normal contact stress code with quad 4 node element

8/14/2019 normal contact stress code with quad 4 node element

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#include

#include

#include

#define ABS(x) (x < 0 ? -(x) : (x))

#define EPS 0.00001

/* Begin-Function definitions */

integ(float xni[][2]);

dmat(int,float*,int*,int,float*,float*,int,float d[][3]);

dbmat(int,float*,int*,float*,float*,float d[][3],float b[][8],float db[][8],float*,float,float);

elemstif(int,int,float se[][8],float tl[8],float xni[][2],float d[][3],float*,float*,float*,float,float,int*);

dbmat2(int,float*,int*,float*,float*,float d[][3],float b[][8],float db[][8],float*,float,float);

elemstif2(int,int,float se[][8],float tl[8],float xni[][2],float d[][3],float*,float*,float*,float,float,int*);

GSolve(float **,int ,float *);

/* End-Function definitions */

/* Begin-Main Code */main()

{// Begin-Declaring variables in main code

FILE *fptr; //pointer to a file

int n,i,j,k,ii,jj; //dummy integers for storing values temporarily and for using in loops

int nmin,nmax,nrt1,nct1,nrt,nct,it,jt;

int ip,nr1,nc1,nr,nc,in;

char dummy[81], title[81], file1[81], file3[81],file4[81],file5[81];

int ne,nn,nq,nm,nd,nl,nen,ndn,ndim,npr,nbw,opt,nbw2,nq1,nq2,nbw3,nbw4;// Numbers of---> ne: elements; nn: nodes; nq: total d.o.f; nm: material

s// nd: disp. BCs; nl: load BCs; nen:el. nodal conn.=4; ndn: dof per node

=2// ndim: 2-dim; npr: mat. properties=3 (E,nu,alpha); nbw, nbw3: band wid

th of specimen// nbw2, nbw4: band width for punch; opt: option for plane stress/strain// nq1,nq2: dof for specimen and punch

int ne1=857,ne2=510,nn1=896,nn2=544;// ne1: no. of el. in spec.; ne2: no. of el. in punch


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printf("output file name:");gets(file5);printf("\n");

printf(" 1 plane stress analysis\n");

printf(" 2 plane strain analysis\n");

printf(" enter 1 or 2 ");

scanf("%d", &opt);

if (opt < 1 opt > 2)

opt = 2;

// Begin-reading data from input filefptr = fopen(file1, "r");

fgets(dummy,80,fptr); // stores first line in a dummy variable

fgets(title,80,fptr); // stores second line in a dummy variable

fgets(dummy,80,fptr); // stores third line in a dummy variable

fscanf(fptr,"%d %d %d %d %d %d\n", &nn, &ne, &nm, &ndim, &nen, &ndn);// scanning values from fourth line

fgets(dummy, 80, fptr); // stores fifth line in a dummy variable

fscanf(fptr,"%d %d\n", &nd, &nl); // scanning values from 6th line

npr = 3; /* Material properties E, Nu, Alpha */

/* ----- begin-memory allocation ----- */

x = (float *) calloc(nn*ndim, sizeof(float));

g =(float *)calloc(nn*ndim, sizeof(float));xx1 = (float *)calloc(nn1*ndim, sizeof(float));

xx2 = (float *)calloc(nn2*ndim, sizeof(float));

noc = (int *) calloc(ne*nen, sizeof(int));

noc1 = (int *) calloc(ne1*nen, sizeof(int));

noc2 = (int *) calloc(ne2*nen, sizeof(int));

u = (float *) calloc(nd, sizeof(float));

nu = (int *) calloc(nd, sizeof(int));

mat = (int *) calloc(ne,sizeof(int));

thick = (float *) calloc(ne, sizeof(float));

f = (float *) calloc(nn*ndn, sizeof(float));


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tempr = (float *) calloc(ne, sizeof(float));

pm = (float *) calloc(nm*npr, sizeof(float));

mat1=(int *) calloc(ne, sizeof(int));thick1=(float *) calloc(ne, sizeof(float));tempr1=(float *) calloc(ne, sizeof(float));

/* ----- total dof is nq ----- */

nq = ndn * nn;

nq1 = ndn*nn1;

nq2 = ndn*nn2;

x1 = (float *) calloc(nq, sizeof(float));

/* ----- end-memory allocation ----- */

/* =============== read data again ==================== */

/* ----- connectivity, material, thickness, temp-change ----- */

fgets(dummy,80,fptr); // stores eighth line in dummy variableprintf("%s I am at beginning of nodes \n",dummy);

/* begin-loop to read element connectivity data line by line */

for (i = 0; i < ne; i++){

fscanf(fptr,"%d", &n); // Element number stored in n

for (j = 0; j < nen; j++){

fscanf(fptr,"%d", &k); // nen=4 Nodes corresponding to nth element

noc[(n-1)*nen+j]=k; // list of nodes attached to all elements ingroups of 4

}

fscanf(fptr,"%d", &k);mat[n-1] = k; // storing material number

fscanf(fptr,"%f",&c);

thick[n-1] = c; // storing thickness

fscanf(fptr,"%f\n",&c);

tempr[n-1] = c; // storing temperature


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}

/* end-loop to read element connectivity data line by line */

for (i=0; i


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fscanf(fptr, "%d %f\n", &k, &c);

f[k-1] = c; // value of force, c, for the corresponding dof, k, replacingthe initialized zero value

}

/* ----- material properties ----- */

fgets(dummy,80,fptr);

for (i = 0; i < nm; i++){

fscanf(fptr, "%d", &k);

for (j = 0; j < npr; j++){

fscanf(fptr, "%f\n", &c);

pm[(k-1)*npr+j] = c;

}

}

fclose (fptr);

// End-reading data from input file

/* ----- coordinates ----- */

printf("\nenter the step number or increment number\n");scanf("%d",&inc);

//begin-reading node coordinatesif(inc==1){// Reads from old co-ordinates file

fptr=fopen(file3,"r");fgets(dummy,80,fptr); // Header saying node no, x-coord and y-coord

for (i = 0; i < nn; i++)

{

fscanf(fptr, "%d", &n); // Node number

for (j = 0; j < ndim; j++){

fscanf(fptr, "%f\n", &c);

x[ndim*(n-1)+j] = c; // coordinates stored alternately

}


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}

for (i=0;i


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}

printf ("the bandwidth for punch is %d\n", nbw3);

/* ----- allocate memory for banded stiffness array----- */

s1 = (float *) calloc(nq1*nbw, sizeof(float));

s2 = (float *) calloc(nq2*nbw3, sizeof(float));

for (i=0; i< nq1*nbw; i++){

s1[i]=0;}

for (i=0; i< nq2*nbw3; i++)

{ s2[i]=0;}

/* ----- global stiffness matrix, corner nodes and integrationpoints ----- */

integ(xni);

for (n = 0; n < ne1; n++){//begin- n loop going element by element in spec

printf("forming stiffness matrix of specimen %d\n", n+1);

dmat(n,pm,mat,npr,&pnu,&al,opt,d); // Constitutive matrix

/* --- element stiffness --- */

elemstif(n,opt,se,tl,xni,d,thick,tempr,xx1,al,pnu,noc1);printf (".... placing in global locations\n");

for (ii = 0; ii < nen; ii++){//begin - ii loop to go through four nodes corresonding to each element

nrt1 = ndn * (noc1[nen*n + ii] - 1);

for (it = 0; it < ndn; it++){//begin - it loop to go through dimensions

nr1 = nrt1 + it; // gives position of Ux and Uy (row number in banded matrix)

i = ndn * ii + it; // goes from 0 to 7, corresponding to local stiffness matrix

for (jj = 0; jj < nen; jj++){// begin - jj loop similar to ii


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nct1 = ndn * (noc1[nen*n+jj] - 1);

for (jt = 0; jt < ndn; jt++){//begin - jt loop similar to it

nc1 = nct1 + jt - nr1; // corresponds to column number in ba

nded matrix

j = ndn * jj + jt; // goes from 0 to 7, corresponding to local stiffness matrix

if (nc1 >= 0)

s1[nbw*nr1+nc1] = s1[nbw*nr1+nc1] + se[i][j];}//end - jt loop

}//end - jj loop}//end - it loop

}//end - ii loop

}//end- n loop going element by element in spec

for (n = 0;n < ne2;n++){

printf("forming stiffness matrix of punch %d\n", n+1);

dmat(n,pm,mat1,npr,&pnu,&al,opt,d);

/* --- element stiffness --- */

elemstif2(n,opt,se,tl,xni,d,thick1,tempr1,xx2,al,pnu,noc2);printf (".... placing in global locations\n");

for (ii = 0; ii < nen; ii++){

nrt = ndn*(noc2[nen*n + ii] - nn1-1);

for (it = 0; it < ndn; it++){

nr = nrt + it;

i = ndn * ii + it;

for (jj = 0; jj < nen; jj++){

nct = ndn * (noc2[nen*n+jj] - nn1-1);

for (jt = 0; jt < ndn; jt++)

{

j = ndn * jj + jt;


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nc = nct + jt - nr;if (nc >= 0)

s2[nbw3*nr+nc] = s2[nbw3*nr+nc] + se[i][j];

}

}

}

}}

printf("\nNOW ASSEMBLING,CACULATING AND THEN DISPLAYING THE RESULTS,PLEASE BE PATIENT\n");

/*allocating memory for SPECIMEN stiffness matrix */

k1 = (float **)malloc((nq1)*sizeof(float *));

for (i=0;i


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{

nbw2--; // Last few rows have decreasing band width !!

}

for(j=i;j


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nbw4=nbw3;

for(i=0;i=nq2-nbw3+1)

{

nbw4--;

}

for(j=i;j


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kk[i] = (float *)malloc(nq*sizeof(float));

for(i=0;i


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kk[i][j]=kk[i][j]+k2[i-1792][j-1792];

}

}

/* ----- decide penalty parameter cnst ----- */

cnst = 0.;

for (i = 0; i < nq; i++) {

if (cnst < kk[i][i])

cnst = kk[i][i];

}

cnst = cnst * 10000.;

/* ----- modify for displacement boundary conditions ----- */

for (i = 0; i < nd; i++) {

k = nu[i];kk[k-1][k-1] = kk[k-1][k-1]+ cnst;

f[k-1] = f[k-1] + cnst * u[i];

}

/*---------------------------------------------------------------------------------------*/

a = (float **)malloc((nq+1)*sizeof(float *));

for (i=0;i


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{

a[nq][i]=f[i];

}

GSolve(a,nq,x1);

/* ----- solution of equations using gauss solver ----- ----------------------------------------------------------------*/

/* bandsolv(s,f,nq,nbw); */

/* ----- printing displacements ----- */

fptr = fopen(file5, "w");//opening of a file in which disp will be printed

printf("\n%s\n", title);

fprintf(fptr, "\n%s\n", title);

fprintf(fptr,"bandwidth for spcimen is %d\n",nbw);fprintf(fptr,"bandwidth for punch is %d\n",nbw3);

if (opt == 1)

fprintf(fptr, "plane stress analysis\n");

if (opt == 2)

fprintf(fptr, "plane strain analysis\n");

fprintf(fptr, "nodulal x-displ y-displ\n");

printf ("node x-displ y-displ\n");

for (i = 0; i < nn; i++) {

printf(" %4d %11.4e %11.4e\n",i+1,x1[2*i],x1[2*i+1]);

fprintf(fptr," %4d %11.4e %11.4e\n",i+1,x1[2*i],x1[2*i+1]);

}

fclose(fptr);//closing of this file/*NOW FINDING OVERALL DISP OF EACH NODE*//*allocating memory for new displacements*/np=(float *) calloc(nn*ndn, sizeof(float));if(inc==1){

printf("\n now writing final coordinates for increment1 in user choice file 4

");for(i=0;i


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g[2*i]=x[2*i]+x1[2*i]; //the final x-coordinate after deformation with increment1

g[2*i+1]=x[2*i+1]+x1[2*i+1];//the final y-coordinat after deformation with increment1

}fptr=fopen(file4,"w");

for(i=0;i


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fprintf(fptr,"%.15f\n",reldisp[i]);}fclose(fptr);}

printf("\nthanks for ur patience..for complete results,check the output filesin this folder");return(0);

}

integ(xni)

float xni[][2];

{

float c;

/* ----- integration points xni() ----- */

c = 0.57735026919;

xni[0][0] = -c;

xni[0][1] = -c;

xni[1][0] = c;

xni[1][1] = -c;

xni[2][0] = c;

xni[2][1] = c;

xni[3][0] = -c;

xni[3][1] = c;

return(0);

}

dmat(n,pm,mat,npr,pnu1,al1,opt,d)

int opt,n,npr,*mat;

float *pm,*pnu1,*al1,d[][3];

{

int m;

float e,c,c1,c2,c3,pnu,al;

/* ----- d() matrix ----- */

/* --- material properties --- */


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m = mat[n]-1;

e = pm[npr*m];

pnu= pm[npr*m+1];

al = pm[npr*m+2];

*pnu1 = pnu;

*al1 = al;

/* --- d() matrix --- */

if (opt == 1) {

/* --- plane stress --- */

c1 = e / (1 - pnu * pnu);

c2 = c1 * pnu;

}

else {

/* --- plane strain --- */

c = e / ((1 + pnu) * (1 - 2 * pnu));

c1 = c * (1 - pnu);

c2 = c * pnu;

}

c3 = .5 * e / (1 + pnu);

d[0][0] = c1;

d[0][1] = c2;

d[0][2] = 0;

d[1][0] = c2;

d[1][1] = c1;

d[1][2] = 0;

d[2][0] = 0;

d[2][1] = 0;

d[2][2] = c3;

return(0);

}


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elemstif(n,opt,se,tl,xni,d,thick,tempr,x,al,pnu,noc)

int n,opt,*noc;

float al,pnu;

float *x,*tempr,*thick,d[][3],tl[8],se[][8],xni[][2];

{

int i,j,k,ip;

float dte,c,xi,eta,th,dj,b[3][8],db[3][8];

/* ----- element stiffness and temperature load ----- */

for (i = 0; i < 8;i++) {

for (j = 0; j < 8; j++) {

se[i][j] = 0.;

}

tl[i] = 0.;

}

dte = tempr[n];

/* --- weight factor is one --- */

/* --- loop on integration points --- */

for (ip = 0; ip < 4; ip++) {

/* --- get db matrix at integration point ip --- */

xi = xni[ip][0];

eta = xni[ip][1];

dbmat(n,x,noc,thick,&th,d,b,db,&dj,xi,eta);

/* --- element stiffness matrix se --- */

for (i = 0; i < 8; i++) {

for (j = 0; j < 8; j++) {

c = 0;

for (k = 0; k < 3; k++) {

c = c + b[k][i] * db[k][j] * dj * th;

}


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se[i][j] = se[i][j] + c;

}

}

/* --- determine temperature load tl --- */

c = al * dte;

if (opt == 2)

c = (1 + pnu) * c;

for (i = 0; i < 8; i++) {

tl[i] = tl[i] + th * dj * c * (db[0][i] + db[1][i]);

}

}

return(0);

}

dbmat(n,x,noc,thick,th1,d,b,db,dj1,xi,eta)

float *x,*dj1,*thick,*th1,xi,eta;

float d[][3],b[][8],db[][8];

int n,*noc;

{

int n1,n2,n3,n4,i,j,k;

float x1,y1,x2,y2,x3,y3,x4,y4,tj11,tj12,tj21,tj22,dj,c;

float th,a[3][4],g[4][8];

/* ----- db() matrix ----- */

/* --- nodal coordinates --- */

th = thick[n];

*th1 = th;

n1 = noc[4*n];

n2 = noc[4*n+1];

n3 = noc[4*n+2];

n4 = noc[4*n+3];

x1 = x[2*(n1-1)];


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y1 = x[2*(n1-1)+1];

x2 = x[2*(n2-1)];

y2 = x[2*(n2-1)+1];

x3 = x[2*(n3-1)];

y3 = x[2*(n3-1)+1];

x4 = x[2*(n4-1)];

y4 = x[2*(n4-1)+1];

/* --- formation of jacobian tj --- */

tj11 = ((1 - eta) * (x2 - x1) + (1 + eta) * (x3 - x4)) / 4;

tj12 = ((1 - eta) * (y2 - y1) + (1 + eta) * (y3 - y4)) / 4;

tj21 = ((1 - xi) * (x4 - x1) + (1 + xi) * (x3 - x2)) / 4;

tj22 = ((1 - xi) * (y4 - y1) + (1 + xi) * (y3 - y2)) / 4;

/* --- determinant of the jacobian --- */

dj = tj11 * tj22 - tj12 * tj21;

*dj1 = dj;

/* --- a[3,4] matrix relates strains to --- */

/* --- local derivatives of u --- */

a[0][0] = tj22 / dj;

a[1][0] = 0;

a[2][0] = -tj21 / dj;

a[0][1] = -tj12 / dj;

a[1][1] = 0;

a[2][1] = tj11 / dj;

a[0][2] = 0;

a[1][2] = -tj21 / dj;

a[2][2] = tj22 / dj;

a[0][3] = 0;

a[1][3] = tj11 / dj;

a[2][3] = -tj12 / dj;

/* --- g[4,8] matrix relates local derivatives of u --- */


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/* --- to local nodal displacements q[8] --- */

for (i = 0; i < 4; i++) {

for (j = 0; j < 8; j++) {

g[i][j] = 0;

}

}

g[0][0] = -(1 - eta) / 4;

g[1][0] = -(1 - xi) / 4;

g[2][1] = -(1 - eta) / 4;

g[3][1] = -(1 - xi) / 4;

g[0][2] = (1 - eta) / 4;

g[1][2] = -(1 + xi) / 4;

g[2][3] = (1 - eta) / 4;

g[3][3] = -(1 + xi) / 4;

g[0][4] = (1 + eta) / 4;

g[1][4] = (1 + xi) / 4;

g[2][5] = (1 + eta) / 4;

g[3][5] = (1 + xi) / 4;

g[0][6] = -(1 + eta) / 4;

g[1][6] = (1 - xi) / 4;

g[2][7] = -(1 + eta) / 4;

g[3][7] = (1 - xi) / 4;

/* --- b[3,8] matrix relates strains to q --- */

for (i = 0; i < 3; i++) {

for (j = 0; j < 8; j++) {

c = 0;

for (k = 0; k < 4; k++) {

c = c + a[i][k] * g[k][j];

}

b[i][j] = c;


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}

}

/* --- db[3,8] matrix relates stresses to q[8] --- */

for (i = 0; i < 3; i++) {

for (j = 0; j < 8; j++) {

c = 0;

for (k = 0; k < 3; k++) {

c = c + d[i][k] * b[k][j];

}

db[i][j] = c;

}

}

return(0);

}

/*repeating functions for punch*/elemstif2(n,opt,se,tl,xni,d,thick,tempr,x,al,pnu,noc)

int n,opt,*noc;

float al,pnu;

float *x,*tempr,*thick,d[][3],tl[8],se[][8],xni[][2];

{

int i,j,k,ip;

float dte,c,xi,eta,th,dj,b[3][8],db[3][8];

/* ----- element stiffness and temperature load ----- */

for (i = 0; i < 8;i++) {

for (j = 0; j < 8; j++) {

se[i][j] = 0.;

}

tl[i] = 0.;

}

dte = tempr[n];


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/* --- weight factor is one --- */

/* --- loop on integration points --- */

for (ip = 0; ip < 4; ip++) {

/* --- get db matrix at integration point ip --- */

xi = xni[ip][0];

eta = xni[ip][1];

dbmat2(n,x,noc,thick,&th,d,b,db,&dj,xi,eta);

/* --- element stiffness matrix se --- */

for (i = 0; i < 8; i++) {

for (j = 0; j < 8; j++) {

c = 0;

for (k = 0; k < 3; k++) {

c = c + b[k][i] * db[k][j] * dj * th;

}

se[i][j] = se[i][j] + c;

}

}

/* --- determine temperature load tl --- */

c = al * dte;

if (opt == 2)

c = (1 + pnu) * c;

for (i = 0; i < 8; i++) {

tl[i] = tl[i] + th * dj * c * (db[0][i] + db[1][i]);

}

}

return(0);

}

dbmat2(n,x,noc,thick,th1,d,b,db,dj1,xi,eta)

float *x,*dj1,*thick,*th1,xi,eta;

float d[][3],b[][8],db[][8];


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int n,*noc;

{

int n1,n2,n3,n4,i,j,k;

float x1,y1,x2,y2,x3,y3,x4,y4,tj11,tj12,tj21,tj22,dj,c;

float th,a[3][4],g[4][8];

/* ----- db() matrix ----- */

/* --- nodal coordinates --- */

th = thick[n];

*th1 = th;

n1 = noc[4*n];

n2 = noc[4*n+1];

n3 = noc[4*n+2];

n4 = noc[4*n+3];

x1 = x[2*(n1-1)-1792];

y1 = x[2*(n1-1)+1-1792];

x2 = x[2*(n2-1)-1792];

y2 = x[2*(n2-1)+1-1792];

x3 = x[2*(n3-1)-1792];

y3 = x[2*(n3-1)+1-1792];

x4 = x[2*(n4-1)-1792];

y4 = x[2*(n4-1)+1-1792];

/* --- formation of jacobian tj --- */

tj11 = ((1 - eta) * (x2 - x1) + (1 + eta) * (x3 - x4)) / 4;

tj12 = ((1 - eta) * (y2 - y1) + (1 + eta) * (y3 - y4)) / 4;

tj21 = ((1 - xi) * (x4 - x1) + (1 + xi) * (x3 - x2)) / 4;

tj22 = ((1 - xi) * (y4 - y1) + (1 + xi) * (y3 - y2)) / 4;

/* --- determinant of the jacobian --- */

dj = tj11 * tj22 - tj12 * tj21;

*dj1 = dj;

/* --- a[3,4] matrix relates strains to --- */


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/* --- local derivatives of u --- */

a[0][0] = tj22 / dj;

a[1][0] = 0;

a[2][0] = -tj21 / dj;

a[0][1] = -tj12 / dj;

a[1][1] = 0;

a[2][1] = tj11 / dj;

a[0][2] = 0;

a[1][2] = -tj21 / dj;

a[2][2] = tj22 / dj;

a[0][3] = 0;

a[1][3] = tj11 / dj;

a[2][3] = -tj12 / dj;

/* --- g[4,8] matrix relates local derivatives of u --- */

/* --- to local nodal displacements q[8] --- */

for (i = 0; i < 4; i++) {

for (j = 0; j < 8; j++) {

g[i][j] = 0;

}

}

g[0][0] = -(1 - eta) / 4;

g[1][0] = -(1 - xi) / 4;

g[2][1] = -(1 - eta) / 4;

g[3][1] = -(1 - xi) / 4;

g[0][2] = (1 - eta) / 4;

g[1][2] = -(1 + xi) / 4;

g[2][3] = (1 - eta) / 4;

g[3][3] = -(1 + xi) / 4;

g[0][4] = (1 + eta) / 4;

g[1][4] = (1 + xi) / 4;


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g[2][5] = (1 + eta) / 4;

g[3][5] = (1 + xi) / 4;

g[0][6] = -(1 + eta) / 4;

g[1][6] = (1 - xi) / 4;

g[2][7] = -(1 + eta) / 4;

g[3][7] = (1 - xi) / 4;

/* --- b[3,8] matrix relates strains to q --- */

for (i = 0; i < 3; i++) {

for (j = 0; j < 8; j++) {

c = 0;

for (k = 0; k < 4; k++) {

c = c + a[i][k] * g[k][j];

}

b[i][j] = c;

}

}

/* --- db[3,8] matrix relates stresses to q[8] --- */

for (i = 0; i < 3; i++) {

for (j = 0; j < 8; j++) {

c = 0;

for (k = 0; k < 3; k++) {

c = c + d[i][k] * b[k][j];

}

db[i][j] = c;

}

}

return(0);

}/* ----- band solver ----- */

/* -----gauss solver ----- */

GSolve(float **a,int nq,float *x1)


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{

int i,j,k,maxrow;

float tmp;

for (i=0;i


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normal contact stress code with quad 4 node element

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