def _unloaded(self, bearing, bypass, w=0.):
"""Lekhnitskii's unloaded hole solution
Parameters
----------
bearing : array_like
1D 1x2 array [Px, Py]
bypass : array_like
1D 1x3 array [Nx, Ny, Nxy]
w : float, default 0.
pitch or width in bearing load direction
(set to 0. for infinite plate)
Returns
-------
bjsfm.lekhnitskii.UnloadedHole
"""
d = self.r*2
t = self.t
a_inv = self.a_inv
bearing = np.array(bearing, dtype=float)
bypass = np.array(bypass, dtype=float)
p, theta = self.bearing_angle(bearing)
if w: # DeJong correction for finite width
brg_dir_bypass = lk.rotate_plane_stress(bypass, angle=theta)
sign = np.sign(brg_dir_bypass[0]) if abs(brg_dir_bypass[0]) > 0 else 1.
bypass += lk.rotate_plane_stress(np.array([p/(2*w)*sign, 0., 0.]), angle=-theta)
return lk.UnloadedHole(bypass, d, t, a_inv)
def test_strain_rotation(self):
bearing = [0, 0]
bypass = [100, 0, 0]
angles = map(np.deg2rad, [0, 45, 90, -45, 60, -60])
for angle in angles:
rotated_stresses = rotate_plane_stress(self.analysis.stresses(
bearing, bypass),
angle=angle)
assert_array_almost_equal(
(self.analysis.a_inv
@ (rotated_stresses * self.analysis.t).T).T,
rotate_strains(self.analysis.strains(bearing, bypass),
angle=angle),
)
def test_strain_rotation(self):
bearing = [0, 0]
bypass = [100, 0, 0]
angles = [np.deg2rad(45.), np.deg2rad(-45.)]
for angle in angles:
rotated_stresses = rotate_plane_stress(self.analysis.stresses(
bearing, bypass),
angle=angle)
assert_array_almost_equal(
(self.analysis.a_inv
@ (rotated_stresses * self.analysis.t).T).T,
self.analysis._rotate_strains(self.analysis.strains(
bearing, bypass),
angle=angle),
)
def test_width_45_angle(self):
w = 6 * DIAMETER
bearing = [100, 100]
bypass = [0, 0, 0]
p, theta = self.analysis.bearing_angle(bearing)
bypass_correction = rotate_plane_stress(np.array([p / (2 * w), 0, 0]),
angle=-theta)
brg = LoadedHole(p, DIAMETER, QUASI_THICK, QUASI_INV, theta=theta)
byp = UnloadedHole(bypass_correction, DIAMETER, QUASI_THICK, QUASI_INV)
x, y = self.analysis.xy_points(rc=0., num=100)
byp_stress = byp.stress(x, y)
brg_stress = brg.stress(x, y)
total_stress = byp_stress + brg_stress
analysis_stress = self.analysis.stresses(bearing,
bypass,
rc=0.,
num=100,
w=w)
assert_array_almost_equal(total_stress, analysis_stress)
def test_max_strain(self):
rc = 0.15
num = 4
bearing = [0, 0]
bypass = [100., 0., 0.]
margins = self.analysis.analyze(bearing, bypass, rc=rc, num=num)
e0, e90, es0 = self.analysis.strains(bearing, bypass, rc=rc,
num=num)[1]
s0, s90, ss0 = self.analysis.stresses(bearing, bypass, rc=rc,
num=num)[1]
calc_strains = QUASI_INV @ np.array([s0, s90, ss0]) * QUASI_THICK
self.assertAlmostEqual(e0, calc_strains[0])
self.assertAlmostEqual(e90, calc_strains[1])
self.assertAlmostEqual(es0, calc_strains[2])
s45, sn45, ss45 = rotate_plane_stress(np.array([s0, s90, ss0]),
angle=np.deg2rad(45.))
e45, en45, es45 = QUASI_INV @ np.array([s45, sn45, ss45]) * QUASI_THICK
self.assertAlmostEqual(margins[1, 0], QUASI_UNT / e0 - 1)
self.assertAlmostEqual(margins[1, 1], -QUASI_UNC / e90 - 1)
self.assertAlmostEqual(margins[1, 2], QUASI_SBS / abs(es0) - 1)
self.assertAlmostEqual(margins[1, 3], QUASI_UNT / e45 - 1)
self.assertAlmostEqual(margins[1, 4], QUASI_UNT / en45 - 1)
self.assertAlmostEqual(margins[1, 5], QUASI_SBS / abs(es45) - 1)