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_strains[1],laminae_midplane_stress_expected)
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)