/*********************************************************************** * * ***** *** *** * * * * * * * * *** *** * * * * * * * ***** *** *** * * 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: cshe88 - Elementsteifigkeitsroutine * cb88 - 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 cb88(FR_DOUBLE *det,FR_DOUBLE *r,FR_DOUBLE *s, FR_DOUBLE *xbar,FR_INT4 *ktyp); /*********************************************************************** * hier beginnt Function cshe88 ***********************************************************************/ int cshe88(void) { extern FR_DOUBLEAY se; extern FR_DOUBLE xk[],yk[]; extern FR_DOUBLE b[],xx[],d[]; extern FR_DOUBLE emode,rnuee,qparae; extern FR_INT4 ktyp,intore; FR_DOUBLE db[5]; FR_DOUBLE pi2= 6.283185307; FR_DOUBLE facesz,facasz,r,s,det,xbar,wt,stiff; FR_INT4 ne= 24,i,ist,lx,ly,j,k,l; int iret; /*---------------------------------------------------------------------- * Gauss-Legendre Stuetzstellen *---------------------------------------------------------------------*/ static FR_DOUBLE xg[17]= { 0., 0., -.5773502691896, -.7745966692415, -.8611363115941, 0., +.5773502691896, 0., -.3399810435849, 0., 0., +.7745966692415, +.3399810435849, 0., 0., 0., +.8611363115941 }; /*---------------------------------------------------------------------- * Gauss-Legendre Integrationsgewichte *---------------------------------------------------------------------*/ static FR_DOUBLE wgt[17]= { 0., 2., 1., +.5555555555556, +.3478548451375, 0., 1., +.8888888888889, +.6521451548625, 0., 0., +.5555555555556, +.6521451548625, 0., 0., 0., +.3478548451375 }; /*---------------------------------------------------------------------- * xk und yk umspeichern *---------------------------------------------------------------------*/ for(i = 1;i <= 12;i++) { xx[i ] = xk[i]; xx[12+i]= yk[i]; } /*---------------------------------------------------------------------- * Materialkonstanten *---------------------------------------------------------------------*/ facesz= emode/(1. - rnuee*rnuee); facasz= emode*(1. - rnuee)/( (1. + rnuee)*(1. - 2*rnuee) ); /*---------------------------------------------------------------------- * Elastizitaetsmatrix aufstellen: ebener Spannungszustand *---------------------------------------------------------------------*/ if (ktyp == 2) { d[1] = facesz; d[5] = facesz * rnuee; d[9] = 0.; d[2] = d[5]; d[6] = facesz; d[10]= 0.; d[3] = 0.; d[7] = 0.; d[11]= facesz * .5 * (1. - rnuee); } /*---------------------------------------------------------------------- * Elastizitaetsmatrix aufstellen: ebener Verzerrungszustand *---------------------------------------------------------------------*/ if (ktyp == 1) { d[1] = facasz; d[5] = facasz * rnuee / (1. - rnuee); d[9] = 0.; d[2] = d[5]; d[6] = facasz; d[10]= 0.; d[3] = 0.; d[7] = 0.; d[11]= emode / (2.*(1. + rnuee)); qparae= 1.; } /*---------------------------------------------------------------------- * Elastizitaetsmatrix aufstellen: axialsymmetrischer Spannungszustand *---------------------------------------------------------------------*/ if (ktyp == 0) { d[1] = facasz; d[5] = facasz * rnuee / (1. - rnuee); d[9] = 0.; d[13]= d[5]; d[2] = d[5]; d[6] = facasz; d[10]= 0.; d[14]= d[5]; d[3] = 0.; d[7] = 0.; d[11]= emode / (2.*(1. + rnuee)); d[15]= 0.; d[4]= d[5]; d[8]= d[5]; d[12]= 0.; d[16]= facasz; } /*---------------------------------------------------------------------- * Elementsteifigkeitsmatrix aufstellen *---------------------------------------------------------------------*/ for(i = 1;i <= 576;i++) se[i]= 0.; ist= 3; if(ktyp == 0) ist= 4; for(lx = 1;lx <= intore;lx++) /* 90 */ { r= xg[(lx-1)*4 + intore]; for(ly = 1;ly <= intore;ly++) /* 80 */ { s= xg[(ly-1)*4 + intore]; /*====================================================================== * Matrix b der partiellen Ableitungen & Jacobi Determinante holen *=====================================================================*/ iret= cb88(&det,&r,&s,&xbar,&ktyp); if(iret != 0) return(iret); if(ktyp > 0) xbar= qparae; if(ktyp == 0) xbar= xbar*pi2; wt= wgt[(lx-1)*4 + intore] * wgt[(ly-1)*4 + intore] * xbar * det; for(j = 1;j <= 24;j++) /* 70 */ { for(k = 1;k <= ist;k++) /* 40 */ { db[k]= 0.; for(l = 1;l <= ist;l++) /* 30 */ { db[k]= db[k] + d[(k-1)*4 + l] * b[(l-1)*24 + j]; } /* e 30 */ } /* e 40 */ for(i = j;i <= 24;i++) /* 60 */ { stiff= 0.; for(l = 1;l <= ist;l++) /* 50 */ { stiff+= b[(l-1)*24 + i] * db[l]; } /* e 50 */ se[i+ne*(j-1)]= se[i+ne*(j-1)] + stiff * wt; } /* e 60 */ } /* e 70 */ } /* e 80 */ } /* e 90 */ for(j = 1;j <= 24;j++) { /* 110 */ for(i = j;i <= 24;i++) /* 100 */ { se[j+ne*(i-1)]= se[i+ne*(j-1)]; } /* e 100 */ } /* e 110 */ return(0); } /*********************************************************************** * hier beginnt Function cb88 ***********************************************************************/ int cb88(FR_DOUBLE *det,FR_DOUBLE *r,FR_DOUBLE *s, FR_DOUBLE *xbar,FR_INT4 *ktyp) { /*--------------------------------------------------------------------- * xx geht rein, unveraendert (ex) * b geht raus, neu (ex) * det geht raus, neu * r,s gehen rein, unveraendert * xbar geht raus, neu * ktyp geht rein, unveraendert *--------------------------------------------------------------------*/ extern FR_DOUBLE h[]; extern FR_DOUBLE b[],xx[],p[]; FR_DOUBLE xj[5], xji[5]; /* ist 2x2 +1 */ FR_DOUBLE epr,emr,eps,ems,emrr,emss,rr27; FR_DOUBLE ss27,rr9,ss9,r18,s18,r2,s2,r3,s3,dum; FR_INT4 i,j,k,k2; /*---------------------------------------------------------------------- * Klammern der Formfunktionen belegen *---------------------------------------------------------------------*/ epr= 1. + (*r) ; emr= 1. - (*r) ; eps= 1. + (*s) ; ems= 1. - (*s) ; emrr= 1. - (*r) * (*r) ; emss= 1. - (*s) * (*s) ; rr27= 27. * (*r) * (*r) ; ss27= 27. * (*s) * (*s) ; rr9 = 9. * (*r) * (*r) ; ss9 = 9. * (*s) * (*s) ; r18 = 18. * (*r) ; s18 = 18. * (*s) ; r2 = 2. * (*r) ; s2 = 2. * (*s) ; r3 = 3. * (*r) ; s3 = 3. * (*s) ; /*---------------------------------------------------------------------- * Formfunktionen *---------------------------------------------------------------------*/ h[1 ]= .03125 * epr * eps * ( rr9 + ss9 - 10.); h[2 ]= .03125 * emr * eps * ( rr9 + ss9 - 10.); h[3 ]= .03125 * emr * ems * ( rr9 + ss9 - 10.); h[4 ]= .03125 * epr * ems * ( rr9 + ss9 - 10.); h[5 ]= .28125 * eps * emrr* ( 1. + r3); h[6 ]= .28125 * eps * emrr* ( 1. - r3); h[7 ]= .28125 * emr * emss* ( 1. + s3); h[8 ]= .28125 * emr * emss* ( 1. - s3); h[9 ]= .28125 * ems * emrr* ( 1. - r3); h[10]= .28125 * ems * emrr* ( 1. + r3); h[11]= .28125 * epr * emss* ( 1. - s3); h[12]= .28125 * epr * emss* ( 1. + s3); /*---------------------------------------------------------------------- * Partielle Ableitung der Formfunktionen nach r *---------------------------------------------------------------------*/ p[1 ]= .03125 * eps * ( rr27 + ss9 - 10. + r18); p[2 ]= .03125 * eps * (-rr27 - ss9 + 10. + r18); p[3 ]= .03125 * ems * (-rr27 - ss9 + 10. + r18); p[4 ]= .03125 * ems * ( rr27 + ss9 - 10. + r18); p[5 ]= .28125 * eps * (-rr9 - r2 + 3.); p[6 ]= .28125 * eps * ( rr9 - r2 - 3.); p[7 ]= -.28125 * emss *( 1. + s3); p[8 ]= -.28125 * emss *( 1. - s3); p[9 ]= .28125 * ems * ( rr9 - r2 - 3.); p[10]= .28125 * ems * (-rr9 - r2 + 3.); p[11]= .28125 * emss* ( 1. - s3); p[12]= .28125 * emss* ( 1. + s3); /*---------------------------------------------------------------------- * Partielle Ableitung der Formfunktionen nach s *---------------------------------------------------------------------*/ p[13]= .03125 * epr * ( ss27 + rr9 - 10. + s18); p[14]= .03125 * emr * ( ss27 + rr9 - 10. + s18); p[15]= .03125 * emr * (-ss27 - rr9 + 10. + s18); p[16]= .03125 * epr * (-ss27 - rr9 + 10. + s18); p[17]= .28125 * emrr* ( 1. + r3); p[18]= .28125 * emrr* ( 1. - r3); p[19]= .28125 * emr * (-ss9 - s2 + 3.); p[20]= .28125 * emr * ( ss9 - s2 - 3.); p[21]= -.28125 * emrr* ( 1. - r3); p[22]= -.28125 * emrr* ( 1. + r3); p[23]= .28125 * epr * ( ss9 - s2 - 3.); p[24]= .28125 * epr * (-ss9 - s2 + 3.); /*---------------------------------------------------------------------- * 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 <= 12;k++) { dum+= p[(i-1)*12 + k] * xx[(j-1)*12 + 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 b *---------------------------------------------------------------------*/ for(i = 1;i <= 96;i++) b[i]= 0.; k2= 0; for(k = 1;k <= 12;k++) { k2+= 2; b[k2-1]= 0.; b[k2 ]= 0.; b[24 + k2-1]= 0.; b[24 + k2 ]= 0.; for(i = 1;i <= 2;i++) { b[ k2-1]= b[ k2-1] + xji[ i] * p[(i-1)*12 + k]; b[24 + k2 ]= b[24 + k2 ] + xji[2 +i] * p[(i-1)*12 + k]; } b[48 + k2 ]= b[ k2-1]; b[48 + k2-1]= b[24 +k2 ]; } if((*ktyp) > 0) return(0); /*---------------------------------------------------------------------- * im Falle des axialsymmetrischen Toruselementes * die folgende Normalspannungskomponente einfuegen *---------------------------------------------------------------------*/ /*====================================================================== * Radius am Punkt (r,s) berechnen *=====================================================================*/ (*xbar)= 0.; for(k = 1;k <= 12;k++) (*xbar)= (*xbar) + h[k] * xx[k]; if((*xbar) <= 0.00000001) { /*====================================================================== * Radius ist null *=====================================================================*/ for(k = 1;k <= 24;k++) b[72 + k]= b[k]; return(0); } else { /*====================================================================== * Radius ist nicht null *=====================================================================*/ dum=1./(*xbar); k2= 0; for(k = 1;k <= 12;k++) { k2+= 2; b[72 + k2 ]= 0.; b[72 + k2-1]= h[k] * dum; } } /**********************************************************************/ return(0); }