def test_laminate_applied_force_for_strains(self):
"""Apply a force and calculate the resultant laminate midplane strains.
'Fiber-Reinforced Composites' by Mallick (3rd edition),
Example 3.13
Test will check that the resultant strains match the expected
strains from example 3.13 with a maximum normalized error of
2 decimal places (< 1% error)
"""
ply = Ply(E1=133.4e9, E2=8.78e9, nu12=0.26, G12=3.254e9, h=0.006) # h is in [mm]
laminae_pos45 = Laminae(ply=ply, theta_rad=(45.0*np.pi/180.0))
laminae_neg45 = Laminae(ply=ply, theta_rad=(-45.0*np.pi/180.0))
laminae_list = [laminae_pos45, laminae_neg45]
laminate = Laminate(laminae_list)
N = np.matrix.transpose(np.matrix([100.0e3, 0.0, 0.0])); # N[0] is in [N/m]
M = np.matrix.transpose(np.matrix([0.0, 0.0, 0.0]));
strain_dictionary = laminate.applied_stress(N,M)
Epsilon = strain_dictionary['Epsilon']
Kappa = strain_dictionary['Kappa']
Epsilon_expected = np.matrix.transpose(np.matrix([77.385e-5, -50.715e-5, 0.0]))
Kappa_expected = np.matrix.transpose(np.matrix([0.0, 0.0, 0.060354]))
Epsilon_diff_norm_max = np.nanmax(np.abs(Epsilon_expected -Epsilon)/Epsilon)
Kappa_diff_norm_max = np.nanmax(np.abs(Kappa_expected -Kappa)/Kappa)
max_norm_diff = np.nanmax([Epsilon_diff_norm_max, Kappa_diff_norm_max])
self.assertAlmostEqual(max_norm_diff,0.0,places=2)
def test_laminate_applied_force_for_laminae_midplane_stress(self):
"""Apply a force to a laminate and determine the midplane stresses
of the laminae in the laminate.
'Fiber-Reinforced Composites' by Mallick (3rd edition),
Example 3.13
Test will look at the midplane stresses of the two laminae in
the laminate.
"""
ply = Ply(E1=133.4e9, E2=8.78e9, nu12=0.26, G12=3.254e9, h=0.006) # h is in [mm]
laminae_pos45 = Laminae(ply=ply, theta_rad=(45.0*np.pi/180.0))
laminae_neg45 = Laminae(ply=ply, theta_rad=(-45.0*np.pi/180.0))
laminae_list = [laminae_pos45, laminae_neg45]
laminate = Laminate(laminae_list)
N = np.matrix.transpose(np.matrix([100.0e3, 0.0, 0.0])); # N[0] is in [N/m]
M = np.matrix.transpose(np.matrix([0.0, 0.0, 0.0]));
strain_dictionary = laminate.applied_stress(N,M)
Epsilon = strain_dictionary['Epsilon']
Kappa = strain_dictionary['Kappa']
laminae_midplane_strains = laminate.laminae_midplane_strain(Epsilon, Kappa)
laminae_midplane_stresses = laminate.laminae_stress(Epsilon, Kappa)
laminae_midplane_stress_expected = np.power(10.0,6.0)*np.matrix.transpose(np.matrix([8.33, 0.0, 2.09]))
self.assertMatrixAlmostEqualPercent(laminae_midplane_stresses[0],laminae_midplane_stress_expected)
laminae_midplane_stress_expected = np.power(10.0,6.0)*np.matrix.transpose(np.matrix([8.33, 0.0, -2.09]))
self.assertMatrixAlmostEqualPercent(laminae_midplane_stresses[1],laminae_midplane_stress_expected)
def test_laminate_matrix_symmetricbalanced(self):
""" Test a symmetric balanced ply laminate matrix against a
known example.
'Fiber-Reinforced Composites' by Mallick (3rd edition),
Example 3.7b
Test will check that the laminate stiffness matrix matches
the expected stiffness matrices from example 3.7b with a
maximum normalized error of 3 decimal places (< 0.1% error)
Symmetric Laminate should have A16, A26 = 0, B = 0
"""
ply = Ply(E1=133.4e9, E2=8.78e9, nu12=0.26, G12=3.254e9, h=0.006) # h is in [mm]
laminae_pos45 = Laminae(ply=ply, theta_rad=(45.0*np.pi/180.0))
laminae_neg45 = Laminae(ply=ply, theta_rad=(-45.0*np.pi/180.0))
laminae_list = [laminae_pos45, laminae_neg45,
laminae_neg45, laminae_pos45]
laminate = Laminate(laminae_list)
A_expected = np.power(10.0,6.0)*np.matrix([[962.64, 806.64, 0.0],
[806.64, 962.64, 0.0],
[0.0, 0.0, 829.68]]);
A_diff_norm_max = np.nanmax(np.abs(A_expected -laminate.A)/laminate.A)
B_expected = np.matrix([[0.0, 0.0, 0.0],
[0.0, 0.0, 0.0],
[0.0, 0.0, 0.0]])
B_diff_norm_max = np.max(np.abs(B_expected -laminate.B))
D_expected = np.power(10.,3.)*np.matrix([[46.21, 38.72, 27.04],
[38.72, 46.21, 27.04],
[27.04, 27.04, 39.82]])
D_diff_norm_max = np.nanmax(np.abs(D_expected -laminate.D)/laminate.D)
max_norm_diff = np.max([A_diff_norm_max,B_diff_norm_max,D_diff_norm_max])
self.assertAlmostEqual(max_norm_diff,0.0,places=3)
def test_laminate_matrix_inverse(self):
"""Checks the inverse (A1,B1,C1,D1) matrices to see they form properly.
'Fiber-Reinforced Composites' by Mallick (3rd edition),
Example 3.13
Test will use data from expample 3.13 to check the "inverse"
relationship stiffness matrices with a maximum normalized
error of 2 decimal places (< 1% error).
"""
ply = Ply(E1=133.4e9, E2=8.78e9, nu12=0.26, G12=3.254e9, h=0.006) # h is in [mm]
laminae_pos45 = Laminae(ply=ply, theta_rad=(45.0*np.pi/180.0))
laminae_neg45 = Laminae(ply=ply, theta_rad=(-45.0*np.pi/180.0))
laminae_list = [laminae_pos45, laminae_neg45]
laminate = Laminate(laminae_list)
A1_expected = np.power(10.0,-9.0)*np.matrix([[7.7385, -5.0715, 0.0],
[-5.0715, 7.7385, 0.0],
[0.0, 0.0, 5.683]]);
A1_diff_norm_max = np.nanmax(np.abs(A1_expected -laminate.A_1)/laminate.A_1)
B1_expected = np.power(10.0,-9.0)*np.matrix([[0.0, 0.0, 603.54],
[0.0, 0.0, 603.54],
[602.74, 602.74, 0.0]])
B1_diff_norm_max = np.nanmax(np.abs(B1_expected -laminate.B_1)/laminate.B_1)
C1_expected = np.power(10.0,-9.0)*np.matrix([[0.0, 0.0, 602.74],
[0.0, 0.0, 602.74],
[603.54, 603.54, 0.0]])
C1_diff_norm_max = np.nanmax(np.abs(C1_expected -laminate.C_1)/laminate.C_1)
D1_expected = np.power(10.,-4.0)*np.matrix([[6.45, -4.23, 0.0],
[-4.23, 6.45, 0.0],
[0.0, 0.0, 4.74]])
D1_diff_norm_max = np.nanmax(np.abs(D1_expected -laminate.D_1)/laminate.D_1)
max_norm_diff = np.nanmax([A1_diff_norm_max,B1_diff_norm_max,C1_diff_norm_max,D1_diff_norm_max])
self.assertAlmostEqual(max_norm_diff,0.0,places=2)
def test_laminate_matrix_angleply(self):
""" Test an angle ply laminate matrix against a known example.
'Fiber-Reinforced Composites' by Mallick (3rd edition),
Example 3.7a
Test will check that the laminate stiffness matrix matches
the expected stiffness matrices from example 3.7a with a
maximum normalized error of 3 decimal places (< 0.1% error)
This test will throw a 'RuntimeWarning: invalid value encountered
in divide' because of the zero elements in the A, B and D
matrices, this is okay, ignore the warning.
"""
ply = Ply(E1=133.4e9, E2=8.78e9, nu12=0.26, G12=3.254e9, h=0.006) # h is in [mm]
laminae_pos45 = Laminae(ply=ply, theta_rad=(45.0*np.pi/180.0))
laminae_neg45 = Laminae(ply=ply, theta_rad=(-45.0*np.pi/180.0))
laminae_list = [laminae_pos45, laminae_neg45]
laminate = Laminate(laminae_list)
A_expected = np.power(10.0,6.0)*np.matrix([[481.32, 403.32, 0.0],
[403.32, 481.32, 0.0],
[0.0, 0.0, 414.84]]);
A_diff_norm_max = np.nanmax(np.abs(A_expected -laminate.A)/laminate.A)
B_expected = np.power(10.0,3.0)*np.matrix([[0.0, 0.0, -1126.8],
[0.0, 0.0, -1126.8],
[-1126.8, -1126.8, 0.0]])
B_diff_norm_max = np.nanmax(np.abs(B_expected -laminate.B)/laminate.B)
D_expected = np.matrix([[5775.84, 4839.84, 0.0],
[4839.84, 5775.84, 0.0],
[0.0, 0.0, 4978.08]])
D_diff_norm_max = np.nanmax(np.abs(D_expected -laminate.D)/laminate.D)
max_norm_diff = np.max([A_diff_norm_max,B_diff_norm_max,D_diff_norm_max])
self.assertAlmostEqual(max_norm_diff,0.0,places=3)