Category : Science and Education
Archive : MOHRS.ZIP
Filename : MOHRS.CPP
Output of file : MOHRS.CPP contained in archive : MOHRS.ZIP
/*program name - Mohrs.cpp/
/*Randall F. Dartt - 2/4/94*/
/* Solves for roots of general cubic equation for triaxial principle stresses*/
// solution source: Handbook of Engineering Fundamentals,
// Ovid C.Eshbach and Mott Souders,
// Wiley Engineering Handbook Series, John Wiley And Sons,
// New York, 1975
// =============================================================================
#include
#include
#include
#include
#include
#include
#include
//==============================================================================
//function definitions
#ifdef __cplusplus
double max (double value1, double value2);
double max(double value1, double value2)
{
return ( (value1 > value2) ? value1 : value2);
}
#endif
#ifdef __cplusplus
double min (double value1, double value2);
double min(double value1, double value2)
{
return ( (value1 < value2) ? value1 : value2);
}
#endif
//==============================================================================
// root calculation
//==============================================================================
double sx,sy,sz,txy,tyz,tzx;
double sigma1,sigma2,sigma3;
double b,c,d,q,r,s1,s2,y1,y2,y3,crit,w,pwr,sum1,sum2;
complex I,x1,x2,x3;
double max (double,double);
double min (double,double);
void clrscr(void);
double main(void)
{
//==============================================================================
/*INITIALIZE ALL VALUES BEFORE CALCULATION*/
//==============================================================================
double x = -3.0, y =0; /*imaginary and real parts of (-3)*/
sx=0,sy=0, sz=0, txy=0,tyz=0,tzx=0; /*set input values to zero*/
//==============================================================================
//get input stresses from operator
//==============================================================================
printf("enter sx ....");
scanf("%lf",&sx);
printf("enter sy ....");
scanf("%lf",&sy);
printf("enter sz ....");
scanf("%lf",&sz);
printf("enter tau_xy....");
scanf("%lf",&txy);
printf("enter tau_yz....");
scanf("%lf",&tyz);
printf("enter tau_zx....");
scanf("%lf",&tzx);
clrscr();
//==============================================================================
//Initialize remaining variables
//==============================================================================
b=0,c=0,d=0,q=0,r=0; /*equation coeficients*/
sigma1=0,sigma2=0,sigma3=0; /*principle stresses*/
s1=0,s2=0,y1=0,y2=0,y3=0,I=0; /*intermediate calclulation variables*/
w=0,x1=0,x2=0,x3=0;
pwr=1.0/3.0;
sum1=0,sum2=0;
crit=0;
//==============================================================================
//perform root finding calculation
//==============================================================================
complex z = complex(x,y); /*define imaginary value(z) for (-3)*/
I = sqrt(z); /*I=sqrt(-3)*/
b=-(sx+sy+sz)/3; /*calculate coefficients*/
c=(sx*sy+sx*sz+sy*sz-pow(txy,2)-pow(tyz,2)-pow(tzx,2))/3;
d=-(sx*sy*sz+2*txy*tyz*tzx-sx*pow(tyz,2)-sy*pow(tzx,2)-sz*pow(txy,2));
q=c-pow(b,2);
r=(3*b*c-d)/2-pow(b,3);
crit=pow(q,3)+pow(r,2); /*calculate evaluation criteria*/
cout << "q=" << q;
cout << ", r=" << r << "\n\n";
cout << "Evaluation criteria = q^3+r^2 = " << crit << "\n Is criteria >=0 ?\n ANSWER:";
if(crit>=0) /*if criteria >=0, compute roots using*/
{ /*Eshbach algebraic method*/
cout << " Yes, calculation is using algebraic solution. \n\n";
w=sqrt(crit);
sum1=(r+w);
sum2=(r-w);
if(sum1>=0)
s1=pow(sum1,pwr);
else
s1=-(pow(-sum1,pwr));
if(sum2>=0)
s2=pow(sum2,pwr);
else
s2=-(pow(-sum2,pwr));
x1=(s1+s2-b);
x2=-((s1+s2)/2)+(I/2*(s1-s2))-b;
x3=-((s1+s2)/2)-(I/2*(s1-s2))-b;
if(fabs(real(x1))<.000005) /*set very small root values to zero*/
x1=0.0;
if(fabs(real(x2))<.000005)
x2=0.0;
if(fabs(real(x3))<.000005)
x3=0.0;
}
else /*if criteria <0 use,Eshbach trigonometric method*/
{
cout << " No, calculation is using trigonometric solution. \n\n";
if(q<0)
{
if(r<=0)
{
y1=-2*sqrt(-q)*cos((acos(-r/sqrt(pow(-q,3))))/3);
y2=-2*sqrt(-q)*cos((acos(-r/sqrt(pow(-q,3)))+(2*M_PI))/3);
y3=-2*sqrt(-q)*cos((acos(-r/sqrt(pow(-q,3)))+(4*M_PI))/3);
}
else
{
y1=2*sqrt(-q)*cos((acos(r/sqrt(pow(-q,3))))/3);
y2=2*sqrt(-q)*cos((acos(r/sqrt(pow(-q,3)))+(2*M_PI))/3);
y3=2*sqrt(-q)*cos((acos(r/sqrt(pow(-q,3)))+(4*M_PI))/3);
}
}
else
{
cout << "criteria <0 & q>0 \n; solution not valid";
}
x1=y1-b;
x2=y2-b;
x3=y3-b;
if(fabs(real(x1))<0.000005) /*set very small root values to zero*/
x1=0.0;
if(fabs(real(x2))<0.000005)
x2=0.0;
if(fabs(real(x3))<0.000005)
x3=0.0;
}
//==============================================================================
//sort roots in descending order
//==============================================================================
double max (double, double);
double min (double, double);
sigma1=max((real(x1)),(real(x2)));
sigma1=max((sigma1),(real(x3)));
sigma2=min((real(x1)),(real(x2)));
sigma2=max((sigma2),(real(x3)));
sigma3=min((real(x1)),(real(x2)));
sigma3=min((sigma3),(real(x3)));
//==============================================================================
//Output results to screen
//==============================================================================
cout << "Input Values: \n";
cout << " sx = " << sx;
cout << ", sy = " << sy;
cout << ", sz = " << sz;
cout << ", txy = " << txy;
cout << ", tzx = " << tzx;
cout << ", tyz = " << tyz << "\n\n";
cout << "Poloynomial Coefficients:\n b = " <
cout << ", d = " << d << "\n\n";
cout << "Intermediate Roots: \n s1 = " << s1;
cout << ", s2 = " << s2 << "\n";
cout << " y1 = " << y1;
cout << ", y2 = " << y2;
cout << ", y3 = " << y3 << "\n\n";
cout << "SOLUTIONS: \n x1 = " << real(x1);
cout << ", x2 = " << real(x2);
cout << " x3 = " << real(x3) << "\n\n";
cout << " SIGMA 1 = " << sigma1;
cout << ", SIGMA 2 = " << sigma2;
cout << ", SIGMA 3 = " << sigma3;
return 0;
}
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