def test_random_allowables(self):
rc = 0.15
num = 4
bearing = [0, 0]
bypass = [1000., 0., 0.]
analysis = MaxStrain(QUASI,
QUASI_THICK,
DIAMETER,
et={0: QUASI_UNT},
ec={90: QUASI_UNC})
margins = analysis.analyze(bearing, bypass, rc=rc, num=num)
strains = analysis.strains(bearing, bypass, rc=rc, num=num)
compare_margins = np.empty((num, 4))
with np.errstate(divide='ignore'):
# axial strains
x_strains = strains[:, 0]
compare_margins[:, 0] = np.select(
[x_strains > 0, x_strains < 0],
[QUASI_UNT / x_strains - 1, -np.inf / x_strains - 1])
# shear strains
xy_strains = np.abs(strains[:, 2])
compare_margins[:, 1] = np.inf / xy_strains - 1
rotated_strains = rotate_strains(strains, angle=np.deg2rad(90))
# axial strains
x_strains = rotated_strains[:, 0]
compare_margins[:, 2] = np.select(
[x_strains > 0, x_strains < 0],
[np.inf / x_strains - 1, -abs(QUASI_UNC) / x_strains - 1])
# shear strains
xy_strains = np.abs(rotated_strains[:, 2])
compare_margins[:, 3] = np.inf / xy_strains - 1
assert_array_almost_equal(margins, compare_margins)
def setUp(self):
self.analysis = MaxStrain(
QUASI,
QUASI_THICK,
DIAMETER,
et0=QUASI_UNT,
et90=QUASI_UNT,
et45=QUASI_UNT,
etn45=QUASI_UNT,
ec0=QUASI_UNC,
ec90=QUASI_UNC,
ec45=QUASI_UNC,
ecn45=QUASI_UNC,
es0=QUASI_SBS,
es90=QUASI_SBS,
es45=QUASI_SBS,
esn45=QUASI_SBS,
)
def setUp(self):
self.analysis = MaxStrain(
QUASI,
QUASI_THICK,
DIAMETER,
et={
0: QUASI_UNT,
90: QUASI_UNT,
45: QUASI_UNT,
-45: QUASI_UNT
},
ec={
0: QUASI_UNC,
90: QUASI_UNC,
45: QUASI_UNC,
-45: QUASI_UNC
},
es={
0: SHEAR_STRN,
90: SHEAR_STRN,
45: SHEAR_STRN,
-45: SHEAR_STRN
},
)
def test_equalize_dicts(self):
analysis = MaxStrain(
QUASI,
QUASI_THICK,
DIAMETER,
et={
0: QUASI_UNT,
30: QUASI_UNT
},
ec={
90: QUASI_UNC,
60: QUASI_UNC
},
es={45: SHEAR_STRN},
)
self.assertTrue(
analysis.et.keys() == analysis.ec.keys() == analysis.es.keys())
self.assertAlmostEquals(analysis.et[0], QUASI_UNT)
self.assertAlmostEquals(analysis.et[30], QUASI_UNT)
self.assertAlmostEquals(analysis.ec[90], QUASI_UNC)
self.assertAlmostEquals(analysis.ec[60], QUASI_UNC)
self.assertAlmostEquals(analysis.es[45], SHEAR_STRN)
self.assertEqual(analysis.et[90], np.inf)
class TestMaxStrainQuasi(unittest.TestCase):
def setUp(self):
self.analysis = MaxStrain(
QUASI,
QUASI_THICK,
DIAMETER,
et0=QUASI_UNT,
et90=QUASI_UNT,
et45=QUASI_UNT,
etn45=QUASI_UNT,
ec0=QUASI_UNC,
ec90=QUASI_UNC,
ec45=QUASI_UNC,
ecn45=QUASI_UNC,
es0=QUASI_SBS,
es90=QUASI_SBS,
es45=QUASI_SBS,
esn45=QUASI_SBS,
)
def test_xy_points(self):
rc = 0.
num = 4
x, y = self.analysis.xy_points(rc=rc, num=num)
radius = DIAMETER / 2
self.assertAlmostEqual(x[0], radius)
self.assertAlmostEqual(x[1], 0.)
self.assertAlmostEqual(x[2], -radius)
self.assertAlmostEqual(x[3], 0.)
self.assertAlmostEqual(y[0], 0.)
self.assertAlmostEqual(y[1], radius)
self.assertAlmostEqual(y[2], 0.)
self.assertAlmostEqual(y[3], -radius)
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_0_bearing_0_angle(self):
bearing = [0, 0]
p, theta = self.analysis.bearing_angle(bearing)
self.assertAlmostEqual(p, 0.)
self.assertAlmostEqual(np.rad2deg(theta), 0.)
def test_bearing_0_angle(self):
bearing = [100, 0]
p, theta = self.analysis.bearing_angle(bearing)
self.assertAlmostEqual(p, 100.)
self.assertAlmostEqual(np.rad2deg(theta), 0.)
def test_bearing_90_angle(self):
bearing = [0, 100]
p, theta = self.analysis.bearing_angle(bearing)
self.assertAlmostEqual(p, 100.)
self.assertAlmostEqual(np.rad2deg(theta), 90.)
def test_bearing_180_angle(self):
bearing = [-100, 0]
p, theta = self.analysis.bearing_angle(bearing)
self.assertAlmostEqual(p, 100.)
self.assertAlmostEqual(np.rad2deg(theta), 180.)
def test_bearing_n90_angle(self):
bearing = [0, -100]
p, theta = self.analysis.bearing_angle(bearing)
self.assertAlmostEqual(p, 100.)
self.assertAlmostEqual(np.rad2deg(theta), -90.)
def test_bearing_45_angle(self):
bearing = [100, 100]
p, theta = self.analysis.bearing_angle(bearing)
self.assertAlmostEqual(p, np.sqrt(np.sum(np.square(bearing))))
self.assertAlmostEqual(np.rad2deg(theta), 45.)
def test_width_0_angle(self):
w = 6 * DIAMETER
bearing = [100, 0]
bypass = [0, 0, 0]
bypass_correction = [100 / (2 * w), 0, 0]
brg = LoadedHole(bearing[0],
DIAMETER,
QUASI_THICK,
QUASI_INV,
theta=0.)
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_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)
class TestMaxStrainQuasi(unittest.TestCase):
def setUp(self):
self.analysis = MaxStrain(
QUASI,
QUASI_THICK,
DIAMETER,
et={
0: QUASI_UNT,
90: QUASI_UNT,
45: QUASI_UNT,
-45: QUASI_UNT
},
ec={
0: QUASI_UNC,
90: QUASI_UNC,
45: QUASI_UNC,
-45: QUASI_UNC
},
es={
0: SHEAR_STRN,
90: SHEAR_STRN,
45: SHEAR_STRN,
-45: SHEAR_STRN
},
)
def test_equalize_dicts(self):
analysis = MaxStrain(
QUASI,
QUASI_THICK,
DIAMETER,
et={
0: QUASI_UNT,
30: QUASI_UNT
},
ec={
90: QUASI_UNC,
60: QUASI_UNC
},
es={45: SHEAR_STRN},
)
self.assertTrue(
analysis.et.keys() == analysis.ec.keys() == analysis.es.keys())
self.assertAlmostEquals(analysis.et[0], QUASI_UNT)
self.assertAlmostEquals(analysis.et[30], QUASI_UNT)
self.assertAlmostEquals(analysis.ec[90], QUASI_UNC)
self.assertAlmostEquals(analysis.ec[60], QUASI_UNC)
self.assertAlmostEquals(analysis.es[45], SHEAR_STRN)
self.assertEqual(analysis.et[90], np.inf)
def test_xy_points(self):
rc = 0.
num = 4
x, y = self.analysis.xy_points(rc=rc, num=num)
radius = DIAMETER / 2
self.assertAlmostEqual(x[0], radius)
self.assertAlmostEqual(x[1], 0.)
self.assertAlmostEqual(x[2], -radius)
self.assertAlmostEqual(x[3], 0.)
self.assertAlmostEqual(y[0], 0.)
self.assertAlmostEqual(y[1], radius)
self.assertAlmostEqual(y[2], 0.)
self.assertAlmostEqual(y[3], -radius)
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_0_bearing_0_angle(self):
bearing = [0, 0]
p, theta = self.analysis.bearing_angle(bearing)
self.assertAlmostEqual(p, 0.)
self.assertAlmostEqual(np.rad2deg(theta), 0.)
def test_bearing_0_angle(self):
bearing = [100, 0]
p, theta = self.analysis.bearing_angle(bearing)
self.assertAlmostEqual(p, 100.)
self.assertAlmostEqual(np.rad2deg(theta), 0.)
def test_bearing_90_angle(self):
bearing = [0, 100]
p, theta = self.analysis.bearing_angle(bearing)
self.assertAlmostEqual(p, 100.)
self.assertAlmostEqual(np.rad2deg(theta), 90.)
def test_bearing_180_angle(self):
bearing = [-100, 0]
p, theta = self.analysis.bearing_angle(bearing)
self.assertAlmostEqual(p, 100.)
self.assertAlmostEqual(np.rad2deg(theta), 180.)
def test_bearing_n90_angle(self):
bearing = [0, -100]
p, theta = self.analysis.bearing_angle(bearing)
self.assertAlmostEqual(p, 100.)
self.assertAlmostEqual(np.rad2deg(theta), -90.)
def test_bearing_45_angle(self):
bearing = [100, 100]
p, theta = self.analysis.bearing_angle(bearing)
self.assertAlmostEqual(p, np.sqrt(np.sum(np.square(bearing))))
self.assertAlmostEqual(np.rad2deg(theta), 45.)
def test_width_0_angle(self):
w = 6 * DIAMETER
bearing = [100, 0]
bypass = [0, 0, 0]
bypass_correction = [100 / (2 * w), 0, 0]
brg = LoadedHole(bearing[0],
DIAMETER,
QUASI_THICK,
QUASI_INV,
theta=0.)
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_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 = [1000., 0., 0.]
margins = self.analysis.analyze(bearing, bypass, rc=rc, num=num)
strains = self.analysis.strains(bearing, bypass, rc=rc, num=num)
compare_margins = np.empty((num, 2 * len(self.analysis.et)))
with np.errstate(divide='ignore'):
for iangle, angle in enumerate(self.analysis.et):
rotated_strains = rotate_strains(strains,
angle=np.deg2rad(angle))
# axial strains
x_strains = rotated_strains[:, 0]
compare_margins[:, iangle * 2] = np.select(
[x_strains > 0, x_strains < 0], [
QUASI_UNT / x_strains - 1,
-abs(QUASI_UNC) / x_strains - 1
])
# shear strains
xy_strains = np.abs(rotated_strains[:, 2])
compare_margins[:, iangle * 2 +
1] = abs(SHEAR_STRN) / xy_strains - 1
assert_array_almost_equal(margins, compare_margins)
def test_random_allowables(self):
rc = 0.15
num = 4
bearing = [0, 0]
bypass = [1000., 0., 0.]
analysis = MaxStrain(QUASI,
QUASI_THICK,
DIAMETER,
et={0: QUASI_UNT},
ec={90: QUASI_UNC})
margins = analysis.analyze(bearing, bypass, rc=rc, num=num)
strains = analysis.strains(bearing, bypass, rc=rc, num=num)
compare_margins = np.empty((num, 4))
with np.errstate(divide='ignore'):
# axial strains
x_strains = strains[:, 0]
compare_margins[:, 0] = np.select(
[x_strains > 0, x_strains < 0],
[QUASI_UNT / x_strains - 1, -np.inf / x_strains - 1])
# shear strains
xy_strains = np.abs(strains[:, 2])
compare_margins[:, 1] = np.inf / xy_strains - 1
rotated_strains = rotate_strains(strains, angle=np.deg2rad(90))
# axial strains
x_strains = rotated_strains[:, 0]
compare_margins[:, 2] = np.select(
[x_strains > 0, x_strains < 0],
[np.inf / x_strains - 1, -abs(QUASI_UNC) / x_strains - 1])
# shear strains
xy_strains = np.abs(rotated_strains[:, 2])
compare_margins[:, 3] = np.inf / xy_strains - 1
assert_array_almost_equal(margins, compare_margins)
if instructions:
print(
'Input far field stresses, off-axis angle, bearing stress and bolt loading angle [Px, Py, Pxy, alpha, Pbr, theta]'
)
px, py, pxy, alpha, pbr, theta = list(map(float, input().split(',')))
if instructions:
print('Input width (0.0 for infinte plate)')
width = float(input())
if instructions:
print(
'Input bolt diameter, number of output points, step increment and number of steps desired'
)
diameter, num_pts, step, num_steps = list(map(float, input().split(',')))
if 5 in output:
analysis = MaxStrain([[a11, a12, a16], [a12, a22, a26], [a16, a26, a66]],
thickness,
diameter,
et=dict(zip(angles, tension)),
ec=dict(zip(angles, compression)),
es=dict(zip(angles, shear)))
else:
analysis = MaxStrain([[a11, a12, a16], [a12, a22, a26], [a16, a26, a66]],
thickness, diameter)
def output_streses():
pass