/*********************************************************************** * * ***** *** *** * * * * * * * * *** *** * * * * * * * ***** *** *** * * 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: stet88 - Elementsteifigkeitsroutine * st88 - 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 #endif /*********************************************************************** * Fuer Windows 95 ***********************************************************************/ #ifdef FR_WIN95 #include #include /* fprintf */ #include #endif /*********************************************************************** * Functions ***********************************************************************/ int st88(FR_DOUBLE *r,FR_DOUBLE *s,FR_DOUBLE *t); FR_DOUBLE hexgh(FR_DOUBLE sig[]); /*********************************************************************** * hier beginnt Function stet88 ***********************************************************************/ int stet88(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[5]; FR_DOUBLE r,s,t,xs,ys,zs,sigv,ax,ay,az,rmin; FR_DOUBLE f0,f1,f2; FR_INT4 jp[5]; FR_INT4 i,igauss,j,k,lx,jk; int iret; /*---------------------------------------------------------------------- * Gauss-Legendre Stuetzstellen, variable Integrationsordnung *---------------------------------------------------------------------*/ 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 Stuetzstellen, fixe Integrationsordnung fuer Z88O *---------------------------------------------------------------------*/ static FR_DOUBLE rgo[5]= { 0., 0.13819660, 0.58541020, 0.13819660, 0.13819660}; static FR_DOUBLE sgo[5]= { 0., 0.13819660, 0.13819660, 0.58541020, 0.13819660}; static FR_DOUBLE tgo[5]= { 0., 0.13819660, 0.13819660, 0.13819660, 0.58541020}; /*---------------------------------------------------------------------- * natuerliche Koordinaten der Eckknoten, numerisch instabil fuer Z88O *---------------------------------------------------------------------*/ static FR_DOUBLE rkr[5]= { 0., 0.,1.,0.,0. }; static FR_DOUBLE rks[5]= { 0., 0.,0.,1.,0. }; static FR_DOUBLE rkt[5]= { 0., 0.,0.,0.,1. }; /*---------------------------------------------------------------------- * xk und yk umspeichern *---------------------------------------------------------------------*/ for(i = 1;i <= 10;i++) { xx[i] = xk[i]; xx[10+i]= yk[i]; xx[20+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(igauss = 1;igauss <= nint;igauss++) { r= rg[igauss + nint*4]; s= sg[igauss + nint*4]; t= tg[igauss + nint*4]; /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * Matrix b der partiellen Ableitungen & Formfunktionen holen *~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ iret= st88(&r,&s,&t); if(iret != 0) return(iret); /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * Dehnungen berechnen *~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ for(k = 1;k <= 6;k++) { eps[k]= 0.; for(j = 1;j <= 30;j++) { eps[k]= eps[k] + b[(k-1)*30 + 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 <= 10;j++) { xs+= h[j] * xx[ j]; ys+= h[j] * xx[10+j]; zs+= h[j] * xx[20+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; /* Mittelwert berechnen */ /*====================================================================== * die Eckpunkte berechnen *=====================================================================*/ for(igauss = 1;igauss <= 4;igauss++) { r= rkr[igauss]; s= rks[igauss]; t= rkt[igauss]; /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * Matrix b der partiellen Ableitungen & Formfunktionen holen *~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ iret= st88(&r,&s,&t); if(iret != 0) return(iret); /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * Integrationspunkte in echte Koordinaten umrechnen *~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ xs= 0.; ys= 0.; zs= 0.; for(j = 1;j <= 10;j++) { xs+= h[j] * xx[ j]; ys+= h[j] * xx[10+j]; zs+= h[j] * xx[20+j]; } /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * welcher Knoten ist's wirklich? *~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ for(j = 1;j <= 4;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 <= 4;j++) { if(rv[j] < rmin) { rmin= rv[j]; jk= j; } } jp[igauss]= jk; } /*====================================================================== * Spannungen in den Gauss-Punkten berechnen, fix fuer Z88O *=====================================================================*/ for(igauss = 1;igauss <= 4;igauss++) { r= rgo[igauss]; s= sgo[igauss]; t= tgo[igauss]; /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * Matrix b der partiellen Ableitungen & Formfunktionen holen *~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ iret= st88(&r,&s,&t); if(iret != 0) return(iret); /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * Dehnungen berechnen *~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ for(k = 1;k <= 6;k++) { eps[k]= 0.; for(j = 1;j <= 30;j++) { eps[k]= eps[k] + b[(k-1)*30 + 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[igauss]-1]]+= sigv; jsm[koi[koffs[kc]+jp[igauss]-1]]++; } /* Ende Z88O */ } /* Ende Gausspunkte variabel */ /*---------------------------------------------------------------------- * Spannungen in den Eckknoten berechnen *---------------------------------------------------------------------*/ if(nint == 0) { for(lx = 1;lx <= 4;lx++) { r= rkr[lx]; s= rks[lx]; t= rkt[lx]; /*====================================================================== * Matrix b der partiellen Ableitungen & Formfunktionen holen *=====================================================================*/ iret= st88(&r,&s,&t); if(iret != 0) return(iret); /*====================================================================== * Dehnungen berechnen *=====================================================================*/ for(k = 1;k <= 6;k++) { eps[k]= 0.; for(j = 1;j <= 30;j++) { eps[k]= eps[k] + b[(k-1)*30 + 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 <= 10;j++) { xs+= h[j] * xx[ j]; ys+= h[j] * xx[10+j]; zs+= h[j] * xx[20+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]); } } return(0); } /*********************************************************************** * hier beginnt Function st88 ***********************************************************************/ int st88(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 rr2,ss2,tt2,rs4,rt4,st4,r4,s4,t4; FR_DOUBLE dum,det; FR_INT4 i,j,k,k3; /*---------------------------------------------------------------------- * Einige Faktoren fuer Formfunktionen *---------------------------------------------------------------------*/ rr2= 2* (*r)*(*r); ss2= 2* (*s)*(*s); tt2= 2* (*t)*(*t); rs4= 4* (*r)*(*s); rt4= 4* (*r)*(*t); st4= 4* (*s)*(*t); r4= 4* (*r); s4= 4* (*s); t4= 4* (*t); /*---------------------------------------------------------------------- * Formfunktionen *---------------------------------------------------------------------*/ h[1] = rr2 + ss2 + tt2 +rs4 +rt4 + st4 - 3*(*r) - 3*(*s) - 3*(*t) + 1.; h[2] = rr2 - (*r); h[3] = ss2 - (*s); h[4] = tt2 - (*t); h[5] = r4 - 2*rr2 - rs4 -rt4; h[6] = rs4; h[7] = s4 - rs4 - 2*ss2 - st4; h[8] = rt4; h[9] = st4; h[10]= t4 - rt4 - st4 -2*tt2; /*---------------------------------------------------------------------- * Partielle Ableitung der Formfunktionen nach r *---------------------------------------------------------------------*/ p[1]= r4 + s4 + t4 - 3.; p[2]= r4 - 1.; p[3]= 0.; p[4]= 0.; p[5]= 4. - 2*r4 - s4 - t4; p[6]= s4; p[7]= -s4; p[8]= t4; p[9]= 0.; p[10]= -t4; /*---------------------------------------------------------------------- * Partielle Ableitung der Formfunktionen nach s *---------------------------------------------------------------------*/ p[11]= s4 + r4 + t4 - 3.; p[12]= 0.; p[13]= s4 - 1.; p[14]= 0.; p[15]= -r4 ; p[16]= r4; p[17]= 4. - r4 - 2*s4 - t4; p[18]= 0.; p[19]= t4; p[20]= -t4; /*---------------------------------------------------------------------- * Partielle Ableitung der Formfunktionen nach t *---------------------------------------------------------------------*/ p[21]= t4 + r4 + s4 - 3.; p[22]= 0.; p[23]= 0.; p[24]= t4 - 1.; p[25]= -r4; p[26]= 0.; p[27]= -s4; p[28]= r4; p[29]= s4; p[30]= 4. - r4 - s4 - 2.*t4; /*---------------------------------------------------------------------- * 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 <= 10;k++) { dum+= p[(i-1)*10 + k] * xx[(j-1)*10 + 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(fabs(det) < 0.00000001) /* if(fabs(det) < 0.0000000001) */ 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 <= 180;i++) b[i]= 0.; k3= 0; for(k = 1;k <= 10;k++) { k3+= 3; for(i = 1;i <= 3;i++) { b[ k3-2]= b[ k3-2] + xji[ i] * p[(i-1)*10 + k]; b[30 + k3-1]= b[30 + k3-1] + xji[3 + i] * p[(i-1)*10 + k]; b[60 + k3 ]= b[60 + k3 ] + xji[6 + i] * p[(i-1)*10 + k]; } b[90 + k3-2]= b[30 + k3-1]; b[90 + k3-1]= b[ k3-2]; b[120 + k3-1]= b[60 + k3 ]; b[120 + k3 ]= b[30 + k3-1]; b[150 + k3-2]= b[60 + k3 ]; b[150 + k3 ]= b[ k3-2]; } return(0); }