1., 1.,-1.,-1., 1., 1.,-1.,-1. }; static FR_DOUBLE rkt[9]= { 0., 1., 1., 1., 1.,-1.,-1.,-1.,-1. }; /*---------------------------------------------------------------------- * xk und yk umspeichern *---------------------------------------------------------------------*/ for(i = 1;i <= 8;i++) { xx[i] = xk[i]; xx[8 +i]= yk[i]; xx[16+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; /*---------------------------------------------------------------------- * Spannungen in den Gauss-Punkten berechnen *---------------------------------------------------------------------*/ if(nint > 0) { /*====================================================================== * Spannungen in den Gauss-Punkten berechnen, variabel *=====================================================================*/ for(lx = 1;lx <= nint;lx++) { r= xg[(lx-1)*4 + nint]; for(ly = 1;ly <= nint;ly++) { s= xg[(ly-1)*4 + nint]; for(lz = 1;lz <= nint;lz++) { t= xg[(lz-1)*4 + nint]; /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * Matrix b der partiellen Ableitungen & Formfunktionen holen *~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ iret= sl88(&r,&s,&t); if(iret != 0) return(iret); /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * Dehnungen berechnen *~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ for(k = 1;k <= 6;k++) { eps[k]= 0.; for(j = 1;j <= 24;j++) { eps[k]= eps[k] + b[(k-1)*24 + j] * ul[j]; } } /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * Spannungen berechnen *~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ for(k = 1;k <= 6;k++) { sig[k]= 0.; for(j = 1;j <= 6;j++) { sig[k]= sig[k] + d[(k-1)*6 + j] * eps[j]; } } /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * Integrationspunkte in echte Koordinaten umrechnen *~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ xs= 0.; ys= 0.; zs= 0.; for(j = 1;j <= 8;j++) { xs+= h[j] * xx[ j]; ys+= h[j] * xx[8 +j]; zs+= h[j] * xx[16+j]; } /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * Spannungen ausschreiben *~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ if(isflag == 0) { fprintf(fo3,"\n%+#10.2lE %+#10.2lE %+#10.2lE\ %+#11.3lE %+#11.3lE %+#11.3lE %+#11.3lE %+#11.3lE %+#11.3lE" ,xs,ys,zs,sig[1],sig[2],sig[3],sig[4],sig[5],sig[6]); } if(isflag == 1) { sigv= hexgh(sig); fprintf(fo3,"\n%+#10.2lE %+#10.2lE %+#10.2lE\ %+#11.3lE %+#11.3lE %+#11.3lE %+#11.3lE %+#11.3lE %+#11.3lE\ %+#11.3lE",xs,ys,zs,sig[1],sig[2],sig[3],sig[4],sig[5],sig[6],sigv); fprintf(fo5,"\n%+#11.3lE %+#11.3lE %+#11.3lE %+#11.3lE", xs,ys,zs,sigv); gmw[kc]+= sigv; } } } } gmw[kc]/= nint*nint*nint; /* Mittelwert berechnen */ /*====================================================================== * die Eckknoten berechnen *=====================================================================*/ for(lx = 1;lx <= 8;lx++) { r= xgo[lx]; s= ygo[lx]; t= zgo[lx]; /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * Matrix b der partiellen Ableitungen & Formfunktionen holen *~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ iret= sl88(&r,&s,&t); if(iret != 0) return(iret); /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * Integrationspunkte in echte Koordinaten umrechnen *~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ xs= 0.; ys= 0.; zs= 0.; for(j = 1;j <= 8;j++) { xs+= h[j] * xx[ j]; ys+= h[j] * xx[8 +j]; zs+= h[j] * xx[16+j]; } /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * welcher Knoten ist's wirklich? *~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ for(j = 1;j <= 8;j++) { ax = xk[j] - xs; ay = yk[j] - ys; az = zk[j] - zs; rv[j]= FR_SQRT(ax*ax + ay*ay + az*az); } rmin= 1e88; for(j = 1;j <= 8;j++) { if(rv[j] < rmin) { rmin= rv[j]; jk= j; } } jp[lx]= jk; } /*====================================================================== * Spannungen in den Gauss-Punkten berechnen, fix fuer Z88O *=====================================================================*/ for(lx = 1;lx <= 8;lx++) { r= xgo[lx]; s= ygo[lx]; t= zgo[lx]; /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * Matrix b der partiellen Ableitungen & Formfunktionen holen *~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ iret= sl88(&r,&s,&t); if(iret != 0) return(iret); /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * Dehnungen berechnen *~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ for(k = 1;k <= 6;k++) { eps[k]= 0.; for(j = 1;j <= 24;j++) { eps[k]= eps[k] + b[(k-1)*24 + j] * ul[j]; } } /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * Spannungen berechnen *~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ for(k = 1;k <= 6;k++) { sig[k]= 0.; for(j = 1;j <= 6;j++) { sig[k]= sig[k] + d[(k-1)*6 + j] * eps[j]; } } /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * Vergleichsspannungen aufaddieren *~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ sigv= hexgh(sig); smw[koi[koffs[kc]+jp[lx]-1]]+= sigv; jsm[koi[koffs[kc]+jp[lx]-1]]++; } } /* Ende Gausspunkte variabel */ /* e if */ /*---------------------------------------------------------------------- * Spannungen in den Eckknoten berechnen *---------------------------------------------------------------------*/ if(nint == 0) { for(lx = 1;lx <= 8;lx++) { r= rkr[lx]; s= rks[lx]; t= rkt[lx]; /*====================================================================== * Matrix b der partiellen Ableitungen & Formfunktionen holen *=====================================================================*/ iret= sl88(&r,&s,&t); if(iret != 0) return(iret); /*====================================================================== * Dehnungen berechnen *=====================================================================*/ for(k = 1;k <= 6;k++) { eps[k]= 0.; for(j = 1;j <= 24;j++) { eps[k]= eps[k] + b[(k-1)*24 + j] * ul[j]; } } /*====================================================================== * Spannungen berechnen *=====================================================================*/ for(k = 1;k <= 6;k++) { sig[k]= 0.; for(j = 1;j <= 6;j++) { sig[k]= sig[k] + d[(k-1)*6 + j] * eps[j]; } } /*====================================================================== * Eckpunkte in echte Koordinaten umrechnen *=====================================================================*/ xs= 0.; ys= 0.; zs= 0.; for(j = 1;j <= 8;j++) { xs+= h[j] * xx[ j]; ys+= h[j] * xx[8 +j]; zs+= h[j] * xx[16+j]; } /*====================================================================== * Spannungen ausschreiben *=====================================================================*/ fprintf(fo3,"\n%+#10.2lE %+#10.2lE %+#10.2lE\ %+#11.3lE %+#11.3lE %+#11.3lE %+#11.3lE %+#11.3lE %+#11.3lE" ,xs,ys,zs,sig[1],sig[2],sig[3],sig[4],sig[5],sig[6]); } /* e 170 */ } /* e if */ return(0); } /*********************************************************************** * hier beginnt Function sl88 ***********************************************************************/ int sl88(FR_DOUBLE *r,FR_DOUBLE *s,FR_DOUBLE *t) { /*--------------------------------------------------------------------- * xx geht rein, unveraendert (ex) * h geht raus, neu (ex) * b geht raus, neu (ex) * r,s,t gehen rein, unveraendert *--------------------------------------------------------------------*/ extern FR_DOUBLE h[]; extern FR_DOUBLE b[],xx[],p[]; FR_DOUBLE xj[10], xji[10]; /* ist 3x3 +1 */ FR_DOUBLE dum,rs,rt,st,rst,det; FR_INT4 i,j,k,k3; /*---------------------------------------------------------------------- * Faktoren der Formfunktionen belegen *---------------------------------------------------------------------*/ rs= (*r) * (*s) ; rt= (*r) * (*t) ; st= (*s) * (*t) ; rst=(*r) * (*s) * (*t); /*---------------------------------------------------------------------- * Formfunktionen *---------------------------------------------------------------------*/ h[1]= .125 *(1. + (*r) + (*s) + rs + (*t) + rt + st + rst); h[2]= .125 *(1. - (*r) + (*s) - rs + (*t) - rt + st - rst); h[3]= .125 *(1. - (*r) - (*s) + rs + (*t) - rt - st + rst); h[4]= .125 *(1. + (*r) - (*s) - rs + (*t) + rt - st - rst); h[5]= .125 *(1. + (*r) + (*s) + rs - (*t) - rt - st - rst); h[6]= .125 *(1. - (*r) + (*s) - rs - (*t) + rt - st + rst); h[7]= .125 *(1. - (*r) - (*s) + rs - (*t) + rt + st - rst); h[8]= .125 *(1. + (*r) - (*s) - rs - (*t) - rt + st + rst); /*---------------------------------------------------------------------- * Partielle Ableitung der Formfunktionen nach r *---------------------------------------------------------------------*/ p[1]= .125 *(+1. + (*s) + (*t) + st); p[2]= .125 *(-1. - (*s) - (*t) - st); p[3]= .125 *(-1. + (*s) - (*t) + st); p[4]= .125 *(+1. - (*s) + (*t) - st); p[5]= .125 *(+1. + (*s) - (*t) - st); p[6]= .125 *(-1. - (*s) + (*t) + st); p[7]= .125 *(-1. + (*s) + (*t) - st); p[8]= .125 *(+1. - (*s) - (*t) + st); /*---------------------------------------------------------------------- * Partielle Ableitung der Formfunktionen nach s *---------------------------------------------------------------------*/ p[9] = .125 *(+1. + (*r) + (*t) + rt); p[10]= .125 *(+1. - (*r) + (*t) - rt); p[11]= .125 *(-1. + (*r) - (*t) + rt); p[12]= .125 *(-1. - (*r) - (*t) - rt); p[13]= .125 *(+1. + (*r) - (*t) - rt); p[14]= .125 *(+1. - (*r) - (*t) + rt); p[15]= .125 *(-1. + (*r) + (*t) - rt); p[16]= .125 *(-1. - (*r) + (*t) + rt); /*---------------------------------------------------------------------- * Partielle Ableitung der Formfunktionen nach t *---------------------------------------------------------------------*/ p[17]= .125 *(+1. + (*r) + (*s) + rs); p[18]= .125 *(+1. - (*r) + (*s) - rs); p[19]= .125 *(+1. - (*r) - (*s) + rs); p[20]= .125 *(+1. + (*r) - (*s) - rs); p[21]= .125 *(-1. - (*r) - (*s) - rs); p[22]= .125 *(-1. + (*r) - (*s) + rs); p[23]= .125 *(-1. + (*r) + (*s) - rs); p[24]= .125 *(-1. - (*r) + (*s) + rs); /*---------------------------------------------------------------------- * 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 <= 8;k++) { dum+= p[(i-1)*8 + k] * xx[(j-1)*8 + 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 <= 144;i++) b[i]= 0.; k3= 0; for(k = 1;k <= 8;k++) { k3+= 3; for(i = 1;i <= 3;i++) { b[ k3-2]= b[ k3-2] + xji[ i] * p[(i-1)*8 + k]; b[24 + k3-1]= b[24 + k3-1] + xji[3 + i] * p[(i-1)*8 + k]; b[48 + k3 ]= b[48 + k3 ] + xji[6 + i] * p[(i-1)*8 + k]; } b[72 + k3-2]= b[24 + k3-1]; b[72 + k3-1]= b[ k3-2]; b[96 + k3-1]= b[48+ k3 ]; b[96 + k3 ]= b[24 + k3-1]; b[120 + k3-2]= b[48 +k3 ]; b[120 + k3 ]= b[ k3-2]; } return(0); }