/********     program axiquad       **********/
/* axisymmetric stress analysis using 4-node */
/*  quadrilateral elements with temperature  */
/*    t.r.chandrupatla and a.d.belegundu     */
/*********************************************/
#include <stdio.h>
#include <math.h>
main()
{
   FILE *fptr1, *fptr2;
   int n,i,j,k,m,i1,i2,i3,ii,jj,m1,nmin,nmax,nrt,nct,it,jt;
   int ip,nr,nc,in;
   char dummy[81], title[81], file1[81], file2[81], file3[81];
   int ne,nn,nq,nm,nd,nl,nen,ndn,ndim,npr,nbw,nmpc,lc,ipl;
   int *noc, *nu, *mat, *mpc;
   float *x, *thick, *pm, *u, *tempr, *s, *f, *beta;
   float xi,eta,th,q[8],c1,c2,sv,rad;
   float c, dj, al, pnu, tld, cnst, reaction, s1, s2, s3, ang, r;
   float b[4][8],d[4][4],db[4][8],se[8][8],str[4],tl[8],xni[4][2];
/*-------------------------------------------------------*/
   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 %d %d\n", &nd, &nl, &nmpc);
   npr = 3;   /* Material properties E, Nu, Alpha */
/* ----- 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));
   tempr = (float *) calloc(ne, sizeof(float));
   pm = (float *) calloc(nm*npr, sizeof(float));
   mpc = (int *) calloc(2*nmpc, sizeof(int));
   beta = (float *) calloc(3*nmpc, sizeof(float));
   printf("\n\n    PLOT CHOICE\n");
   printf("  1) no plot data\n");
   printf("  2) create data file for von mises stress\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 for plot data < dr:fn.ext >:\n");
      gets(file3);
      }
/* ----- total dof is  nq ----- */
     nq = ndn * nn;
/* ===============  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, temp-change ----- */
   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", &k);
       mat[n-1] = k;
       fscanf(fptr1,"%f\n",&c);
       tempr[n-1] = c;
   }
/* ----- displacement bc  ----- */
   fgets(dummy,80,fptr1);
   for (i = 0; i < nd; i++) {
      fscanf(fptr1, "%d %f\n", &k, &c);
      nu[i] = k;
      u[i] = c;
   }
/* ----- component loads ----- */
   fgets(dummy,80,fptr1);
   for (i = 0; i < nl; i++) {
      fscanf(fptr1, "%d %f\n", &k, &c);
      f[k-1] = c;
   }
/* ----- material properties ----- */
   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;
      }
   }
/* ----- multipoint constraints ----- */
   if (nmpc > 0) 
      { fgets(dummy,80,fptr1);
	for(j=0;j<nmpc;j++){
	   fscanf(fptr1,"%f",&c);
	   beta[3*j]=c;
	   fscanf(fptr1,"%d",&k);
	   mpc[2*j]=k;
           fscanf(fptr1,"%f",&c);
	   beta[3*j+1]=c;
           fscanf(fptr1,"%d",&k);
           mpc[2*j+1]=k;
           fscanf(fptr1,"%f",&c);
	   beta[3*j+2]=c;
	   }
	}
   fclose (fptr1);
/* ----- bandwidth nbw from connectivity noc() and mpc ----- */
   nbw = 0;
   for (i = 0; i < ne; i++) {
        nmin = noc[nen*i];
        nmax = nmin;
        for (j = 1; 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;
   }    
   for (i = 0; i < nmpc; i++) {
        n = abs(mpc[2*i] - mpc[2*i+1]) + 1;
        if (nbw < n)
           nbw = n;
        }
     printf ("the bandwidth is %d\n", nbw);
/* ----- allocate memory for stiffness ----- */
   s = (float *) calloc(nq*nbw, sizeof(float));
/* ----- global stiffness matrix -----*/
    /* ----- corner nodes and integrationpoints ----- */
    integ(xni);
    for (n = 0; n < ne; n++) {
	printf("forming stiffness matrix of element %d\n", n+1);
	dmatrix(n,pm,mat,npr,&al,d);
	/* --- element stiffness --- */
	elstif(n,se,tl,xni,d,tempr,x,al,noc);
	printf (".... placing in global locations\n");
	for (ii = 0; ii < nen; ii++) {
	   nrt = ndn * (noc[nen*n + ii] - 1);
	   for (it = 0; it < ndn; it++) {
	      nr = nrt + it;
	      i = ndn * ii + it;
	      for (jj = 0; jj < nen; jj++) {
		 nct = ndn * (noc[nen*n+jj] - 1);
		 for (jt = 0; jt < ndn; jt++) {
		    j = ndn * jj + jt;
		    nc = nct + jt - nr;
		    if (nc >= 0)
		       s[nbw*nr+nc] = s[nbw*nr+nc] + se[i][j];
		    }
		 }
	      f[nr] = f[nr] + tl[i];
	      }
	   }
     }
/* ----- decide penalty parameter cnst ----- */
     cnst = 0.;
     for (i = 0; i < nq; i++) {
	 if (cnst < s[i*nbw])
	    cnst = s[i*nbw];
	 }
     cnst = cnst * 10000.;
/* ----- modify for displacement boundary conditions ----- */
   for (i = 0; i < nd; i++) {
      k = nu[i];
      s[(k-1)*nbw] = s[(k-1)*nbw] + cnst;
      f[k-1] = f[k-1] + cnst * u[i];
   }
/* ----- modify for multipoint constraints ----- */
   for (i = 0; i < nmpc; i++){
       i1 = mpc[2*i]-1;
       i2 = mpc[2*i+1]-1;
       s[i1*nbw] = s[i1*nbw] + cnst*beta[3*i]*beta[3*i];
       s[i2*nbw] = s[i2*nbw] + cnst*beta[3*i+1]*beta[3*i+1];
       n=i1;
       if (n > i2)
       n = i2;
       m = abs(i2-i1);
       s[n*nbw+m] = s[n*nbw+m]+cnst*beta[3*i]*beta[3*i+1];
       f[i1] = f[i1] + cnst*beta[3*i]*beta[3*i+2];
       f[i2] = f[i2] + cnst*beta[3*i+1]*beta[3*i+2];
       }
/* ----- solution of equations using band solver ----- */
       bansol(s,f,nq,nbw);
/* ----- printing displacements ----- */
   fptr1 = fopen(file2, "w");
   printf("\n%s\n", title);
   fprintf(fptr1, "\n%s\n", title);
   fprintf(fptr1, "bandwidth = %d\n",nbw);
     fprintf(fptr1, "node#     r-displ      z-displ\n");
     printf ("node#     r-displ      z-displ\n");
     for (i = 0; i < nn; i++) {
	 printf(" %4d  %11.4e  %11.4e\n",i+1,f[2*i],f[2*i+1]);
	 fprintf(fptr1," %4d  %11.4e  %11.4e\n",i+1,f[2*i],f[2*i+1]);
	 }
/* ----- reaction calculation ----- */
   printf("node#    reaction\n");
   fprintf(fptr1, "node#     reaction\n");
   for (i = 0; i < nd; i++) {
      k = nu[i];
      reaction = cnst * (u[i] - f[k-1]);
      printf(" %4d  %11.4e\n", k, reaction);
      fprintf(fptr1, " %4d  %11.4e\n", k, reaction);
      }
     if (ipl > 1){
        fptr2 = fopen(file3, "w");
	  fprintf(fptr2, "von Mises stress (element) for data in file  %s\n", file1);
        }
/* -----  stress calculations ----- */
     fprintf (fptr1, "elem#    von mises stresses at 4 integration points\n");
   /* ----- stresses at integration points ----- */

     for (n = 0; n < ne; n++) {
        fprintf (fptr1, "%4d ", n+1);
        for (ip = 0; ip < 4; ip++) {
	   xi = xni[ip][0];
	   eta = xni[ip][1];
	   dmatrix(n,pm,mat,npr,&al,d);
	   dbmat(n,x,noc,d,b,db,&dj,&rad,xi,eta);
	   /* --- stress evaluation --- */
	   for (i = 0; i < nen; i++) {
	      in = ndn * (noc[nen*n+i] - 1);
	      ii = ndn * i;
	      for (j = 0; j < ndn; j++) {
		 q[ii + j] = f[in + j];
		 }
	      }
	   c1 = al * tempr[n];
           for (i = 0; i < 4; i++) {
              c = 0;
              for (k = 0; k < 8; k++) {
                  c = c + db[i][k] * q[k];
                  }
                 str[i] = c - c1 * (d[i][0] + d[i][1] + d[i][3]);
              }
        /* --- von mises stress at integration point --- */
	   c1 = str[0] + str[1] + str[3];
           c2 = str[0] * str[1] + str[1] * str[3] + str[3] * str[0];
           c2 = c2 - str[2] * str[2];
           sv = sqrt((double)(c1 * c1 - 3 * c2));