mohr diagram.py

import math
from random import randrange
import matplotlib.pyplot as plt

def stress_tensor(sigma_x, sigma_y, tau_xy, theta, twotheta):
    print("-----RESULTS-----")
        
    sigma_theta = sigma_x * math.cos(math.radians(theta))**2 + sigma_y * math.sin(math.radians(theta))**2 + tau_xy * math.sin(math.radians(twotheta))
    print("sigma x' =", sigma_theta)

    sigma_y_prime = sigma_x * math.sin(math.radians(theta))**2 + sigma_y * math.cos(math.radians(theta))**2 - tau_xy * math.sin(math.radians(twotheta))
    print("sigma y' =", sigma_y_prime)

    tau_theta = ((sigma_y - sigma_x)/2) * math.sin(math.radians(twotheta)) + tau_xy * math.cos(math.radians(twotheta))
    print("Tau x'y' =", tau_theta)

    theta_1 = 0.5 * math.degrees(math.atan(((2 * tau_xy) / (sigma_x - sigma_y))))
    print("theta_1 =", theta_1)

    sigma_max = 0.5 * (sigma_x + sigma_y) + math.sqrt(((sigma_x - sigma_y) / 2)**2 + (tau_xy)**2)
    sigma_min = 0.5 * (sigma_x + sigma_y) - math.sqrt(((sigma_x - sigma_y) / 2)**2 + (tau_xy)**2)
    
    if abs(sigma_max) > abs(sigma_min):
        sigma_1 = sigma_max
        sigma_3 = sigma_min

    else:
        sigma_1 = sigma_min
        sigma_3 = sigma_max

    print("sigma_1 =", sigma_1)
    print("sigma_3 =", sigma_3)

    #drawing the mohr circle
    radius = (sigma_max - sigma_min) / 2
    circle_center = sigma_max - radius

    fig = plt.figure(figsize=(10, 6))
    ax = fig.add_subplot()
    mohr_circle = plt.Circle((circle_center, 0), radius, fill = False)
    ax.add_patch(mohr_circle)
    ax.axis('equal')

    # Move the x-axis to y = 0
    ax.spines['bottom'].set_position('zero')
    ax.spines['left'].set_position('zero')
    ax.spines['top'].set_visible(False)
    ax.spines['right'].set_visible(False)

    #plotting the scatter points on the circle
    x = [sigma_x, sigma_y]
    y = [tau_xy, tau_xy * -1]
    t = (sigma_theta, circle_center)
    h = (tau_theta, 0)

    # Create a line connecting the two points
    plt.plot(x, y, linestyle='-')
    plt.plot(t, h, linestyle='-')

    plt.scatter(x, y)
    plt.scatter(t, h)
    plt.title('mohr diagram')
    plt.show()

    return {
        "sigma_theta": sigma_theta,
        "sigma_y_prime": sigma_y_prime,
        "tau_theta": tau_theta,
        "sigma_max": sigma_max,
        "sigma_min": sigma_min,
        "radius": radius,
        "circle_center": circle_center,
        "mohr_circle": mohr_circle,
        "fig": fig,
        "ax": ax,
        "x": x,
        "y": y,
        "t": t,
        "h": h,
        "sigma_1": sigma_1,
        "sigma_3": sigma_3,
        "theta_1": theta_1,
    }


def generator(sigma_x, sigma_y, tau_xy, theta, twotheta):
    
    print("sigma x =", sigma_x)
    print("sigma y =", sigma_y)
    print("tau xy =", tau_xy)
    print("theta =", theta)
    print("2 * theta = ", twotheta)

    result = stress_tensor(sigma_x, sigma_y, tau_xy, theta, twotheta)
    return result

print("Select operation.")
print("1. question generator")
print("2. stress tensor by inputs")

while True:
    #taking input
    choice = input("Enter choice (1/2): ")

    #checking the choice
    if choice == '1':
        sigma_x = randrange(-50, 50)
        sigma_y = randrange(-50, 50)
        tau_xy = randrange(-20, 20)
        theta = randrange(1, 10) * 5
        twotheta = theta * 2
        qa = generator(sigma_x, sigma_y, tau_xy, theta, twotheta)
        print(qa)
        
    elif choice == '2':
        sigma_x = float(input("Enter sigma_x: "))
        sigma_y = float(input("Enter sigma_y: "))
        tau_xy = float(input("Enter tau_xy: "))
        theta = float(input("Enter theta: "))
        twotheta = theta * 2

        stress_tensor(sigma_x, sigma_y, tau_xy, theta, twotheta)
        print(stress_tensor)

    else:
        print("invalid input")
        break