This program is written by salar delavar qashqai Salardqashqai.blogfa.com

1. >> IN THE NAME OF GOD <<
Nonlinear Analysis of Fixed Support Beam with Hinge by Hinge Method in C programming
C program is written by Salar Delavar Ghashghaei – Publication Date: 01/July/2018
E‐mail: salar.d.ghashghaei@gmail.com
C Code:
#include <stdio.h>
#include <windows.h> // text color
#include <conio.h>
#define NN 3 // Degree of freedom
#define Ne 2 // number of element
void IMPORT_DATA01(double &Length,double &EA,double &EI,double &Ultimate_Mom);
void Matrix_Stiffness(double EA,double EI,double L[],double lanX[],double lanY[],double A[],double B[],double C[],double D[],double E[],double K[][6],double K_G[][6],int I,int II);
void MatrixDetermination(double [][NN],int );
void MatrixInverse(double [][NN], double [][NN],int );
void MatrixMulti01(double [][NN], double [], double [],int );
void Matrix_Transpose(double A[6][6],double B[6][6]);
void Matrix_Multiplication(double A[6][6],double B[6][6],double C[6][6]);
void ElementInternalForce(double K[][6],double U[],double lanX[],double lanY[],double ee[][6],int I);// Calculate internal element force
void ELEMNT_FORCE_OUTPUT(double eleF[2][6],double ELE_FORCE[3][12],double SUM_ELE_FORCE[12],double u[],double sum_u[], int I);
double ABS(double);
double MIN(double A[],int n);
double SQRT2(double D);
void MessageInitialData(double L,double EI,double EA,double Ultimate_Moment);
void MessageAnalysisReport();
void MessageErrorReportTEXT();
void MessageInputDataTEXT();
void MessageCheck_IMPORT_DATA01(double Length,double EA,double EI,double Ultimate_Mom);
void MessageResult(double A[],double B[3][3],int n);

2. void OUTPUT_excel(double A[3][3],double B[3],double C[3][12],int n);
void OUTPUT_matlab(double A[3][3],double B[3],double C[3][12],int n);
void ANALYSIS(double Length,double EI,double EA,double Ultimate_Moment);
void Distance(int);
void textcolor(int ForgC);
void DATE_TIME();
int main(){
double Length,EI,EA,Ultimate_Moment;
IMPORT_DATA01(Length,EA,EI,Ultimate_Moment);
MessageCheck_IMPORT_DATA01(Length,EI,EA,Ultimate_Moment);
textcolor(14);
MessageInitialData(Length,EI,EA,Ultimate_Moment);
textcolor(11);
MessageAnalysisReport();
ANALYSIS(Length,EI,EA,Ultimate_Moment);
getch();
return 0;
}
void MatrixInverse(double A[][NN], double C[][NN],int n){
int i,j,l;
double c_A[NN][NN],B[NN][NN],m,Sum;
for (i=0;i<NN;i++)
for (j=0;j<NN;j++)
c_A[i][j]=A[i][j];
// Inverse [Kinit]
for (i=0;i<NN;i++)
for (j=0;j<NN;j++){
if (i==j)
B[i][j]=1;
else
B[i][j]=0;
}
for (j=0;j<NN-1;j++)
for (i=j+1;i<NN;i++){
m=c_A[i][j]/c_A[j][j];
for (l=0;l<NN;l++){
c_A[i][l] -= m*c_A[j][l];
B[i][l] -= m*B[j][l];
}
}
// backward substitutions
for (i=NN-1;i>=0;i--)
for (j=0;j<NN;j++){
Sum=0;
for (l=i+1;l<NN;l++)
Sum += c_A[i][l]*C[l][j];
C[i][j]=(B[i][j]-Sum)/c_A[i][i];
}
}
void ElementInternalForce(double K[][6],double U[],double lanX[],double lanY[],double ee[][6],int I){
double lan[6][6],UU[6],ff,ll[6][6];
int II;
lan[0][0]=lanX[I];lan[0][1]=lanY[I];lan[0][2]=0;lan[0][3]=0;lan[0][4]=0;lan[0][5]=0;

3. lan[1][0]=-lanY[I];lan[1][1]=lanX[I];lan[1][2]=0;lan[1][3]=0;lan[1][4]=0;lan[1][5]=0;
lan[2][0]=0;lan[2][1]=0;lan[2][2]=1;lan[2][3]=0;lan[2][4]=0;lan[2][5]=0;
lan[3][0]=0;lan[3][1]=0;lan[3][2]=0;lan[3][3]=lanX[I];lan[3][4]=lanY[I];lan[3][5]=0;
lan[4][0]=0;lan[4][1]=0;lan[4][2]=0;lan[4][3]=-lanY[I];lan[4][4]=lanX[I];lan[4][5]=0;
lan[5][0]=0;lan[5][1]=0;lan[5][2]=0;lan[5][3]=0;lan[5][4]=0;lan[5][5]=1;
if (I == 0){
UU[0]=0;UU[1]=0;UU[2]=0;UU[3]=U[0];UU[4]=U[1];UU[5]=U[2];
}
if (I == 1){
UU[0]=U[0];UU[1]=U[1];UU[2]=U[2];UU[3]=0;UU[4]=0;UU[5]=0;
}
int i,j;
// [f] = [K] * [u]
Matrix_Multiplication(K,lan,ll);
for (i=0; i<6; i++){
ff=0;
for (j=0; j<6; j++)
ff += ll[i][j]*UU[j];
ee[I][i] = ff;
}
}
void MatrixMulti01(double A[][NN], double B[], double C[],int n){
int i,j;
double ff;
// [u] = [Kinv] * [f]
for (i=0; i<n; i++)
{
ff=0;
for (j=0; j<n; j++)
ff += A[i][j]*B[j];
C[i] = ff;
}
}
double ABS(double B){
if (B < 0)
B = -B;//Absolute number
else
B = B;
return B;
}
double MIN(double A[],int n){
int i;
double Cmin;
Cmin = A[0];
// Max of abs
for (i=0;i<n;i++){
if(Cmin > A[i])
Cmin = A[i];
}
return Cmin;
}
void Distance(int i){
if (i < 10)

4. printf("bt");
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");
}
void MessageInitialData(double L,double EI,double EA,double Ultimate_Moment){
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<72;i++)
printf("%c",Qb);
printf("%cn",Qc);
printf("tttt%c >> IN THE NAME OF GOD << %cn",Qf,Qf);
printf("tttt%c Nonlinear Analysis of Fixed Support Beam with Hinge by Hinge Method %cn",Qf,Qf);
printf("tttt%c UNIT: Free Unit %cn",Qf,Qf);
printf("tttt%c",Qg);
for (i=1;i<72;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<72;i++)
printf("%c",Qb);
printf("%cn",Qe);
MessageInputDataTEXT();
printf(" Length : %.3en",L);
printf(" Section flextural rigidity - EI: %.3en",EI);
printf(" Section axial rigidity - EA: %.3en",EA);
printf(" Section ultimate capacity moment: %.3en",Ultimate_Moment);
}
void MessageAnalysisReport(){
int i;
char Ql=176;
printf("n ");
for (i=1;i<64;i++)
printf("%c",Ql);
printf(" Analysis Report ");
for (i=1;i<64;i++)
printf("%c",Ql);
printf("n");
}
void MessageCheck_IMPORT_DATA01(double L,double EI,double EA,double Ultimate_Moment){
if ( L < 0 || EI < 0 || EA < 0 || Ultimate_Moment < 0){
MessageErrorReportTEXT();
printf(" Please check this file! -> [ PushoverHingeByHingeMethodFixedSupportBeam-inputDATA.csv ]n");

5. printf(" *** Negative data input value is not acceptable ***n");
printf(" Length of element: %.3en",L);
printf(" Section flextural rigidity - EI: %.3en",EI);
printf(" Section axial rigidity - EA: %.3en",EA);
printf(" Section ultimate capacity moment: %.3en",Ultimate_Moment);
Sleep(40000);
exit(1);
}
}
void MessageErrorReportTEXT(){
int i;
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 OUTPUT_txt(){
}
void OUTPUT_matlab(double A[3][3],double B[3],double C[3][12],int n){
// MATLAB OUTPUT
int i;
FILE *OutputFile;
OutputFile = fopen("PushoverHingeByHingeMethodFixedSupportBeam-outputMATLAB.m", "w");
fprintf(OutputFile," %% Nonlinear Analysis of Fixed Support Beam with Hinge by Hinge Method %%n");
fprintf(OutputFile,"disp_Dof5=[0n");
for(i=0;i<n;i++)
fprintf(OutputFile,"%en",A[i][1]);
fprintf(OutputFile,"];nn");
fprintf(OutputFile,"disp_Dof6=[0n");
for(i=0;i<n;i++)
fprintf(OutputFile,"%en",A[i][2]);
fprintf(OutputFile,"];nn");
fprintf(OutputFile,"ele_Dof3=[0n");
for(i=0;i<n;i++)
fprintf(OutputFile,"%en",C[i][2]);
fprintf(OutputFile,"];nn");

6. fprintf(OutputFile,"ele_Dof5=[0n");
for(i=0;i<n;i++)
fprintf(OutputFile,"%en",C[i][4]);
fprintf(OutputFile,"];nn");
fprintf(OutputFile,"ele_Dof6=[0n");
for(i=0;i<n;i++)
fprintf(OutputFile,"%en",C[i][5]);
fprintf(OutputFile,"];nn");
fprintf(OutputFile,"ele_Dof12=[0n");
for(i=0;i<n;i++)
fprintf(OutputFile,"%en",C[i][11]);
fprintf(OutputFile,"];nn");
fprintf(OutputFile,"base_shear=[0n");
for(i=0;i<n;i++)
fprintf(OutputFile,"%en",B[i]);
fprintf(OutputFile,"];nn");
fprintf(OutputFile,"figure(1)n");
fprintf(OutputFile,"plot(disp_Dof6,ele_Dof6,'LineWidth',3);n");
fprintf(OutputFile,"title(['## ELEMENT INTERAL MOMENT - ROTATION DIAGRAM #'],'Color','b');n");
fprintf(OutputFile,"xlabel('ROTATION [DOF(6)]');ylabel('ELEMENT INTERAL MOMENT [DOF(6)]');grid on;n");
fprintf(OutputFile,"figure(2)n");
fprintf(OutputFile,"plot(disp_Dof6,ele_Dof12,'LineWidth',3);n");
fprintf(OutputFile,"title(['## ELEMENT INTERAL MOMENT - ROTATION DIAGRAM #'],'Color','b');n");
fprintf(OutputFile,"xlabel('ROTATION [DOF(6)]');ylabel('ELEMENT INTERAL MOMENT [DOF(12)]');grid on;n");
fprintf(OutputFile,"figure(3)n");
fprintf(OutputFile,"plot(disp_Dof5,ele_Dof5,'LineWidth',3);n");
fprintf(OutputFile,"title(['# ELEMENT INTERAL SHEAR - DISPLACEMENT DIAGRAM #'],'Color','b');n");
fprintf(OutputFile,"xlabel('DISPLACEMENT [DOF(11)]');ylabel('ELEMENT INTERAL SHEAR [DOF(2)]');grid on;n");
fprintf(OutputFile,"figure(4)n");
fprintf(OutputFile,"plot(disp_Dof5,base_shear,'LineWidth',3);n");
fprintf(OutputFile,"title(['## BASE SHEAR - DISPLACEMENT DIAGRAM #'],'Color','b');n");
fprintf(OutputFile,"xlabel('DISPLACEMENT [DOF(5)]');ylabel('BASE SHEAR [DOF(2)]+[DOF(8)]');grid on;n");
}
void OUTPUT_excel(double A[3][3],double B[3],double C[3][12],int n){
// EXCEL OUTPUT
int i;
FILE *OutputFile;
OutputFile = fopen("PushoverHingeByHingeMethodFixedSupportBeam-outputEXCEL.csv", "w");
fprintf(OutputFile," ### Nonlinear Analysis of Fixed Support Beam with Hinge by Hinge Method ###n");
fprintf(OutputFile,"Increment,Base Shear[DOF(2)]+[DOF(8)],Displacement [DOF(4)],Displacement [DOF(5)],Rotation [DOF(6)],Ele.1 Axial[DOF(1)],Ele.1 Shear[DOF(2)],Ele.1 Moment[DOF(3)],
Ele.1 Axial[DOF(4)],Ele.1 Shear[DOF(5)],Ele.1 Moment[DOF(6)],Ele.2 Axial[DOF(4)],Ele.2 Shear[DOF(5)],Ele.2 Moment[DOF(6)],Ele.2 Axial[DOF(7)],Ele.2 Shear[DOF(8)],Ele.2 Moment[DOF(9)]n");
for(i=0;i<n;i++)
fprintf(OutputFile,"%d,%e,%e,%e,%e,%e,%e,%e,%e,%e,%e,%e,%e,%e,%e,%e,%en",i+1,B[i],A[i][0],A[i][1],A[i][2],C[i][0],C[i][1],C[i][2],C[i][3],C[i][4],C[i][5],C[i][6],C[i][7],C[i][8],C[i][9],
C[i][10],C[i][11]);
}
void MatrixDetermination(double A[][NN],int n){
// row operations
int i,j,k;
double Product,m,B[n][n];

7. for (i=0;i<n;i++)
for (j=0;j<n;j++)
B[i][j]=A[i][j];
for (k=0;k<n-1;k++)
for (i=k+1;i<n;i++){
m = B[i][k]/B[k][k];
for (j=0;j<n;j++)
B[i][j] -= m*B[k][j];
}
Product=1;
for (i=0;i<n;i++)
Product *= B[i][i];
// display results
if (Product == 0){
printf("ant ### it Seens that Golobal Matrix is singular or structure is unstable!!! ###n");
Sleep(40000);
exit(1);
}
}
void IMPORT_DATA01(double &Length,double &EA,double &EI,double &Ultimate_Mom){
double Import_Data[4];
int i=0;
FILE *InputFile;
InputFile = fopen("PushoverHingeByHingeMethodFixedSupportBeam-inputDATA.csv", "r");
if (!InputFile){
MessageErrorReportTEXT();
printf(" File is not available! -> [PushoverHingeByHingeMethodFixedSupportBeam-inputDATA.csv] n");
Sleep(6000);
exit(1);
}
char line[100],a[100];
while(i < 4 && fgets(line,sizeof(line),InputFile) != NULL){
sscanf(line,"%s",a);
//printf("a[%d]: %sn",i,a);
Import_Data[i]= atof(a);
i++;
}
Length=Import_Data[0];
EI=Import_Data[1];
EA=Import_Data[2];
Ultimate_Mom=Import_Data[3];
}
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

8. wColor = (csbi.wAttributes & 0xF0) + (ForgC & 0x0F);
SetConsoleTextAttribute(hStdOut, wColor);
}
return;
}
void ANALYSIS(double Length,double EI,double EA,double Ultimate_Moment){
int i;
double K[NN][NN],Kinv[NN][NN],eleF[2][6],ELE_FORCE[3][12],SUM_ELE_FORCE[12];
double L[Ne],lanX[Ne],lanY[Ne],AA[Ne],BB[Ne],CC[Ne],DD[Ne],EE[Ne],f[NN],F[NN],u[3],sum_u[3],Mi[4];
double output_u[3][3],output_base[3];
double MS[6][6],KG[6][6],LANNDA[4],LANNDA_min;
double x[3],y[3];
for (i=0;i<NN;i++){
F[i]=0;f[i] = 0;u[i] = 0;sum_u[i] = 0;
}
for(int j=0;j<3;j++){
for(i=0;i<6*Ne;i++)
ELE_FORCE[j][i] = 0;
}
for(i=0;i<6*Ne;i++)
SUM_ELE_FORCE[i] = 0;
for (i=0;i<4;i++)
Mi[i] = 0;
// SATAGE: 01
F[1]=-1;
x[0] = 0;y[0]=0;
x[1] = Length;y[1]=0+sum_u[1];
x[2] = 3*Length;y[2]=0;
L[0] = SQRT2((x[1]-x[0])*(x[1]-x[0])+(y[1]-y[0])*(y[1]-y[0]));
L[1] = SQRT2((x[2]-x[1])*(x[2]-x[1])+(y[2]-y[1])*(y[2]-y[1]));
lanX[0]=(x[1]-x[0])/L[0];lanY[0]=(y[1]-y[0])/L[0];
lanX[1]=(x[2]-x[1])/L[1];lanY[1]=(y[2]-y[1])/L[1];
Matrix_Stiffness(EA,EI,L,lanX,lanY,AA,BB,CC,DD,EE,MS,KG,0,1);
K[0][0]= KG[3][3];//DOF(4)
K[0][1]= KG[3][4];//DOF(4)
K[0][2]= KG[3][5];//DOF(4)
K[1][0]= KG[4][3];//DOF(5)
K[1][1]= KG[4][4];//DOF(5)
K[1][2]= KG[4][5];//DOF(5)
K[2][0]= KG[5][3];//DOF(6)
K[2][1]= KG[5][4];//DOF(6)
K[2][2]= KG[5][5];//DOF(6)
Matrix_Stiffness(EA,EI,L,lanX,lanY,AA,BB,CC,DD,EE,MS,KG,1,1);
K[0][0]+= KG[0][0];//DOF(4)
K[0][1]+= KG[0][1];//DOF(4)
K[0][2]+= KG[0][2];//DOF(4)
K[1][0]+= KG[1][0];//DOF(5)

9. K[1][1]+= KG[1][1];//DOF(5)
K[1][2]+= KG[1][2];//DOF(5)
K[2][0]+= KG[2][0];//DOF(6)
K[2][1]+= KG[2][1];//DOF(6)
K[2][2]+= KG[2][2];//DOF(6)
MatrixDetermination(K,NN);
MatrixInverse(K,Kinv,NN);// Inverse [Kinit]
MatrixMulti01(Kinv,F,u,NN);
Matrix_Stiffness(EA,EI,L,lanX,lanY,AA,BB,CC,DD,EE,MS,KG,0,1);
ElementInternalForce(MS,u,lanX,lanY,eleF,0);
Matrix_Stiffness(EA,EI,L,lanX,lanY,AA,BB,CC,DD,EE,MS,KG,1,1);
ElementInternalForce(MS,u,lanX,lanY,eleF,1);
LANNDA[0]=(Ultimate_Moment-ABS(Mi[0]))/ABS(eleF[0][2]);
LANNDA[1]=(Ultimate_Moment-ABS(Mi[1]))/ABS(eleF[0][5]);
LANNDA[2]=(Ultimate_Moment-ABS(Mi[2]))/ABS(eleF[1][2]);
LANNDA[3]=(Ultimate_Moment-ABS(Mi[3]))/ABS(eleF[1][5]);
LANNDA_min = MIN(LANNDA,4);
for (i=0;i<NN;i++)
u[i]=LANNDA_min*u[i];
Matrix_Stiffness(EA,EI,L,lanX,lanY,AA,BB,CC,DD,EE,MS,KG,0,1);
ElementInternalForce(MS,u,lanX,lanY,eleF,0);
Matrix_Stiffness(EA,EI,L,lanX,lanY,AA,BB,CC,DD,EE,MS,KG,1,1);
ElementInternalForce(MS,u,lanX,lanY,eleF,1);
Mi[0]=eleF[0][2];
Mi[1]=eleF[0][5];
Mi[2]=eleF[1][2];
Mi[3]=eleF[1][5];
ELEMNT_FORCE_OUTPUT(eleF,ELE_FORCE,SUM_ELE_FORCE,u,sum_u,0);
for (i=0;i<NN;i++)
output_u[0][i]=sum_u[i];//output displacement
output_base[0]=-SUM_ELE_FORCE[1]-SUM_ELE_FORCE[10];//output base shear
// So plastic hinge has formed in node 1
// SATAGE: 02
x[0] = 0;y[0]=0;
x[1] = Length;y[1]=0+sum_u[1];
x[2] = 3*Length;y[2]=0;
L[0] = SQRT2((x[1]-x[0])*(x[1]-x[0])+(y[1]-y[0])*(y[1]-y[0]));
L[1] = SQRT2((x[2]-x[1])*(x[2]-x[1])+(y[2]-y[1])*(y[2]-y[1]));
lanX[0]=(x[1]-x[0])/L[0];lanY[0]=(y[1]-y[0])/L[0];
lanX[1]=(x[2]-x[1])/L[1];lanY[1]=(y[2]-y[1])/L[1];
Matrix_Stiffness(EA,EI,L,lanX,lanY,AA,BB,CC,DD,EE,MS,KG,0,2);
K[0][0]= KG[3][3];//DOF(4)
K[0][1]= KG[3][4];//DOF(4)
K[0][2]= KG[3][5];//DOF(4)
K[1][0]= KG[4][3];//DOF(5)
K[1][1]= KG[4][4];//DOF(5)
K[1][2]= KG[4][5];//DOF(5)
K[2][0]= KG[5][3];//DOF(6)

10. K[2][1]= KG[5][4];//DOF(6)
K[2][2]= KG[5][5];//DOF(6)
Matrix_Stiffness(EA,EI,L,lanX,lanY,AA,BB,CC,DD,EE,MS,KG,1,1);
K[0][0]+= KG[0][0];//DOF(4)
K[0][1]+= KG[0][1];//DOF(4)
K[0][2]+= KG[0][2];//DOF(4)
K[1][0]+= KG[1][0];//DOF(5)
K[1][1]+= KG[1][1];//DOF(5)
K[1][2]+= KG[1][2];//DOF(5)
K[2][0]+= KG[2][0];//DOF(6)
K[2][1]+= KG[2][1];//DOF(6)
K[2][2]+= KG[2][2];//DOF(6)
MatrixDetermination(K,3);
MatrixInverse(K,Kinv,NN);// Inverse [Kinit]
MatrixMulti01(Kinv,F,u,NN);
Matrix_Stiffness(EA,EI,L,lanX,lanY,AA,BB,CC,DD,EE,MS,KG,0,2);
ElementInternalForce(MS,u,lanX,lanY,eleF,0);
Matrix_Stiffness(EA,EI,L,lanX,lanY,AA,BB,CC,DD,EE,MS,KG,1,1);
ElementInternalForce(MS,u,lanX,lanY,eleF,1);
LANNDA[0]=(Ultimate_Moment-ABS(Mi[0]))/ABS(eleF[0][2]);
LANNDA[1]=(Ultimate_Moment-ABS(Mi[1]))/ABS(eleF[0][5]);
LANNDA[2]=(Ultimate_Moment-ABS(Mi[2]))/ABS(eleF[1][2]);
LANNDA[3]=(Ultimate_Moment-ABS(Mi[3]))/ABS(eleF[1][5]);
LANNDA_min = MIN(LANNDA,4);
for (i=0;i<NN;i++)
u[i]=LANNDA_min*u[i];
Matrix_Stiffness(EA,EI,L,lanX,lanY,AA,BB,CC,DD,EE,MS,KG,0,2);
ElementInternalForce(MS,u,lanX,lanY,eleF,0);
Matrix_Stiffness(EA,EI,L,lanX,lanY,AA,BB,CC,DD,EE,MS,KG,1,1);
ElementInternalForce(MS,u,lanX,lanY,eleF,1);
Mi[0]=eleF[0][2];
Mi[1]=eleF[0][5];
Mi[2]=eleF[1][2];
Mi[3]=eleF[1][5];
ELEMNT_FORCE_OUTPUT(eleF,ELE_FORCE,SUM_ELE_FORCE,u,sum_u,1);
for (i=0;i<NN;i++)
output_u[1][i]=sum_u[i];//output displacement
output_base[1]=-SUM_ELE_FORCE[1]-SUM_ELE_FORCE[10];//output base shear
// So plastic hinge has formed in node 2
// SATAGE: 03
x[0] = 0;y[0]=0;
x[1] = Length;y[1]=0+sum_u[1];
x[2] = 3*Length;y[2]=0;
L[0] = SQRT2((x[1]-x[0])*(x[1]-x[0])+(y[1]-y[0])*(y[1]-y[0]));
L[1] = SQRT2((x[2]-x[1])*(x[2]-x[1])+(y[2]-y[1])*(y[2]-y[1]));
lanX[0]=(x[1]-x[0])/L[0];lanY[0]=(y[1]-y[0])/L[0];
lanX[1]=(x[2]-x[1])/L[1];lanY[1]=(y[2]-y[1])/L[1];
Matrix_Stiffness(EA,EI,L,lanX,lanY,AA,BB,CC,DD,EE,MS,KG,0,4);
K[0][0]= KG[3][3];//DOF(4)

11. K[0][1]= KG[3][4];//DOF(4)
K[0][2]= KG[3][5];//DOF(4)
K[1][0]= KG[4][3];//DOF(5)
K[1][1]= KG[4][4];//DOF(5)
K[1][2]= KG[4][5];//DOF(5)
K[2][0]= KG[5][3];//DOF(6)
K[2][1]= KG[5][4];//DOF(6)
K[2][2]= KG[5][5];//DOF(6)
Matrix_Stiffness(EA,EI,L,lanX,lanY,AA,BB,CC,DD,EE,MS,KG,1,2);
K[0][0]+= KG[0][0];//DOF(4)
K[0][1]+= KG[0][1];//DOF(4)
K[0][2]+= KG[0][2];//DOF(4)
K[1][0]+= KG[1][0];//DOF(5)
K[1][1]+= KG[1][1];//DOF(5)
K[1][2]+= KG[1][2];//DOF(5)
K[2][0]+= KG[2][0];//DOF(6)
K[2][1]+= KG[2][1];//DOF(6)
K[2][2]+= KG[2][2];//DOF(6)
MatrixInverse(K,Kinv,NN-1);// Inverse [Kinit]
MatrixMulti01(Kinv,F,u,NN-1);
Matrix_Stiffness(EA,EI,L,lanX,lanY,AA,BB,CC,DD,EE,MS,KG,0,4);
ElementInternalForce(MS,u,lanX,lanY,eleF,0);
Matrix_Stiffness(EA,EI,L,lanX,lanY,AA,BB,CC,DD,EE,MS,KG,1,2);
ElementInternalForce(MS,u,lanX,lanY,eleF,1);
LANNDA[0]=(Ultimate_Moment-ABS(Mi[0]))/ABS(eleF[0][2]);
LANNDA[1]=(Ultimate_Moment-ABS(Mi[1]))/ABS(eleF[0][5]);
LANNDA[2]=(Ultimate_Moment-ABS(Mi[2]))/ABS(eleF[1][2]);
LANNDA[3]=(Ultimate_Moment-ABS(Mi[3]))/ABS(eleF[1][5]);
LANNDA_min = MIN(LANNDA,4);
for (i=0;i<NN;i++)
u[i]=LANNDA_min*u[i];
Matrix_Stiffness(EA,EI,L,lanX,lanY,AA,BB,CC,DD,EE,MS,KG,0,4);
ElementInternalForce(MS,u,lanX,lanY,eleF,0);
Matrix_Stiffness(EA,EI,L,lanX,lanY,AA,BB,CC,DD,EE,MS,KG,1,2);
ElementInternalForce(MS,u,lanX,lanY,eleF,1);
Mi[0]=eleF[0][2];
Mi[1]=eleF[0][5];
Mi[2]=eleF[1][2];
Mi[3]=eleF[1][5];
ELEMNT_FORCE_OUTPUT(eleF,ELE_FORCE,SUM_ELE_FORCE,u,sum_u,2);
for (i=0;i<3;i++)
output_u[2][i]=sum_u[i];//output displacement
output_base[2]=-SUM_ELE_FORCE[1]-SUM_ELE_FORCE[10];//output base shear
MessageResult(output_base,output_u,3);
//MatrixDetermination(K,3);
OUTPUT_excel(output_u,output_base,ELE_FORCE,2);

12. OUTPUT_matlab(output_u,output_base,ELE_FORCE,2);
textcolor(15);
printf("na - Output data is written in Excel and Matlab file -n");
DATE_TIME();
}
void DATE_TIME(){
printf("nt");
system("echo %date%");
printf("t");
system("echo %time%");
}
void Matrix_Stiffness(double EA,double EI,double L[],double lanX[],double lanY[],double A[],double B[],double C[],double D[],double E[],double K[][6],double K_G[][6],int I,int II){
double lan[6][6],lan_Tr[6][6],ans[6][6];
A[I] = 4*EI/L[I];
B[I] = 6*EI/(L[I]*L[I]);
C[I] = 2*EI/L[I];
D[I] = 12*EI/(L[I]*L[I]*L[I]);
E[I] = EA/L[I];
for (int i=0;i<6;i++)
for (int j=0;j<6;j++)
K[i][j] = 0;
//I:2 number of element - II: kind of stiffness matrix
if (II==1){// No plastic hinge
K[0][0]=E[I];K[0][1]=0;K[0][2]=0;K[0][3]=-E[I];K[0][4]=0;K[0][5]=0;
K[1][0]=0;K[1][1]=D[I];K[1][2]=B[I];K[1][3]=0;K[1][4]=-D[I];K[1][5]=B[I];
K[2][0]=0;K[2][1]=B[I];K[2][2]=A[I];K[2][3]=0;K[2][4]=-B[I];K[2][5]=C[I];
K[3][0]=-E[I];K[3][1]=0;K[3][2]=0;K[3][3]=E[I];K[3][4]=0;K[3][5]=0;
K[4][0]=0;K[4][1]=-D[I];K[4][2]=-B[I];K[4][3]=0;K[4][4]=D[I];K[4][5]=-B[I];
K[5][0]=0;K[5][1]=B[I];K[5][2]=C[I];K[5][3]=0;K[5][4]=-B[I];K[5][5]=A[I];
}
if (II==2){// plastic hinge at i
K[0][0]=E[I];K[0][1]=0;K[0][2]=0;K[0][3]=-E[I];K[0][4]=0;K[0][5]=0;
K[1][0]=0;K[1][1]=.25*D[I];K[1][2]=0;K[1][3]=0;K[1][4]=-.25*D[I];K[1][5]=.5*B[I];
K[2][0]=0;K[2][1]=0;K[2][2]=0;K[2][3]=0;K[2][4]=0;K[2][5]=0;
K[3][0]=-E[I];K[3][1]=0;K[3][2]=0;K[3][3]=E[I];K[3][4]=0;K[3][5]=0;
K[4][0]=0;K[4][1]=-.25*D[I];K[4][2]=0;K[4][3]=0;K[4][4]=.25*D[I];K[4][5]=-.5*B[I];
K[5][0]=0;K[5][1]=.5*B[I];K[5][2]=0;K[5][3]=0;K[5][4]=-.5*B[I];K[5][5]=(3/4)*A[I];
}
if (II==3){// plastic hinge at j
K[0][0]=E[I];K[0][1]=0;K[0][2]=0;K[0][3]=-E[I];K[0][4]=0;K[0][5]=0;
K[1][0]=0;K[1][1]=.25*D[I];K[1][2]=.5*B[I];K[1][3]=0;K[1][4]=-.25*D[I];K[1][5]=0;
K[2][0]=0;K[2][1]=.5*B[I];K[2][2]=(3/4)*A[I];K[2][3]=0;K[2][4]=-.5*B[I];K[2][5]=0;
K[3][0]=-E[I];K[3][1]=0;K[3][2]=0;K[3][3]=E[I];K[3][4]=0;K[3][5]=0;
K[4][0]=0;K[4][1]=-.25*D[I];K[4][2]=-.5*B[I];K[4][3]=0;K[4][4]=.25*D[I];K[4][5]=0;
K[5][0]=0;K[5][1]=0;K[5][2]=0;K[5][3]=0;K[5][4]=0;K[5][5]=0;
}
if (II==4){// plastic hinge at i and j
K[0][0]=E[I];K[0][1]=0;K[0][2]=0;K[0][3]=-E[I];K[0][4]=0;K[0][5]=0;
K[1][0]=0;K[1][1]=0;K[1][2]=0;K[1][3]=0;K[1][4]=0;K[1][5]=0;
K[2][0]=0;K[2][1]=0;K[2][2]=0;K[2][3]=0;K[2][4]=0;K[2][5]=0;
K[3][0]=-E[I];K[3][1]=0;K[3][2]=0;K[3][3]=E[I];K[3][4]=0;K[3][5]=0;
K[4][0]=0;K[4][1]=0;K[4][2]=0;K[4][3]=0;K[4][4]=0;K[4][5]=0;
K[5][0]=0;K[5][1]=0;K[5][2]=0;K[5][3]=0;K[5][4]=0;K[5][5]=0;
}
lan[0][0]=lanX[I];lan[0][1]=lanY[I];lan[0][2]=0;lan[0][3]=0;lan[0][4]=0;lan[0][5]=0;

13. lan[1][0]=-lanY[I];lan[1][1]=lanX[I];lan[1][2]=0;lan[1][3]=0;lan[1][4]=0;lan[1][5]=0;
lan[2][0]=0;lan[2][1]=0;lan[2][2]=1;lan[2][3]=0;lan[2][4]=0;lan[2][5]=0;
lan[3][0]=0;lan[3][1]=0;lan[3][2]=0;lan[3][3]=lanX[I];lan[3][4]=lanY[I];lan[3][5]=0;
lan[4][0]=0;lan[4][1]=0;lan[4][2]=0;lan[4][3]=-lanY[I];lan[4][4]=lanX[I];lan[4][5]=0;
lan[5][0]=0;lan[5][1]=0;lan[5][2]=0;lan[5][3]=0;lan[5][4]=0;lan[5][5]=1;
Matrix_Transpose(lan,lan_Tr);
Matrix_Multiplication(lan_Tr,K,ans);
Matrix_Multiplication(ans,lan,K_G);
}
void ELEMNT_FORCE_OUTPUT(double eleF[2][6],double ELE_FORCE[3][12],double SUM_ELE_FORCE[12],double u[],double sum_u[], int I){
int i;
for (i=0;i<6;i++)
ELE_FORCE[I][i]=eleF[0][i];
for (i=6;i<12;i++)
ELE_FORCE[I][i]=eleF[1][i-6];
for (i=0;i<6*Ne;i++)
SUM_ELE_FORCE[i] += ELE_FORCE[I][i];
for (i=0;i<NN;i++)
sum_u[i] += u[i];
}
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;
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 Matrix_Transpose(double A[6][6],double B[6][6]){
int i,j;
for (i=0;i<6;i++)
for (j=0;j<6;j++)
B[j][i]=A[i][j];
}
void Matrix_Multiplication(double A[6][6],double B[6][6],double C[6][6]){
int i,j,k;

14. double sum;
for (i=0;i<6;i++)
for (j=0;j<6;j++){
sum =0;
for (k=0;k<6;k++)
sum += A[i][k]*B[k][j];
C[i][j]=sum;
}
}
void MessageResult(double A[],double B[3][3],int n){
int i;
printf("t ");
for (i=0;i<123;i++)
printf("-");
printf("n");
printf("t Increment Base Shear[DOF(2)]+[DOF(8)] Displacement [DOF(4)] Displacement [DOF(5)] Displacement [DOF(6)] n");
printf("t ");
for (i=0;i<123;i++)
printf("-");
printf("n");
for (i=0;i<n;i++)
printf("tt %dtt %.3ett %.3ett %.3ett %.3en",i+1,A[i],B[i][0],B[i][1],B[i][2]);
}

15. Plot :
Figure(1) Analysis file

16.
Figure(2) Input csv file

17.
Figure(3) Output csv file

18.
Figure(4) Output matlab file

19.
Figure(5) Stiffness matrix and change of plastic hinges in beam during analysis