This C program performs a geometric nonlinearity analysis of springs with rigid elements under displacement-controlled large deformations. It imports input data, performs an incremental analysis to calculate critical buckling loads, and exports output to Excel and HTML files. The analysis calculates forces, displacements, and critical pressures at each increment until the ultimate displacement is reached. Output graphs the displacement versus critical pressure relationship.

1. >> IN THE NAME OF GOD <
Critical Buckling Load Geometric Nonlinearity Analysis of Springs with Rigid Element
Displacement Control Large Deformation Formulated in C programming
C program is written by Salar Delavar Qashqai – Publication Date: 08/April/2021
E-mail: salar.d.ghashghaei@gmail.com

2. C Code:
#include <stdio.h>
#include <windows.h> // text color
#include <conio.h>
#define N 10000
#define ShowText01 "RigidElementSpringDCStrainGNPcr-inputDATA.csv"
#define ShowText02 "RigidElementSpringDCStrainGNPcr-outputEXCEL.csv"
#define ShowText03 "RigidElementSpringDCStrainGNPcr-outputMATLAB.m"
#define ShowText04 "Graph-outputHTML.html"
void IMPORT_DATA01(double Import_Data[]);
void MessageNegative_IMPORT_DATA01(double Import_Data[]);
void MessageInputDataTEXT();
void MessageAnalysisReportTEXT();
void MessageErrorReportTEXT();
void MessageInitialData(double Import_Data[],int n);
void MessageStarinStressTEXT(double STARIN01[],double STRESS01[],double STARIN02[],double STRESS02[],int n);
void textcolor(int ForgC);
void Distance(int i);
void ANALYSIS(double Import_Data[],int n,int m);
double ABS(double B);
double Horizental_Disp(double L,double &x,double y);
double SQRT2(double D);
double MAX_ABS(double A[],int n);
void OUTPUT_excel(double A[],double B[],double C[],int n);
void OUTPUT_HTML_GRAPH(double X[],double Y[],int n,const char text1[],const char text2[],const char text3[]);
int main(){
int k;
double Import_Data[13];
IMPORT_DATA01(Import_Data);
MessageNegative_IMPORT_DATA01(Import_Data);
int m = 1 + ABS(Import_Data[12]/Import_Data[10]);
textcolor(10);
MessageInitialData(Import_Data,m);
textcolor(14);
ANALYSIS(Import_Data,k,m);
getch();
return 0;
}
void IMPORT_DATA01(double Import_Data[]){
int i=0;
FILE *InputFile;
InputFile = fopen(ShowText01, "r");
if (!InputFile){
MessageErrorReportTEXT();
printf(" File is not available! -> [%s] n",ShowText01);
Sleep(6000);
exit(1);
}
char line[100],a[100];
while(i < N && fgets(line,sizeof(line),InputFile) != NULL){
sscanf(line,"%s",a);
//printf("a[%d]: %sn",i,a);
Import_Data[i]= atof(a);
i++;
}
}
void MessageNegative_IMPORT_DATA01(double Import_Data[]){
if ( Import_Data[0] < 0 || Import_Data[1] < 0 || Import_Data[2] < 0 || Import_Data[3] < 0 || Import_Data[4] < 0 || Import_Data[5] < 0 || Import_Data[10] < 0|| Import_Data[12] < 0){
MessageErrorReportTEXT();
printf(" Please check this file! -> [%s]n",ShowText01);
printf(" *** Negative data input value is not acceptable ***n");
printf(" Rotational Spring Stiffness: %fn",Import_Data[0]);
printf(" Length of rigid element: %fn",Import_Data[1]);
printf(" Spring length 1: %fn",Import_Data[2]);
printf(" Spring length 2: %fn",Import_Data[3]);
printf(" Spring area 1: %fn",Import_Data[4]);
printf(" Spring area 2: %fn",Import_Data[5]);
printf(" Spring modulus of elasticity 1: %fn",Import_Data[6]);
printf(" Spring modulus of elasticity 2: %fn",Import_Data[7]);
printf(" External applied load in spring 1: %fn",Import_Data[8]);
printf(" External applied load in spring 2: %fn",Import_Data[9]);
printf(" Initial applied displacement: %fn",Import_Data[10]);
printf(" Distance of spring 1 from rigid element: %fn",Import_Data[11]);
printf(" Ultimate absolute displacement: %fn",Import_Data[12]);
Sleep(40000);
exit(1);
}
}
void textcolor(int ForgC){
WORD wColor;
//This handle is needed to get the current background attribute
HANDLE hStdOut = GetStdHandle(STD_OUTPUT_HANDLE);
CONSOLE_SCREEN_BUFFER_INFO csbi;
//csbi is used for wAttributes word
if(GetConsoleScreenBufferInfo(hStdOut, &csbi)){
//To mask out all but the background attribute, and to add the color
wColor = (csbi.wAttributes & 0xF0) + (ForgC & 0x0F);
SetConsoleTextAttribute(hStdOut, wColor);
}
return;
}
void MessageErrorReportTEXT(){
int i;

3. char Ql;
Ql=176;
textcolor(12);
printf("an ");
for (i=1;i<50;i++)
printf("%c",Ql);
printf(" Error Report ");
for (i=1;i<50;i++)
printf("%c",Ql);
printf("n");
}
void MessageInputDataTEXT(){
int i;
char Ql=176;
printf("n ");
for (i=1;i<50;i++)
printf("%c",Ql);
printf(" Input Data ");
for (i=1;i<50;i++)
printf("%c",Ql);
printf("n");
}
void MessageAnalysisReportTEXT(){
int i;
char Ql=176;
printf("n ");
for (i=1;i<47;i++)
printf("%c",Ql);
printf(" Analysis Report ");
for (i=1;i<47;i++)
printf("%c",Ql);
printf("n");
printf("nt ");
for (i=1;i<98;i++)
printf("-");
printf("n");
printf("t Increment Base Shear Incremental Displacement[DOF(1)] Critical Pressure Load n");
printf("t ");
for (i=1;i<98;i++)
printf("-");
printf("n");
}
void Distance(int i){
if (i < 10)
printf("b");
if (i >= 10 && i <= 99)
printf("btb");
if (i >= 100 && i <= 999)
printf("btbb");
if (i >= 1000 && i <= 9999)
printf("btbbb");
if (i >= 10000 && i <= 20000)
printf("btbbbb");
}
double ABS(double B){
if (B < 0)
B = -B;//Absolute number
else
B = B;
return B;
}
void ANALYSIS(double Import_Data[],int n,int m){
double L,Dx,a=0,Le[2],Area[2],Elas[2],Force[2],K[2],Dini,Dmax,Du,up,K_rotation;
int z,well_done=0;
double output_u[N],output_Pcr[N],output_base[N];
K_rotation = Import_Data[0];
L = Import_Data[1];
Le[0] = Import_Data[2];
Le[1] = Import_Data[3];
Area[0] = Import_Data[4];
Area[1] = Import_Data[5];
Elas[0] = Import_Data[6];
Elas[1] = Import_Data[7];
Force[0] = Import_Data[8];
Force[1] = Import_Data[9];
Dini = Import_Data[10];
Du = Import_Data[11];
Dmax = Import_Data[12];
double F[2],LE[2];
MessageAnalysisReportTEXT();
for (z=0;z<m;z++){
up = Dini*(z+1);// Define the applied Displacement
Horizental_Disp(L,Dx,up);
LE[0] = SQRT2((Le[0]+.5*up)*(Le[0]+.5*up)+Dx*Dx);
K[0] = Elas[0]*Area[0]/LE[0];
F[0] = (((Le[0]+.5*up)/LE[0])*((Le[0]+.5*up)/LE[0]))*K[0]*0.5*up + Import_Data[8];
LE[1] = SQRT2((Le[1]-up)*(Le[1]-up) + Dx*Dx);
K[1] = Elas[1]*Area[1]/LE[1];
F[1] = (((Le[1]-up)/LE[1])*((Le[1]-up)/LE[1]))*K[1]*up + Import_Data[9];
output_u[z] = up;
output_Pcr[z] = (-Import_Data[8]*((.5*L*L)/(L-Dx))-Import_Data[9]*((L*L)/(L-Dx))+F[0]*((.5*L*L)/(L-Dx))+F[1]*((L*L)/(L-Dx))+K_rotation*(up/(L-Dx)))/up;//up/(L-Dx)
output_base[z] = F[0] + F[1];
Distance(z);
printf("tt%dtt%ett%ettt%en",z+1,output_base[z],output_u[z],output_Pcr[z]);
if (ABS(up) >= Dmax){
well_done = 1;
textcolor(13);
printf("ntt Increment displacement reach to ultimate displacementnn");
break;

4. }
}// for
if (well_done == 1){
OUTPUT_excel(output_u,output_Pcr,output_base,z);
OUTPUT_HTML_GRAPH(output_u,output_Pcr,z+1,"Displacement - Critical Buckling Load Graph","Displacement","Critical Buckling Load");
textcolor(15);
printf("na - Output data is written in Excel file -");
system("start /w Graph-outputHTML.html");
}
}
void OUTPUT_excel(double A[],double B[],double C[],int n){
// EXCEL OUTPUT
int i;
FILE *OutputFile;
OutputFile = fopen(ShowText02, "w");
fprintf(OutputFile," ### Critical Pressure Load Geometric Nonlinearity Analysis of Springs with Displacement Control Large Deformation Formulated ###n");
fprintf(OutputFile,"Increment,Displacement [DOF(1)],Critical Pressure Load,Base Shearn");
for(i=0;i<n;i++)
fprintf(OutputFile,"%d,%e,%e,%en",i+1,A[i],B[i],C[i]);
fclose(OutputFile);
}
void MessageInitialData(double Import_Data[],int n){
char Qa,Qb,Qc,Qd,Qe,Qf,Qg,Qk;
int i;
Qa=201;Qb=205;Qc=187;Qd=200;Qe=188,Qf=186,Qg=204,Qk=185;
printf("tttt%c",Qa);
for (i=1;i<71;i++)
printf("%c",Qb);
printf("%cn",Qc);
printf("tttt%c >> IN THE NAME OF GOD << %cn",Qf,Qf);
printf("tttt%c Critical Pressure Load Geometric Nonlinearity Analysis of Springs %cn",Qf,Qf);
printf("tttt%c with Displacement Control Large Deformation Formulated %cn",Qf,Qf);
printf("tttt%c UNIT: Free Unit %cn",Qf,Qf);
printf("tttt%c",Qg);
for (i=1;i<71;i++)
printf("%c",Qb);
printf("%cn",Qk);
printf("tttt%c This program is written by Salar Delavar Ghashghaei %cn",Qf,Qf);
printf("tttt%c E-mail: salar.d.ghashghaei@gmail.com %cn",Qf,Qf);
printf("tttt%c",Qd);
for (i=1;i<71;i++)
printf("%c",Qb);
printf("%cn",Qe);
MessageInputDataTEXT();
printf("t Rotational Spring Stiffness: %fn",Import_Data[0]);
printf("t Length of rigid element: %fn",Import_Data[1]);
printf("t Spring length 1: %fn",Import_Data[2]);
printf("t Spring length 2: %fn",Import_Data[3]);
printf("t Spring area 1: %fn",Import_Data[4]);
printf("t Spring area 2: %fn",Import_Data[5]);
printf("t Spring modulus of elasticity 1: %fn",Import_Data[6]);
printf("t Spring modulus of elasticity 2: %fn",Import_Data[7]);
printf("t External applied load in spring 1: %fn",Import_Data[8]);
printf("t External applied load in spring 2: %fn",Import_Data[9]);
printf("t Initial applied displacement: %fn",Import_Data[10]);
printf("t Distance of spring 1 from rigid element: %fn",Import_Data[11]);
printf("t Ultimate absolute displacement: %fn",Import_Data[12]);
printf("t Number of increments: %dn",n);
}
double Horizental_Disp(double L,double &x,double y){
int it,itermax;
double residual,tolerance,dx,dx_ABS,f,df;
it = 0; // initialize iteration count
itermax = 100000;
residual = 100; // initialize residual
tolerance = 1e-12;
x = 1;// initialize answer
while (residual > tolerance){
f = x*x + y*y - 2*L*x;
df = 2*x - 2*L;
dx = f/df;
x -= dx;
residual = ABS(dx); // abs residual
it = it + 1; // increment iteration count
//printf("f: %f -tdx: %f -tresidual: %fn",f,dx,residual);
if (it == itermax){
printf("tSQRT2(number,power) : SQRT2(%f) - iteration: %d -> ## The solution is not converged ##n",y,it);
break;
}
}
if (it < itermax){
//printf("tSQRT(number,power) - SQRT(%f,%f) : %f n",D,n, x);
return x;
}
}
double SQRT2(double D){
int it,itermax;
double residual,tolerance,x,dx,dx_ABS,f,df;
it = 0; // initialize iteration count
itermax = 100000;
residual = 100; // initialize residual
tolerance = 1e-8;
x = 1;// initialize answer
while (residual > tolerance){
f = x*x - D;
df = 2 * x;
dx = f/df;
x= x - dx;

5. residual = ABS(dx); // abs residual
it = it + 1; // increment iteration count
//printf("f: %f -tdx: %f -tresidual: %fn",f,dx,residual);
if (it == itermax){
printf("tSQRT2(number,power) : SQRT2(%f) - iteration: %d -> ## The solution is not converged ##n",D,it);
break;
}
}
if (it < itermax){
//printf("tSQRT(number,power) - SQRT(%f,%f) : %f n",D,n, x);
return x;
}
}
void OUTPUT_HTML_GRAPH(double X[],double Y[],int n,const char text1[],const char text2[],const char text3[]){
// HTML GRAPH OUTPUT
int i;
double x,y,NorX[N],NorY[N],Xmax,Ymax;
Xmax=MAX_ABS(X,n);
Ymax=MAX_ABS(Y,n);
for (i=0;i<n;i++){
NorX[i] = X[i]/Xmax;
NorY[i] = Y[i]/Ymax;
//printf("t %f %f n",NorX[i],NorY[i]);
}
FILE *OutputFile;
OutputFile = fopen(ShowText04, "w");
fprintf(OutputFile,"<!DOCTYPE HTML><html><body style="background-color:black;"><font color="white"><head><script> n");
fprintf(OutputFile,"window.onload = function(){ n");
fprintf(OutputFile,"var canvas = document.getElementById("myCanvas");var s1 = canvas.getContext("2d");var s2 = canvas.getContext('2d'); n");
fprintf(OutputFile,"var s3 = canvas.getContext("2d");var s4 = canvas.getContext("2d");var s5 = canvas.getContext("2d"); n");
fprintf(OutputFile,"var x=120,y=100,X,Y,Lx=1100,Ly=500,i; n");
fprintf(OutputFile,"s3.beginPath();s3.lineWidth = 3;s3.strokeStyle = "cyan";s3.rect(x,y,Lx,Ly); n");
fprintf(OutputFile,"for(i=0;i<9;i++){s3.moveTo(x+Lx*(i+1)*.1,y+Ly);s3.lineTo(x+Lx*(i+1)*.1,y+Ly-10);}; n");
fprintf(OutputFile,"for(i=0;i<9;i++){s3.moveTo(x,y+Ly*(i+1)*.1);s3.lineTo(x+10,y+Ly*(i+1)*.1);};s3.stroke();n");
fprintf(OutputFile,"s1.beginPath();s1.lineWidth = 3;s1.strokeStyle = "yellow"; n");
for (i=0;i<n-1;i++){
fprintf(OutputFile,"s1.moveTo(%f,%f); n",120+NorX[i]*1100,100+500-NorY[i]*500);
fprintf(OutputFile,"s1.lineTo(%f,%f); n",120+NorX[i+1]*1100,100+500-NorY[i+1]*500);
}
fprintf(OutputFile,"s1.stroke(); n");
fprintf(OutputFile,"s2.beginPath();s2.lineWidth = 1;s2.strokeStyle = "cyan";s2.setLineDash([5, 5]); n");
fprintf(OutputFile,"for(i=0;i<19;i++){s2.moveTo(x+Lx*(i+1)*.05,y);s2.lineTo(x+Lx*(i+1)*.05,y+Ly);} n");
fprintf(OutputFile,"s2.lineWidth = 1;s2.strokeStyle = "cyan";for(i=0;i<19;i++){s2.moveTo(x,y+Ly*(i+1)*.05);s2.lineTo(x+Lx,y+Ly*(i+1)*.05);} s2.stroke();n");
fprintf(OutputFile,"X=x+.25*Lx;Y=.7*y;s4.translate(X,Y);s4.font="30px serif";s4.fillStyle = "#7fff00";s4.fillText("%s",0,0); n",text1);
fprintf(OutputFile,"s4.save();X=-X+.2*x;Y=-Y+y+.6*Ly;s4.translate(X,Y);s4.rotate(3*Math.PI/2);s4.font="15px serif"; n");
fprintf(OutputFile,"s4.fillStyle = "#7fff00";s4.textAlign = "left";s4.fillText("%s",0,0);s4.restore(); n",text3);
fprintf(OutputFile,"s4.save();X=.2*Lx;Y=y+Ly-20;s4.translate(X,Y);s4.rotate(2*Math.PI);s4.font="15px serif";s4.fillStyle = "#7fff00"; n");
fprintf(OutputFile,"s4.textAlign = "left";s4.fillText("%s",0,0);s4.restore(); n",text2);
for(i=0;i<10;i++){
x=.1*(i+1)*Xmax;
fprintf(OutputFile,"s5.save();X=-.29*Lx+Lx*(%d+1)*.1;Y=.3*y+Ly+20;s5.rotate(2*Math.PI);s5.font="16px serif"; n",i);
fprintf(OutputFile,"s5.fillStyle = "#7fff00";s5.textAlign = "left";s5.fillText("%.3e",X,Y);s5.restore(); n",x);
}
for(i=0;i<10;i++){
y=.1*(i+1)*Ymax;
fprintf(OutputFile,"s5.save();X=-.28*Lx-50;Y=Ly+.3*y-Ly*(%d+1)*.1;s5.rotate(2*Math.PI);s5.font="16px serif"; n",i);
fprintf(OutputFile,"s5.fillStyle = "#7fff00";s5.textAlign = "left";s5.fillText("%.3e",X,Y);s5.restore(); n",y);
}
fprintf(OutputFile,"s5.save();X=-.25*Lx;Y=.3*y+Ly+20;s5.rotate(2*Math.PI);s5.font="16px serif";s5.fillStyle = "#7fff00";s5.fillText(0,X,Y);s5.restore(); n");
fprintf(OutputFile,"s5.save();X=-.25*Lx-50;Y=Ly+.3*y;s5.rotate(2*Math.PI);s5.font="16px serif";s5.fillStyle = "#7fff00";s5.textAlign = "left";s5.fillText(0,X,Y);s5.restore();}; n");
fprintf(OutputFile,"</script></head><body><canvas id="myCanvas" width="1300" height="1300" style="border:1px solid black;"></canvas></body></html> n");
fclose(OutputFile);
}
double MAX_ABS(double A[],int n){
int i;
double B[N];
double Amax;
// abs value
for (i=0;i<n;i++){
B[i] = A[i];
if(B[i] < 0)
B[i] = -B[i];
}
// Max of abs
Amax = B[0];
for (i=1;i<n;i++){
if(Amax < B[i])
Amax = B[i];
}
return Amax;
}

6. Plot :
Figure(1) Analysis file

7. Figure(2) Input csv file

8. Figure(3) Displacement-Critical Buckling Load Graph in Html