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bases.py
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import numpy as np
import sys
def bases(basis):
'''
Function to return basis for strain and stress
input:
basis (int) - Index to select a basis
1 - Voigt's strain basis
2 - Voigt's stress basis
3 - Voigt's normalized stress basis
4 - Tape & Tape basis
returns:
B1, B2, B3, B4, B5, B6 (numpy array) - Six basis elements for the chosen basis
'''
s2 = np.sqrt(2)
s3 = np.sqrt(3)
s6 = np.sqrt(6)
if basis == "Voigt_Strain":
# Voigt's strain basis
B1 = np.array([[ 1, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0]])
B2 = np.array([[ 0, 0, 0],
[ 0, 1, 0],
[ 0, 0, 0]])
B3 = np.array([[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 1]])
B4 = 1/2 * np.array([[ 0, 0, 0],
[ 0, 0, 1],
[ 0, 1, 0]])
B5 = 1/2 * np.array([[ 0, 0, 1],
[ 0, 0, 0],
[ 1, 0, 0]])
B6 = 1/2 * np.array([[ 0, 1, 0],
[ 1, 0, 0],
[ 0, 0, 0]])
elif basis == "Voigt_Stress":
# Voigt's stress basis
B1 = np.array([[ 1, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0]])
B2 = np.array([[ 0, 0, 0],
[ 0, 1, 0],
[ 0, 0, 0]])
B3 = np.array([[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 1]])
B4 = np.array([[ 0, 0, 0],
[ 0, 0, 1],
[ 0, 1, 0]])
B5 = np.array([[ 0, 0, 1],
[ 0, 0, 0],
[ 1, 0, 0]])
B6 = np.array([[ 0, 1, 0],
[ 1, 0, 0],
[ 0, 0, 0]])
elif basis == "Phi":
# Voigt's normalized stress basis
B1 = np.array([[ 1, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0]])
B2 = np.array([[ 0, 0, 0],
[ 0, 1, 0],
[ 0, 0, 0]])
B3 = np.array([[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 1]])
B4 = 1/s2 * np.array([[ 0, 0, 0],
[ 0, 0, 1],
[ 0, 1, 0]])
B5 = 1/s2 * np.array([[ 0, 0, 1],
[ 0, 0, 0],
[ 1, 0, 0]])
B6 = 1/s2 * np.array([[ 0, 1, 0],
[ 1, 0, 0],
[ 0, 0, 0]])
elif basis == "TapeTape":
# Tape & Tape basis
B1 = 1/s2 * np.array([[ 0, 0, 0],
[ 0, 0, 1],
[ 0, 1, 0]])
B2 = 1/s2 * np.array([[ 0, 0, 1],
[ 0, 0, 0],
[ 1, 0, 0]])
B3 = 1/s2 * np.array([[ 0, 1, 0],
[ 1, 0, 0],
[ 0, 0, 0]])
B4 = 1/s2 * np.array([[-1, 0, 0],
[ 0, 1, 0],
[ 0, 0, 0]])
B5 = 1/s6 * np.array([[ 1, 0, 0],
[ 0, 1, 0],
[ 0, 0,-2]])
B6 = 1/s3 * np.array([[ 1, 0, 0],
[ 0, 1, 0],
[ 0, 0, 1]])
else:
sys.exit("Error: requested basis index invalid")
return B1,B2,B3,B4,B5,B6