Tutorial: polar plots for laminate stiffness#
Date: 30 of January 2025
Author: Saullo G. P. Castro
Cite this tutorial as:
Castro, SGP. Methods for analysis and design of composites (Version 0.7.1) [Computer software]. 2024. https://doi.org/10.5281/zenodo.2871782
Importing dependencies#
[1]:
import numpy as np
import matplotlib.pyplot as plt
from composites import laminated_plate
Defining material properties#
[2]:
E11 = 100e9 # [N/m^2]
E22 = 8e9 # [N/m^2]
G12 = G23 = G13 = 8e9 # [N/m^2]
nu12 = 0.29
ply_thickness = 1.25e-4 # [m]
laminaprop = E11, E22, nu12, G12, G13, G23
Creating reference laminate#
[3]:
stack_ref = np.asarray([-45, +45, 0, 0, +45, -45], dtype=float)
Calculating membrane stiffness \(A_{11}\) in all directions#
[4]:
angles = np.linspace(0, 360, 1000, endpoint=False)
A11s = np.zeros_like(angles)
for i, angle in enumerate(angles):
lam = laminated_plate(stack=stack_ref-angle, plyt=ply_thickness, laminaprop=laminaprop)
A11s[i] = lam.ABD[0, 0]
Normalizing plots to keep maximum value 1 in the radial coordinate#
[5]:
A11s /= A11s.max()
Creating polar plots#
[6]:
plt.polar(np.deg2rad(angles), A11s, 'k')
ax = plt.gca()
ax.set_yticks([])
ax.set_xticks(np.deg2rad([0, 45, 90, 135, 180, 225, 270, 315]))
ax.set_xticklabels([r"$0^\circ$", r"$+45^\circ$", r"$90^\circ$", "", "", "", "", r"$-45^\circ$"])
ax.grid(linestyle='--', lw=0.5)
plt.show()
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