torsion.c

工程中有限元程序,采用C语言编制,包括所有经典的有限元问题!

/***************************************/
/*         program  torsion2           */
/*   torsion with 3-noded triangles    */
/* t.r.chandrupatla and a.d.belegundu  */
/***************************************/
#include <stdio.h>
#include <math.h>
main()
{
   FILE *fptr1, *fptr2, *fptr3;
   int i,j,k,m,n,ii,jj,nbw,n1,n2,nmax,nmin,i1,i2,i3,ii1,ii2;
   char dummy[121], title[81], file1[81], file2[81], file3[81];
   int nn,ne,nm,ndim,nen,ndn,nd,nl,npr,nmpc,*noc,*mat,*nu,ipl;
   float *x,*pm,*f,*u,*s,bt[2][3],detj,torque,sfac,smod;
   float alpha,tauyz,tauxz;
   float x32,x13,x21,y23,y31,y12,area,sum,cnst,c;
/*-------------------------------------------------------*/
   printf("\n");
   puts("Input file name < dr:fn.ext >: ");
   gets(file1);
   puts("Output file name < dr:fn.ext >: ");
   gets(file2);
   printf("\n");
   fptr1 = fopen(file1, "r");
   fgets(dummy,80,fptr1);
   fgets(title,80,fptr1);
   fgets(dummy,80,fptr1);
   fscanf(fptr1,"%d %d %d %d %d %d\n", &nn, &ne, &nm, &ndim, &nen, &ndn);
   fgets(dummy, 80, fptr1);
   fscanf(fptr1,"%d %d %d \n", &nd, &nl, &nmpc);
   npr = 1;
   nmpc = 0;
   nm = 1;
   /* ---  nd = no. of specified stress function values(displacements) --- */
   /* ---  nl = 0 for stress function formulation of torsion --- */
   /* note!! npr = 1 (shear modulus) and nmpc = 0 for this program */
   /* element characteristic is not used */
   /* number of materials = 1 for this program */
/* -----------    memory allocation    ------------ */
   x = (float *) calloc(nn*ndim, sizeof(float));
   noc = (int *) calloc(ne*nen, sizeof(int));
   u = (float *) calloc(nd, sizeof(float));
   nu = (int *) calloc(nd, sizeof(int));
   mat = (int *) calloc(ne,sizeof(int));
   f = (float *) calloc(nn*ndn, sizeof(float));
   pm = (float *) calloc(nm*npr, sizeof(float));
/* ------------------------------------------------ */ 
   printf("\n\n    PLOT CHOICE\n");
   printf("  1) no plot data\n");
   printf("  2) create data file containing stress function values\n");
   printf("     choose <1 or 2> ");
   scanf("%d%*c", &ipl);
   if(ipl < 1 || ipl > 2)
     ipl = 1;         /* --- default is no data ---*/
   if(ipl > 1){
      printf("Output file name < dr:fn.ext >:\n");
      gets(file3);
      }
/* ===============  read data  ==================== */
/* ----- coordinates ----- */
     fgets(dummy,80,fptr1);
     for (i = 0; i < nn; i++){
        fscanf(fptr1, "%d", &n);
        for (j = 0; j < ndim; j++){
		fscanf(fptr1, "%f\n", &c);
		x[ndim*(n-1)+j] = c;
	    }
	 }
/* ----- connectivity, material# ----- */
   fgets(dummy,80,fptr1);
   for (i = 0; i < ne; i++) {
       fscanf(fptr1,"%d", &n);
       for (j = 0; j < nen; j++) {
           fscanf(fptr1,"%d", &k);
           noc[(n-1)*nen+j]=k;
       }
       fscanf(fptr1,"%d\n", &k);
       mat[n-1] = k;
   }
/* ----- boundary conditions (stress function values) ----- */
   fgets(dummy,80,fptr1);
   printf("%s\n",dummy);
   for (i = 0; i < nd; i++) {
      fscanf(fptr1, "%d %f\n", &k, &c);
      nu[i] = k;
      u[i] = c;
   }
   fgets(dummy,80,fptr1);
/* ----- shear modulus of material ----- */
   fgets(dummy,80,fptr1);
   for (i = 0; i < nm; i++){
      fscanf(fptr1, "%d", &k);
      for (j = 0; j < npr; j++) {
         fscanf(fptr1, "%f\n", &c);
	 pm[(k-1)*npr+j] = c;
      }
   }
/* ----- bandwidth nbw from connectivity noc() ----- */
   nbw = 0;
   for (i = 0; i < ne; i++) {
        nmin = noc[nen*i];
        nmax = nmin;
	for (j = 0; j < 3;j++) {
	    n = noc[nen*i+j];
	    if (nmin > n)
	       nmin = n;
	    if (nmax < n)
	       nmax = n;
	    }
	n = ndn * (nmax - nmin + 1);
	if (nbw < n)
           nbw = n;
   }    
   printf ("the bandwidth is %d\n", nbw);
/* ----- allocate memory for stiffness ----- */
   s = (float *) calloc(nn*nbw, sizeof(float));
     /* --- stiffness matrix --- */
     for (i = 0; i < ne; i++) {
         i1 = noc[nen*i]-1;
	     i2 = noc[nen*i+1]-1;
	     i3 = noc[nen*i+2]-1;
         x32 = x[2*i3] - x[2*i2];
	     x13 = x[2*i1] - x[2*i3];
	     x21 = x[2*i2] - x[2*i1];
         y23 = x[2*i2+1] - x[2*i3+1];
	     y31 = x[2*i3+1] - x[2*i1+1];
         y12 = x[2*i1+1] - x[2*i2+1];
	     detj = x13 * y23 - x32 * y31;
	     area = .5 * fabs(detj);
      /* --- element nodal forces --- */
         c = 2 * area / 3;
         f[i1] = f[i1] + c;
	     f[i2] = f[i2] + c;
	     f[i3] = f[i3] + c;
	 /* --- element stiffness and placing in global loc. --- */
	 bt[0][0] = y23 / detj;
	 bt[0][1] = y31 / detj;
	 bt[0][2] = y12 / detj;
	 bt[1][0] = x32 / detj;
	 bt[1][1] = x13 / detj;
	 bt[1][2] = x21 / detj;
	 for (ii = 0; ii < 3; ii++) {
	     ii1 = noc[nen*i+ii]-1;
	     for (jj = 0; jj < 3; jj++) {
		 ii2 = noc[nen*i+jj]-1;
		 if (ii1 <= ii2) {
		    sum = 0;
		    for (j = 0; j < 2; j++) {
		       sum = sum + bt[j][ii] * bt[j][jj];
			   }
		    n = nbw*ii1+ii2-ii1;
		    s[n] = s[n] + sum * area;
		   }

		}
	     }
	}
       /* --- modify for boundary conditions --- */
       cnst = s[0];
       for (i = 1; i < nn; i++) {
          if (cnst < s[nbw*i])
             cnst = s[nbw*i];
	      }
       cnst = cnst * 1000000;
       for (i = 0; i < nd; i++) {
           n = nu[i]-1;
	   s[nbw*n] = s[nbw*n] + cnst;
           f[n] = f[n] + cnst * u[i];
	       }
/* --- equation solving --- */
     bansol(s,f,nn,nbw);
     fptr2 = fopen(file2, "w");
     fprintf(fptr2, "%s\n", title);
     printf("%s\n", title);
     fprintf(fptr2, "node no.  stress function value\n");
     printf("node no.  stress function value\n");
     for (i = 0; i < nn; i++) {
       fprintf(fptr2, "%4d      %11.4e\n", i+1, f[i]);
       printf("%4d      %11.4e\n", i+1, f[i]);
     }
     if (ipl == 2 ) {
       fptr3 = fopen(file3, "w");
       fprintf( fptr3,  "nodal stress function values\n");
       for (i = 0; i < nn; i++) {
	      fprintf(fptr3, " %11.4e\n", f[i]);
	      }
	   fclose(fptr3);
       printf("\n");
       printf ("nodal stress function value data in file  %s \n", file3);
       printf ("run contourA or contourB to plot costant stress fn contours\n");
       }
     sum = 0;
     for (i = 0; i < ne; i++) {
         i1 = noc[nen*i]-1;
	 i2 = noc[nen*i+1]-1;
	 i3 = noc[nen*i+2]-1;
	 x32 = x[2*i3] - x[2*i2];
	 x13 = x[2*i1] - x[2*i3];
	 x21 = x[2*i2] - x[2*i1];
	 y23 = x[2*i2+1] - x[2*i3+1];
	 y31 = x[2*i3+1] - x[2*i1+1];
	 y12 = x[2*i1+1] - x[2*i2+1];
	 detj = x13 * y23 - x32 * y31;
     sum = sum + fabs(detj) * (f[i1] +f[i2] + f[i3])/3;
     }
     fgets(dummy,80,fptr1);
     fscanf(fptr1, "%f\n", &torque);
     /* symmetry factor (eg. if 1/4 symmetry, then = 4.0) */
     fgets(dummy,80,fptr1);
     fscanf(fptr1, "%f\n", &sfac);
     fclose(fptr1);
     smod = pm[0];
     alpha = torque / smod / sum / sfac;
     fprintf(fptr2, "twist per unit length = %f\n", alpha);
     printf("twist per unit length = %f\n", alpha);
     fprintf(fptr2, "shearing stresses tauyz, tauxz in each element\n");
     fprintf(fptr2, "elem#   tauyz         tauxz\n");
     printf("elem#   tauyz         tauxz\n");
     for (i = 0; i < ne; i++) {
         i1 = noc[nen*i]-1;
	     i2 = noc[nen*i+1]-1;
	     i3 = noc[nen*i+2]-1;
         x32 = x[2*i3] - x[2*i2];
	     x13 = x[2*i1] - x[2*i3];
	     x21 = x[2*i2] - x[2*i1];
         y23 = x[2*i2+1] - x[2*i3+1];
	     y31 = x[2*i3+1] - x[2*i1+1];
         y12 = x[2*i1+1] - x[2*i2+1];
	     detj = x13 * y23 - x32 * y31;
	 bt[0][0] = y23 / detj;
	 bt[0][1] = y31 / detj;
	 bt[0][2] = y12 / detj;
	 bt[1][0] = x32 / detj;
	 bt[1][1] = x13 / detj;
	 bt[1][2] = x21 / detj;
	 tauyz = -(bt[0][0] * f[i1] + bt[0][1] * f[i2] + bt[0][2] * f[i3]);
     tauxz = bt[1][0] * f[i1] + bt[1][1] * f[i2] + bt[1][2] * f[i3];
     tauyz = tauyz * smod * alpha;
     tauxz = tauxz * smod * alpha;
     fprintf(fptr2,"%4d  %11.4e  %11.4e\n", i+1, tauyz, tauxz);
     printf("%4d  %11.4e  %11.4e\n", i+1, tauyz, tauxz);
     }
     fclose(fptr2);
  return(0);
}
/* ----- band solver ----- */
bansol(s,f,nq,nbw)
  int nq, nbw;
  float *s, *f;
{
 int n1,k,nk,i,i1,j,j1,kk;
  float c1;
  /* ----- band solver ----- */
  n1 = nq - 1;
  /* --- forward elimination --- */
  for (k = 1; k <= n1; k++) {
     nk = nq - k + 1;
     if (nk > nbw)
	nk = nbw;
     for (i = 2; i <= nk; i++) {
       c1 = s[nbw*(k-1)+i-1] / s[nbw*(k-1)];
       i1 = k + i - 1;
       for (j = i; j <= nk; j++) {
	j1 = j - i + 1;
	s[nbw*(i1-1)+j1-1] = s[nbw*(i1-1)+j1-1] - c1 * s[nbw*(k-1)+j-1];
	}
       f[i1-1] = f[i1-1] - c1 * f[k-1];
       }
     }
  /* --- back-substitution --- */
  f[nq-1] = f[nq-1] / s[nbw*(nq-1)];
  for (kk = 1; kk <= n1;kk++) {
     k = nq - kk;
     c1 = 1 / s[nbw*(k-1)];
     f[k-1] = c1 * f[k-1];
     nk = nq - k + 1;
     if (nk > nbw)
       nk = nbw;
       for (j = 2; j <= nk; j++) {
	 f[k-1] = f[k-1] - c1 * s[nbw*(k-1)+j-1] * f[k + j - 2];
	}
     }
    return(0);
}