normal and shear stress plot

normal-stress.py

import math
import matplotlib.pyplot as plt

Stress = list[list[float], list[float]]
Vector = list[float]
Angle = float

def normalAndShear(S: Stress, theta: Angle) -> Vector:
    a = math.radians(theta)
    sxx = S[0][0]
    syy = S[1][1]
    sxy = S[0][1]
    cos = math.cos(2*a)
    sin = math.sin(2*a)
    n = 0.5*(sxx + syy) + 0.5*(sxx - syy)*cos + sxy*sin
    s = 0.5*(syy - sxx)*sin + sxy*cos
    return [n, s]

def simplePlots(S: Stress):
    x = []
    yN = []
    yS = []
    
    font = {'family': 'serif',
        'color':  'darkred',
        'weight': 'normal',
        'size': 16,
        }
    
    for theta in range(0, 91):
        x.append(theta)
        ns = normalAndShear(S, theta)
        yN.append( ns[0] )
        yS.append( ns[1] )

    fig, ax = plt.subplots()
    ax.plot(x, yN, label='Normal stress')
    ax.plot(x, yS, label='Shear stress')
    ax.legend()
    
    plt.title('Normal and shear stress on a plane', fontdict=font)
    plt.xlabel('$\Theta$', fontdict=font)
    plt.ylabel('Magnitude', fontdict=font)
    
    ax.axvline(x=45, ymax=0.5, linewidth=1, color='black', linestyle=(0, (5, 5)))
    
    ax.set_xlim(0, 90)
    ax.set_ylim(0, 1)
    plt.show()

# ---------------------------------------------

simplePlots( [[0, 0], [0, 1]] )