def test_reduced_dof_freq_plate():
models = ['plate_clt_donnell_bardell',
'cpanel_clt_donnell_bardell']
for model in models:
print('Test reduced_dof solver, prestress=True, model={0}'.format(model))
p = Panel()
p.model = model
p.a = 1.
p.b = 0.5
p.r = 100.
p.alphadeg = 0.
p.stack = [0, 90, -45, +45]
p.plyt = 1e-3*0.125
p.laminaprop = (142.5e9, 8.7e9, 0.28, 5.1e9, 5.1e9, 5.1e9)
p.mu = 1.3e3
p.m = 11
p.n = 12
p.Nxx = -60.
p.Nyy = -5.
k0 = p.calc_k0(silent=True)
M = p.calc_kM(silent=True)
kG0 = p.calc_kG0(silent=True)
k0 += kG0
eigvals, eigvecs = freq(k0, M, sparse_solver=True, reduced_dof=False, silent=True)
reduced_false = eigvals[0]
freq(k0, M, sparse_solver=True, reduced_dof=True, silent=True)
reduced_true = eigvals[0]
assert np.isclose(reduced_false, reduced_true, rtol=0.001)
def test_reduced_dof_freq_plate():
models = ['plate_clt_donnell_bardell', 'cpanel_clt_donnell_bardell']
for model in models:
print(
'Test reduced_dof solver, prestress=True, model={0}'.format(model))
p = Panel()
p.model = model
p.a = 1.
p.b = 0.5
p.r = 100.
p.alphadeg = 0.
p.stack = [0, 90, -45, +45]
p.plyt = 1e-3 * 0.125
p.laminaprop = (142.5e9, 8.7e9, 0.28, 5.1e9, 5.1e9, 5.1e9)
p.mu = 1.3e3
p.m = 11
p.n = 12
p.Nxx = -60.
p.Nyy = -5.
k0 = p.calc_k0(silent=True)
M = p.calc_kM(silent=True)
kG0 = p.calc_kG0(silent=True)
k0 += kG0
eigvals, eigvecs = freq(k0,
M,
sparse_solver=True,
reduced_dof=False,
silent=True)
reduced_false = eigvals[0]
freq(k0, M, sparse_solver=True, reduced_dof=True, silent=True)
reduced_true = eigvals[0]
assert np.isclose(reduced_false, reduced_true, rtol=0.001)
def test_dynamic_with_TStiff2D():
print('Testing dynamic analysis with TStiff2D')
spb = StiffPanelBay()
spb.a = 2.
spb.b = 1.
spb.stack = [0, 90, 90, 0]
spb.plyt = 1e-3 * 0.125
spb.laminaprop = (142.5e9, 8.7e9, 0.28, 5.1e9, 5.1e9, 5.1e9)
spb.model = 'plate_clt_donnell_bardell'
spb.m = 12
spb.n = 13
spb.mu = 1.3e3
spb.add_panel(y1=0, y2=spb.b / 2., plyt=spb.plyt)
spb.add_panel(y1=spb.b / 2., y2=spb.b, plyt=spb.plyt)
bb = spb.b / 5.
bf = bb
stiff = spb.add_tstiff2d(ys=spb.b / 2.,
bf=bf,
bb=bb,
fstack=[0, 90, 90, 0] * 2,
fplyt=spb.plyt * 1.,
flaminaprop=spb.laminaprop,
bstack=[0, 90, 90, 0] * 1,
bplyt=spb.plyt * 1.,
blaminaprop=spb.laminaprop,
mb=12,
nb=13,
mf=12,
nf=13)
k0 = spb.calc_k0()
M = spb.calc_kM()
eigvals, eigvecs = freq(k0, M, silent=True)
def test_freq_Stiffener2D():
print('Testing frequency analysis for StiffPanelBay with a 2D Stiffener')
spb = StiffPanelBay()
spb.a = 1.
spb.b = 0.5
spb.stack = [0, 90, 90, 0]
spb.plyt = 1e-3 * 0.125
spb.laminaprop = (142.5e9, 8.7e9, 0.28, 5.1e9, 5.1e9, 5.1e9)
spb.model = 'plate_clt_donnell_bardell'
spb.mu = 1.3e3
spb.m = 11
spb.n = 12
spb.add_panel(y1=0, y2=spb.b / 2., plyt=spb.plyt)
spb.add_panel(y1=spb.b / 2., y2=spb.b, plyt=spb.plyt)
spb.add_bladestiff2d(ys=spb.b / 2.,
m1=14,
n1=11,
bf=0.08,
fstack=[0, 90, 90, 0] * 5,
fplyt=spb.plyt,
flaminaprop=spb.laminaprop)
k0 = spb.calc_k0(silent=True)
M = spb.calc_kM(silent=True)
eigvals, eigvecs = freq(k0, M, silent=True)
assert np.isclose(eigvals[0].real, 137.97927190657148, atol=0.01, rtol=0)
def test_freq_Stiffener1D():
print('Testing frequency analysis for StiffPanelBay with a 1D Stiffener')
spb = StiffPanelBay()
spb.a = 2.
spb.b = 0.5
spb.stack = [0, 90, 90, 0]
spb.plyt = 1e-3 * 0.125
spb.laminaprop = (142.5e9, 8.7e9, 0.28, 5.1e9, 5.1e9, 5.1e9)
spb.model = 'plate_clt_donnell_bardell'
spb.mu = 1.3e3
spb.m = 15
spb.n = 16
spb.add_panel(y1=0, y2=spb.b / 2., plyt=spb.plyt)
spb.add_panel(y1=spb.b / 2., y2=spb.b, plyt=spb.plyt)
spb.add_bladestiff1d(ys=spb.b / 2.,
Fx=0.,
bf=0.08,
fstack=[0, 90, 90, 0] * 5,
fplyt=spb.plyt,
flaminaprop=spb.laminaprop)
k0 = spb.calc_k0(silent=True)
M = spb.calc_kM(silent=True)
eigvals, eigvecs = freq(k0, M, silent=True, num_eigvalues=10)
assert np.isclose(eigvals[0].real, 79.5906673583, atol=0.1, rtol=0)
def test_freq_Stiffener2D():
print('Testing frequency analysis for StiffPanelBay with a 2D Stiffener')
spb = StiffPanelBay()
spb.a = 1.
spb.b = 0.5
spb.stack = [0, 90, 90, 0]
spb.plyt = 1e-3*0.125
spb.laminaprop = (142.5e9, 8.7e9, 0.28, 5.1e9, 5.1e9, 5.1e9)
spb.model = 'plate_clt_donnell_bardell'
spb.mu = 1.3e3
spb.m = 11
spb.n = 12
spb.add_panel(y1=0, y2=spb.b/2., plyt=spb.plyt)
spb.add_panel(y1=spb.b/2., y2=spb.b, plyt=spb.plyt)
spb.add_bladestiff2d(ys=spb.b/2., m1=14, n1=11, bf=0.08,
fstack=[0, 90, 90, 0]*5, fplyt=spb.plyt,
flaminaprop=spb.laminaprop)
k0 = spb.calc_k0(silent=True)
M = spb.calc_kM(silent=True)
eigvals, eigvecs = freq(k0, M, silent=True)
assert np.isclose(eigvals[0].real, 137.97927190657148, atol=0.01, rtol=0)
def test_dynamic_with_BladeStiff2D():
print('Testing dynamic analysis with TStiff2D')
spb = StiffPanelBay()
spb.a = 2.
spb.b = 1.
spb.stack = [0, 90, 90, 0]
spb.plyt = 1e-3*0.125
spb.laminaprop = (142.5e9, 8.7e9, 0.28, 5.1e9, 5.1e9, 5.1e9)
spb.model = 'plate_clt_donnell_bardell'
spb.m = 10
spb.n = 10
spb.mu = 1.3e3
spb.add_panel(y1=0, y2=spb.b/2., plyt=spb.plyt)
spb.add_panel(y1=spb.b/2., y2=spb.b, plyt=spb.plyt)
bb = spb.b/5.
bf = bb
stiff = spb.add_bladestiff2d(ys=spb.b/2., bf=bf, bb=bb,
fstack=[0, 90, 90, 0]*2,
fplyt=spb.plyt*1., flaminaprop=spb.laminaprop,
bstack=[0, 90, 90, 0]*1,
bplyt=spb.plyt*1., blaminaprop=spb.laminaprop,
mf=10, nf=10)
k0 = spb.calc_k0()
M = spb.calc_kM()
eigvals, eigvecs = freq(k0, M, silent=True)
spb.plot_skin(eigvecs[:, 0], filename='tmp_test_bladestiff2d_dynamic_skin.png',
colorbar=True)
spb.plot_stiffener(eigvecs[:, 0], si=0, region='flange',
filename='tmp_test_bladestiff2d_dynamic_stiff_flange.png', colorbar=True)
assert np.isclose(eigvals[0], 25.865835238236173, atol=0.01, rtol=0.001)
def test_Lee_and_Lee_table4():
print('Testing Lee and Lee Table 4')
# Lee and Lee. "Vibration analysis of anisotropic plates with eccentric
# stiffeners". Computers & Structures, Vol. 57, No. 1, pp. 99-105,
# 1995.
models = (('model4', 0.00208, 0.0060, 138.99917796302756),
('model5', 0.00260, 0.0075,
175.00597239286196), ('model7', 0.00364, 0.0105, 205.433509024))
for model, hf, bf, value in models:
spb = StiffPanelBay()
spb.model = 'plate_clt_donnell_bardell'
spb.mu = 1.500e3 # plate material density in kg / m^3
spb.laminaprop = (128.e9, 11.e9, 0.25, 4.48e9, 1.53e9, 1.53e9)
spb.stack = [0, -45, +45, 90, 90, +45, -45, 0]
plyt = 0.00013
spb.plyt = plyt
spb.a = 0.5
spb.b = 0.250
spb.m = 14
spb.n = 15
hf = hf
bf = bf
n = int(hf / plyt)
fstack = [0] * (n // 4) + [90] * (n // 4) + [90] * (n //
4) + [0] * (n // 4)
# clamping
spb.w1rx = 0.
spb.w2rx = 0.
spb.w1ry = 0.
spb.w2ry = 0.
spb.add_panel(y1=0, y2=spb.b / 2.)
spb.add_panel(y1=spb.b / 2., y2=spb.b)
spb.add_bladestiff1d(mu=spb.mu,
ys=spb.b / 2.,
bb=0.,
bf=bf,
fstack=fstack,
fplyt=plyt,
flaminaprop=spb.laminaprop)
k0 = spb.calc_k0(silent=True)
M = spb.calc_kM(silent=True)
eigvals, eigvecs = freq(k0, M, silent=True)
herz = eigvals[0].real / 2 / np.pi
assert np.isclose(herz, value, atol=0.001, rtol=0.001)
def test_dynamic_with_BladeStiff2D():
print('Testing dynamic analysis with TStiff2D')
spb = StiffPanelBay()
spb.a = 2.
spb.b = 1.
spb.stack = [0, 90, 90, 0]
spb.plyt = 1e-3 * 0.125
spb.laminaprop = (142.5e9, 8.7e9, 0.28, 5.1e9, 5.1e9, 5.1e9)
spb.model = 'plate_clt_donnell_bardell'
spb.m = 10
spb.n = 10
spb.mu = 1.3e3
spb.add_panel(y1=0, y2=spb.b / 2., plyt=spb.plyt)
spb.add_panel(y1=spb.b / 2., y2=spb.b, plyt=spb.plyt)
bb = spb.b / 5.
bf = bb
stiff = spb.add_bladestiff2d(ys=spb.b / 2.,
bf=bf,
bb=bb,
fstack=[0, 90, 90, 0] * 2,
fplyt=spb.plyt * 1.,
flaminaprop=spb.laminaprop,
bstack=[0, 90, 90, 0] * 1,
bplyt=spb.plyt * 1.,
blaminaprop=spb.laminaprop,
mf=10,
nf=10)
k0 = spb.calc_k0()
M = spb.calc_kM()
eigvals, eigvecs = freq(k0, M, silent=True)
spb.plot_skin(eigvecs[:, 0],
filename='tmp_test_bladestiff2d_dynamic_skin.png',
colorbar=True)
spb.plot_stiffener(
eigvecs[:, 0],
si=0,
region='flange',
filename='tmp_test_bladestiff2d_dynamic_stiff_flange.png',
colorbar=True)
assert np.isclose(eigvals[0], 25.865835238236173, atol=0.01, rtol=0.001)
def test_panel_freq():
for model in [
'plate_clt_donnell_bardell', 'plate_clt_donnell_bardell_w',
'cpanel_clt_donnell_bardell', 'kpanel_clt_donnell_bardell'
]:
for prestress in [True, False]:
print('Frequency Analysis, prestress={0}, model={1}'.format(
prestress, model))
p = Panel()
p.model = model
p.a = 1.
p.b = 0.5
p.r = 1.e8
p.alphadeg = 0.
p.stack = [0, 90, -45, +45]
p.plyt = 1e-3 * 0.125
p.laminaprop = (142.5e9, 8.7e9, 0.28, 5.1e9, 5.1e9, 5.1e9)
p.mu = 1.3e3
p.m = 11
p.n = 12
p.Nxx = -60.
p.Nyy = -5.
k0 = p.calc_k0(silent=True)
M = p.calc_kM(silent=True)
if prestress:
kG0 = p.calc_kG0(silent=True)
k0 += kG0
eigvals, eigvecs = freq(k0,
M,
sparse_solver=True,
reduced_dof=False,
silent=True)
if prestress:
if '_w' in model:
assert np.isclose(eigvals[0], 19.9272, rtol=0.001)
else:
assert np.isclose(eigvals[0], 17.85875, rtol=0.001)
else:
if '_w' in model:
assert np.isclose(eigvals[0], 40.37281, rtol=0.001)
else:
assert np.isclose(eigvals[0], 39.31476, rtol=0.001)
def test_Lee_and_Lee_table4():
print('Testing Lee and Lee Table 4')
# Lee and Lee. "Vibration analysis of anisotropic plates with eccentric
# stiffeners". Computers & Structures, Vol. 57, No. 1, pp. 99-105,
# 1995.
models = (
('model4', 0.00208, 0.0060, 138.99917796302756),
('model5', 0.00260, 0.0075, 175.00597239286196),
('model7', 0.00364, 0.0105, 205.433509024))
for model, hf, bf, value in models:
spb = StiffPanelBay()
spb.model = 'plate_clt_donnell_bardell'
spb.mu = 1.500e3 # plate material density in kg / m^3
spb.laminaprop = (128.e9, 11.e9, 0.25, 4.48e9, 1.53e9, 1.53e9)
spb.stack = [0, -45, +45, 90, 90, +45, -45, 0]
plyt = 0.00013
spb.plyt = plyt
spb.a = 0.5
spb.b = 0.250
spb.m = 14
spb.n = 15
hf = hf
bf = bf
n = int(hf/plyt)
fstack = [0]*(n//4) + [90]*(n//4) + [90]*(n//4) + [0]*(n//4)
# clamping
spb.w1rx = 0.
spb.w2rx = 0.
spb.w1ry = 0.
spb.w2ry = 0.
spb.add_panel(y1=0, y2=spb.b/2.)
spb.add_panel(y1=spb.b/2., y2=spb.b)
spb.add_bladestiff1d(mu=spb.mu, ys=spb.b/2., bb=0., bf=bf,
fstack=fstack, fplyt=plyt, flaminaprop=spb.laminaprop)
k0 = spb.calc_k0(silent=True)
M = spb.calc_kM(silent=True)
eigvals, eigvecs = freq(k0, M, silent=True)
herz = eigvals[0].real/2/np.pi
assert np.isclose(herz, value, atol=0.001, rtol=0.001)
def test_freq_models():
print('Testing frequency analysis for StiffPanelBay with 2 plates')
# From Table 4 of
# Lee and Lee. "Vibration analysis of anisotropic plates with eccentric
# stiffeners". Computers & Structures, Vol. 57, No. 1, pp. 99-105,
# 1995.
for model in [
'plate_clt_donnell_bardell', 'cpanel_clt_donnell_bardell',
'kpanel_clt_donnell_bardell'
]:
spb = StiffPanelBay()
spb.a = 0.5
spb.b = 0.250
spb.plyt = 0.00013
spb.laminaprop = (128.e9, 11.e9, 0.25, 4.48e9, 1.53e9, 1.53e9)
spb.stack = [0, -45, +45, 90, 90, +45, -45, 0]
spb.model = model
spb.r = 1.e6
spb.alphadeg = 0.
spb.mu = 1.5e3
spb.m = 9
spb.n = 10
# clamping
spb.w1rx = 0.
spb.w2rx = 0.
spb.w1ry = 0.
spb.w2ry = 0.
spb.add_panel(0, spb.b / 2., plyt=spb.plyt)
spb.add_panel(spb.b / 2., spb.b, plyt=spb.plyt)
k0 = spb.calc_k0(silent=True)
M = spb.calc_kM(silent=True)
eigvals, eigvecs = freq(k0, M, silent=True)
ref = [
85.12907802 - 0.j, 134.16422850 - 0.j, 206.77295186 - 0.j,
216.45992453 - 0.j, 252.24546171 - 0.j
]
assert np.allclose(eigvals[:5] / 2 / np.pi, ref, atol=0.1, rtol=0)
def test_panel_freq():
for model in ['plate_clt_donnell_bardell',
'plate_clt_donnell_bardell_w',
'cpanel_clt_donnell_bardell',
'kpanel_clt_donnell_bardell']:
for prestress in [True, False]:
print('Frequency Analysis, prestress={0}, model={1}'.format(
prestress, model))
p = Panel()
p.model = model
p.a = 1.
p.b = 0.5
p.r = 1.e8
p.alphadeg = 0.
p.stack = [0, 90, -45, +45]
p.plyt = 1e-3*0.125
p.laminaprop = (142.5e9, 8.7e9, 0.28, 5.1e9, 5.1e9, 5.1e9)
p.mu = 1.3e3
p.m = 11
p.n = 12
p.Nxx = -60.
p.Nyy = -5.
k0 = p.calc_k0(silent=True)
M = p.calc_kM(silent=True)
if prestress:
kG0 = p.calc_kG0(silent=True)
k0 += kG0
eigvals, eigvecs = freq(k0, M, sparse_solver=True, reduced_dof=False, silent=True)
if prestress:
if '_w' in model:
assert np.isclose(eigvals[0], 19.9272, rtol=0.001)
else:
assert np.isclose(eigvals[0], 17.85875, rtol=0.001)
else:
if '_w' in model:
assert np.isclose(eigvals[0], 40.37281, rtol=0.001)
else:
assert np.isclose(eigvals[0], 39.31476, rtol=0.001)
def test_freq_models():
print('Testing frequency analysis for StiffPanelBay with 2 plates')
# From Table 4 of
# Lee and Lee. "Vibration analysis of anisotropic plates with eccentric
# stiffeners". Computers & Structures, Vol. 57, No. 1, pp. 99-105,
# 1995.
for model in ['plate_clt_donnell_bardell',
'cpanel_clt_donnell_bardell',
'kpanel_clt_donnell_bardell']:
spb = StiffPanelBay()
spb.a = 0.5
spb.b = 0.250
spb.plyt = 0.00013
spb.laminaprop = (128.e9, 11.e9, 0.25, 4.48e9, 1.53e9, 1.53e9)
spb.stack = [0, -45, +45, 90, 90, +45, -45, 0]
spb.model = model
spb.r = 1.e6
spb.alphadeg = 0.
spb.mu = 1.5e3
spb.m = 9
spb.n = 10
# clamping
spb.w1rx = 0.
spb.w2rx = 0.
spb.w1ry = 0.
spb.w2ry = 0.
spb.add_panel(0, spb.b/2., plyt=spb.plyt)
spb.add_panel(spb.b/2., spb.b, plyt=spb.plyt)
k0 = spb.calc_k0(silent=True)
M = spb.calc_kM(silent=True)
eigvals, eigvecs = freq(k0, M, silent=True)
ref = [85.12907802-0.j, 134.16422850-0.j, 206.77295186-0.j,
216.45992453-0.j, 252.24546171-0.j]
assert np.allclose(eigvals[:5]/2/np.pi, ref, atol=0.1, rtol=0)
def test_freq_Stiffener1D():
print('Testing frequency analysis for StiffPanelBay with a 1D Stiffener')
spb = StiffPanelBay()
spb.a = 2.
spb.b = 0.5
spb.stack = [0, 90, 90, 0]
spb.plyt = 1e-3*0.125
spb.laminaprop = (142.5e9, 8.7e9, 0.28, 5.1e9, 5.1e9, 5.1e9)
spb.model = 'plate_clt_donnell_bardell'
spb.mu = 1.3e3
spb.m = 15
spb.n = 16
spb.add_panel(y1=0, y2=spb.b/2., plyt=spb.plyt)
spb.add_panel(y1=spb.b/2., y2=spb.b, plyt=spb.plyt)
spb.add_bladestiff1d(ys=spb.b/2., Fx=0., bf=0.08, fstack=[0, 90, 90, 0]*5,
fplyt=spb.plyt, flaminaprop=spb.laminaprop)
k0 = spb.calc_k0(silent=True)
M = spb.calc_kM(silent=True)
eigvals, eigvecs = freq(k0, M, silent=True, num_eigvalues=10)
assert np.isclose(eigvals[0].real, 79.5906673583, atol=0.1, rtol=0)
def tstiff2d_1stiff_freq(a, b, ys, bb, bf, defect_a, mu, plyt, laminaprop,
stack_skin, stack_base, stack_flange,
r=None, m=8, n=8, mb=None, nb=None, mf=None, nf=None):
r"""Frequency T-Stiffened Panel with possible defect at middle
For more details about each parameter and the aerodynamic formulation see
Ref. [castro2016FlutterPanel]_ .
For more details about the theory involved on the assembly of panels, see
[castro2017AssemblyModels]_.
The panel assembly looks like::
skin
_________ _____ _________
| | | |
| | | |
| p01 | p02 | p03 |
| | | |
|_________|_____|_________|
| p04 | p05 | p06 |
|_________|_____|_________|
| | | |
| | | |
| p07 | p08 | p09 |
| | | |
| | | |
|_________|_____|_________|
base flange
_____ _____
| | | |
| | | |
| p10 | | p11 |
| | | |
|_____| |_____|
| p12 | | p13 |
|_____| |_____|
| | | |
| | | |
| p14 | | p15 |
| | | |
| | | |
|_____| |_____|
Parameters
----------
a : float
Total length of the assembly (along `x`).
b : float
Total width of the assembly (along `y`).
ys : float
Position of the stiffener along `y`.
bb : float
Stiffener's base width.
bf : float
Stiffener's flange width.
defect_a : float
Debonding defect/assembly length ratio.
mu : float
Material density.
plyt : float
Ply thickness.
laminaprop : list or tuple
Orthotropic lamina properties: `E_1, E_2, \nu_{12}, G_{12}, G_{13}, G_{23}`.
stack_skin : list or tuple
Stacking sequence for the skin.
stack_base : list or tuple
Stacking sequence for the stiffener's base.
stack_flange : list or tuple
Stacking sequence for the stiffener's flange.
r : float or None, optional
Radius of the stiffened panel.
m, n : int, optional
Number of terms of the approximation function for the skin.
mb, nb : int, optional
Number of terms of the approximation function for the stiffener's base.
mf, nf : int, optional
Number of terms of the approximation function for the stiffener's
flange.
Examples
--------
The following example is one of the test cases:
.. literalinclude:: ../../../../../compmech/panel/assembly/tests/test_tstiff2d_assembly.py
:pyobject: test_tstiff2d_1stiff_freq
"""
defect = defect_a * a
has_defect = True if defect > 0 else False
defect = 0.33*a if defect == 0 else defect # to avoid weird domains
aup = (a - defect)/2.
alow = (a - defect)/2.
bleft = b - ys - bb/2.
bright = ys - bb/2.
mb = m if mb is None else mb
nb = n if nb is None else nb
mf = m if mf is None else mf
nf = n if nf is None else nf
# skin panels
p01 = Panel(group='skin', x0=alow+defect, y0=ys+bb/2., a=aup, b=bleft, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu)
p02 = Panel(group='skin', x0=alow+defect, y0=ys-bb/2., a=aup, b=bb, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu)
p03 = Panel(group='skin', x0=alow+defect, y0=0, a=aup, b=bright, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu)
# defect
p04 = Panel(group='skin', x0=alow, y0=ys+bb/2., a=defect, b=bleft, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu)
p05 = Panel(group='skin', x0=alow, y0=ys-bb/2., a=defect, b=bb, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu)
p06 = Panel(group='skin', x0=alow, y0=0, a=defect, b=bright, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu)
#
p07 = Panel(group='skin', x0=0, y0=ys+bb/2., a=alow, b=bleft, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu)
p08 = Panel(group='skin', x0=0, y0=ys-bb/2., a=alow, b=bb, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu)
p09 = Panel(group='skin', x0=0, y0=0, a=alow, b=bright, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu)
# stiffeners
p10 = Panel(group='base', x0=alow+defect, y0=ys-bb/2., a=aup, b=bb, r=r, m=mb, n=nb, plyt=plyt, stack=stack_base, laminaprop=laminaprop, mu=mu)
p11 = Panel(group='flange', x0=alow+defect, y0=0, a=aup, b=bf, m=mf, n=nf, plyt=plyt, stack=stack_flange, laminaprop=laminaprop, mu=mu)
# defect
p12 = Panel(group='base', x0=alow, y0=ys-bb/2., a=defect, b=bb, r=r, m=mb, n=nb, plyt=plyt, stack=stack_base, laminaprop=laminaprop, mu=mu)
p13 = Panel(group='flange', x0=alow, y0=0, a=defect, b=bf, m=mf, n=nf, plyt=plyt, stack=stack_flange, laminaprop=laminaprop, mu=mu)
#
p14 = Panel(group='base', x0=0, y0=ys-bb/2., a=alow, b=bb, r=r, m=mb, n=nb, plyt=plyt, stack=stack_base, laminaprop=laminaprop, mu=mu)
p15 = Panel(group='flange', x0=0, y0=0, a=alow, b=bf, m=mf, n=nf, plyt=plyt, stack=stack_flange, laminaprop=laminaprop, mu=mu)
# boundary conditions
p01.u1tx = 1 ; p01.u1rx = 1 ; p01.u2tx = 0 ; p01.u2rx = 1
p01.v1tx = 1 ; p01.v1rx = 1 ; p01.v2tx = 0 ; p01.v2rx = 1
p01.w1tx = 1 ; p01.w1rx = 1 ; p01.w2tx = 0 ; p01.w2rx = 1
p01.u1ty = 1 ; p01.u1ry = 1 ; p01.u2ty = 0 ; p01.u2ry = 1
p01.v1ty = 1 ; p01.v1ry = 1 ; p01.v2ty = 0 ; p01.v2ry = 1
p01.w1ty = 1 ; p01.w1ry = 1 ; p01.w2ty = 0 ; p01.w2ry = 1
p02.u1tx = 1 ; p02.u1rx = 1 ; p02.u2tx = 0 ; p02.u2rx = 1
p02.v1tx = 1 ; p02.v1rx = 1 ; p02.v2tx = 0 ; p02.v2rx = 1
p02.w1tx = 1 ; p02.w1rx = 1 ; p02.w2tx = 0 ; p02.w2rx = 1
p02.u1ty = 1 ; p02.u1ry = 1 ; p02.u2ty = 1 ; p02.u2ry = 1
p02.v1ty = 1 ; p02.v1ry = 1 ; p02.v2ty = 1 ; p02.v2ry = 1
p02.w1ty = 1 ; p02.w1ry = 1 ; p02.w2ty = 1 ; p02.w2ry = 1
p03.u1tx = 1 ; p03.u1rx = 1 ; p03.u2tx = 0 ; p03.u2rx = 1
p03.v1tx = 1 ; p03.v1rx = 1 ; p03.v2tx = 0 ; p03.v2rx = 1
p03.w1tx = 1 ; p03.w1rx = 1 ; p03.w2tx = 0 ; p03.w2rx = 1
p03.u1ty = 0 ; p03.u1ry = 1 ; p03.u2ty = 1 ; p03.u2ry = 1
p03.v1ty = 0 ; p03.v1ry = 1 ; p03.v2ty = 1 ; p03.v2ry = 1
p03.w1ty = 0 ; p03.w1ry = 1 ; p03.w2ty = 1 ; p03.w2ry = 1
p04.u1tx = 1 ; p04.u1rx = 1 ; p04.u2tx = 1 ; p04.u2rx = 1
p04.v1tx = 1 ; p04.v1rx = 1 ; p04.v2tx = 1 ; p04.v2rx = 1
p04.w1tx = 1 ; p04.w1rx = 1 ; p04.w2tx = 1 ; p04.w2rx = 1
p04.u1ty = 1 ; p04.u1ry = 1 ; p04.u2ty = 0 ; p04.u2ry = 1
p04.v1ty = 1 ; p04.v1ry = 1 ; p04.v2ty = 0 ; p04.v2ry = 1
p04.w1ty = 1 ; p04.w1ry = 1 ; p04.w2ty = 0 ; p04.w2ry = 1
p05.u1tx = 1 ; p05.u1rx = 1 ; p05.u2tx = 1 ; p05.u2rx = 1
p05.v1tx = 1 ; p05.v1rx = 1 ; p05.v2tx = 1 ; p05.v2rx = 1
p05.w1tx = 1 ; p05.w1rx = 1 ; p05.w2tx = 1 ; p05.w2rx = 1
p05.u1ty = 1 ; p05.u1ry = 1 ; p05.u2ty = 1 ; p05.u2ry = 1
p05.v1ty = 1 ; p05.v1ry = 1 ; p05.v2ty = 1 ; p05.v2ry = 1
p05.w1ty = 1 ; p05.w1ry = 1 ; p05.w2ty = 1 ; p05.w2ry = 1
p06.u1tx = 1 ; p06.u1rx = 1 ; p06.u2tx = 1 ; p06.u2rx = 1
p06.v1tx = 1 ; p06.v1rx = 1 ; p06.v2tx = 1 ; p06.v2rx = 1
p06.w1tx = 1 ; p06.w1rx = 1 ; p06.w2tx = 1 ; p06.w2rx = 1
p06.u1ty = 0 ; p06.u1ry = 1 ; p06.u2ty = 1 ; p06.u2ry = 1
p06.v1ty = 0 ; p06.v1ry = 1 ; p06.v2ty = 1 ; p06.v2ry = 1
p06.w1ty = 0 ; p06.w1ry = 1 ; p06.w2ty = 1 ; p06.w2ry = 1
p07.u1tx = 0 ; p07.u1rx = 1 ; p07.u2tx = 1 ; p07.u2rx = 1
p07.v1tx = 0 ; p07.v1rx = 1 ; p07.v2tx = 1 ; p07.v2rx = 1
p07.w1tx = 0 ; p07.w1rx = 1 ; p07.w2tx = 1 ; p07.w2rx = 1
p07.u1ty = 1 ; p07.u1ry = 1 ; p07.u2ty = 0 ; p07.u2ry = 1
p07.v1ty = 1 ; p07.v1ry = 1 ; p07.v2ty = 0 ; p07.v2ry = 1
p07.w1ty = 1 ; p07.w1ry = 1 ; p07.w2ty = 0 ; p07.w2ry = 1
p08.u1tx = 0 ; p08.u1rx = 1 ; p08.u2tx = 1 ; p08.u2rx = 1
p08.v1tx = 0 ; p08.v1rx = 1 ; p08.v2tx = 1 ; p08.v2rx = 1
p08.w1tx = 0 ; p08.w1rx = 1 ; p08.w2tx = 1 ; p08.w2rx = 1
p08.u1ty = 1 ; p08.u1ry = 1 ; p08.u2ty = 1 ; p08.u2ry = 1
p08.v1ty = 1 ; p08.v1ry = 1 ; p08.v2ty = 1 ; p08.v2ry = 1
p08.w1ty = 1 ; p08.w1ry = 1 ; p08.w2ty = 1 ; p08.w2ry = 1
p09.u1tx = 0 ; p09.u1rx = 1 ; p09.u2tx = 1 ; p09.u2rx = 1
p09.v1tx = 0 ; p09.v1rx = 1 ; p09.v2tx = 1 ; p09.v2rx = 1
p09.w1tx = 0 ; p09.w1rx = 1 ; p09.w2tx = 1 ; p09.w2rx = 1
p09.u1ty = 0 ; p09.u1ry = 1 ; p09.u2ty = 1 ; p09.u2ry = 1
p09.v1ty = 0 ; p09.v1ry = 1 ; p09.v2ty = 1 ; p09.v2ry = 1
p09.w1ty = 0 ; p09.w1ry = 1 ; p09.w2ty = 1 ; p09.w2ry = 1
# base up
p10.u1tx = 1 ; p10.u1rx = 1 ; p10.u2tx = 1 ; p10.u2rx = 1
p10.v1tx = 1 ; p10.v1rx = 1 ; p10.v2tx = 1 ; p10.v2rx = 1
p10.w1tx = 1 ; p10.w1rx = 1 ; p10.w2tx = 1 ; p10.w2rx = 1
p10.u1ty = 1 ; p10.u1ry = 1 ; p10.u2ty = 1 ; p10.u2ry = 1
p10.v1ty = 1 ; p10.v1ry = 1 ; p10.v2ty = 1 ; p10.v2ry = 1
p10.w1ty = 1 ; p10.w1ry = 1 ; p10.w2ty = 1 ; p10.w2ry = 1
# flange up
p11.u1tx = 1 ; p11.u1rx = 1 ; p11.u2tx = 0 ; p11.u2rx = 1
p11.v1tx = 1 ; p11.v1rx = 1 ; p11.v2tx = 0 ; p11.v2rx = 1
p11.w1tx = 1 ; p11.w1rx = 1 ; p11.w2tx = 0 ; p11.w2rx = 1
p11.u1ty = 1 ; p11.u1ry = 1 ; p11.u2ty = 1 ; p11.u2ry = 1
p11.v1ty = 1 ; p11.v1ry = 1 ; p11.v2ty = 1 ; p11.v2ry = 1
p11.w1ty = 1 ; p11.w1ry = 1 ; p11.w2ty = 1 ; p11.w2ry = 1
# base mid
p12.u1tx = 1 ; p12.u1rx = 1 ; p12.u2tx = 1 ; p12.u2rx = 1
p12.v1tx = 1 ; p12.v1rx = 1 ; p12.v2tx = 1 ; p12.v2rx = 1
p12.w1tx = 1 ; p12.w1rx = 1 ; p12.w2tx = 1 ; p12.w2rx = 1
p12.u1ty = 1 ; p12.u1ry = 1 ; p12.u2ty = 1 ; p12.u2ry = 1
p12.v1ty = 1 ; p12.v1ry = 1 ; p12.v2ty = 1 ; p12.v2ry = 1
p12.w1ty = 1 ; p12.w1ry = 1 ; p12.w2ty = 1 ; p12.w2ry = 1
# flange mid
p13.u1tx = 1 ; p13.u1rx = 1 ; p13.u2tx = 1 ; p13.u2rx = 1
p13.v1tx = 1 ; p13.v1rx = 1 ; p13.v2tx = 1 ; p13.v2rx = 1
p13.w1tx = 1 ; p13.w1rx = 1 ; p13.w2tx = 1 ; p13.w2rx = 1
p13.u1ty = 1 ; p13.u1ry = 1 ; p13.u2ty = 1 ; p13.u2ry = 1
p13.v1ty = 1 ; p13.v1ry = 1 ; p13.v2ty = 1 ; p13.v2ry = 1
p13.w1ty = 1 ; p13.w1ry = 1 ; p13.w2ty = 1 ; p13.w2ry = 1
# base low
p14.u1tx = 1 ; p14.u1rx = 1 ; p14.u2tx = 1 ; p14.u2rx = 1
p14.v1tx = 1 ; p14.v1rx = 1 ; p14.v2tx = 1 ; p14.v2rx = 1
p14.w1tx = 1 ; p14.w1rx = 1 ; p14.w2tx = 1 ; p14.w2rx = 1
p14.u1ty = 1 ; p14.u1ry = 1 ; p14.u2ty = 1 ; p14.u2ry = 1
p14.v1ty = 1 ; p14.v1ry = 1 ; p14.v2ty = 1 ; p14.v2ry = 1
p14.w1ty = 1 ; p14.w1ry = 1 ; p14.w2ty = 1 ; p14.w2ry = 1
# flange low
p15.u1tx = 0 ; p15.u1rx = 1 ; p15.u2tx = 1 ; p15.u2rx = 1
p15.v1tx = 0 ; p15.v1rx = 1 ; p15.v2tx = 1 ; p15.v2rx = 1
p15.w1tx = 0 ; p15.w1rx = 1 ; p15.w2tx = 1 ; p15.w2rx = 1
p15.u1ty = 1 ; p15.u1ry = 1 ; p15.u2ty = 1 ; p15.u2ry = 1
p15.v1ty = 1 ; p15.v1ry = 1 ; p15.v2ty = 1 ; p15.v2ry = 1
p15.w1ty = 1 ; p15.w1ry = 1 ; p15.w2ty = 1 ; p15.w2ry = 1
conn = [
# skin-skin
dict(p1=p01, p2=p02, func='SSycte', ycte1=0, ycte2=p02.b),
dict(p1=p01, p2=p04, func='SSxcte', xcte1=0, xcte2=p04.a),
dict(p1=p02, p2=p03, func='SSycte', ycte1=0, ycte2=p03.b),
dict(p1=p02, p2=p05, func='SSxcte', xcte1=0, xcte2=p05.a),
dict(p1=p03, p2=p06, func='SSxcte', xcte1=0, xcte2=p06.a),
dict(p1=p04, p2=p05, func='SSycte', ycte1=0, ycte2=p05.b),
dict(p1=p04, p2=p07, func='SSxcte', xcte1=0, xcte2=p07.a),
dict(p1=p05, p2=p06, func='SSycte', ycte1=0, ycte2=p06.b),
dict(p1=p05, p2=p08, func='SSxcte', xcte1=0, xcte2=p08.a),
dict(p1=p06, p2=p09, func='SSxcte', xcte1=0, xcte2=p09.a),
dict(p1=p07, p2=p08, func='SSycte', ycte1=0, ycte2=p08.b),
dict(p1=p08, p2=p09, func='SSycte', ycte1=0, ycte2=p09.b),
# skin-base
dict(p1=p02, p2=p10, func='SB'),
dict(p1=p05, p2=p12, func='SB', has_defect=has_defect), # defect
dict(p1=p08, p2=p14, func='SB'),
# base-base
dict(p1=p10, p2=p12, func='SSxcte', xcte1=0, xcte2=p12.a),
dict(p1=p12, p2=p14, func='SSxcte', xcte1=0, xcte2=p14.a),
# base-flange
dict(p1=p10, p2=p11, func='BFycte', ycte1=p10.b/2., ycte2=0),
dict(p1=p12, p2=p13, func='BFycte', ycte1=p12.b/2., ycte2=0),
dict(p1=p14, p2=p15, func='BFycte', ycte1=p14.b/2., ycte2=0),
# flange-flange
dict(p1=p11, p2=p13, func='SSxcte', xcte1=0, xcte2=p13.a),
dict(p1=p13, p2=p15, func='SSxcte', xcte1=0, xcte2=p15.a),
]
panels = [p01, p02, p03, p04, p05, p06, p07, p08, p09,
p10, p11, p12, p13, p14, p15]
skin = [p01, p02, p03, p04, p05, p06, p07, p08, p09]
base = [p10, p12, p14]
flange = [p11, p13, p15]
assy = PanelAssembly(panels)
size = assy.get_size()
valid_conn = []
for connecti in conn:
if connecti.get('has_defect'):
continue
valid_conn.append(connecti)
k0 = assy.calc_k0(conn=valid_conn)
kM = assy.calc_kM()
eigvals, eigvecs = freq(k0, kM, tol=0, sparse_solver=True, silent=True,
sort=True, reduced_dof=False,
num_eigvalues=25, num_eigvalues_print=5)
return assy, eigvals, eigvecs
def tstiff2d_1stiff_flutter(a, b, ys, bb, bf, defect_a, mu, plyt,
laminaprop, stack_skin, stack_base, stack_flange,
air_speed=None, rho_air=None, Mach=None, speed_sound=None, flow='x',
Nxx_skin=None, Nxx_base=None, Nxx_flange=None, run_static_case=True,
r=None, m=8, n=8, mb=None, nb=None, mf=None, nf=None):
r"""Flutter of T-Stiffened Panel with possible defect at middle
For more details about each parameter and the aerodynamic formulation see
Ref. [castro2016FlutterPanel]_ .
The panel assembly looks like::
skin
_________ _____ _________
| | | |
| | | |
| p01 | p02 | p03 |
| | | |
|_________|_____|_________|
| p04 | p05 | p06 | /\ x
|_________|_____|_________| |
| | | | |
| | | | |
| p07 | p08 | p09 |
| | | |
| | | |
|_________|_____|_________|
loaded edge
base flange
_____ _____
| | | |
| | | |
| p10 | | p11 |
| | | |
|_____| |_____|
| p12 | | p13 |
|_____| |_____|
| | | |
| | | |
| p14 | | p15 |
| | | |
| | | |
|_____| |_____|
loaded edge loaded edge
Parameters
----------
a : float
Total length of the assembly (along `x`).
b : float
Total width of the assembly (along `y`).
ys : float
Position of the stiffener along `y`.
bb : float
Stiffener's base width.
bf : float
Stiffener's flange width.
defect_a : float
Debonding defect/assembly length ratio.
mu : float
Material density.
plyt : float
Ply thickness.
laminaprop : list or tuple
Orthotropic lamina properties: `E_1, E_2, \nu_{12}, G_{12}, G_{13}, G_{23}`.
stack_skin : list or tuple
Stacking sequence for the skin.
stack_base : list or tuple
Stacking sequence for the stiffener's base.
stack_flange : list or tuple
Stacking sequence for the stiffener's flange.
air_speed : float
Airflow speed.
rho_air : float
Air density.
Mach : float
Mach number.
speed_sound : float
Speed of sound.
flow : "x" or "y"
Direction of airflow.
Nxx_skin : float
Skin load distributed at the assembly edge at `x=0`.
Nxx_base : float
Stiffener's base load distributed at the assembly edge at `x=0`.
Nxx_flange : float
Stiffener's flange load distributed at the assembly edge at `x=0`.
run_static_case : bool, optional
If True a static analysis is run before the linear buckling analysis
to compute the real membrane stress state along the domain, otherwise
it is assumed constant values of `N_{xx}` for all components.
r : float or None, optional
Radius of the stiffened panel.
m, n : int, optional
Number of terms of the approximation function for the skin.
mb, nb : int, optional
Number of terms of the approximation function for the stiffener's base.
mf, nf : int, optional
Number of terms of the approximation function for the stiffener's
flange.
Examples
--------
The following example is one of the test cases:
.. literalinclude:: ../../../../../compmech/panel/assembly/tests/test_tstiff2d_assembly.py
:pyobject: test_tstiff2d_1stiff_flutter
"""
defect = defect_a * a
has_defect = True if defect > 0 else False
defect = 0.33*a if defect == 0 else defect # to avoid weird domains
aup = (a - defect)/2.
alow = (a - defect)/2.
bleft = b - ys - bb/2.
bright = ys - bb/2.
mb = m if mb is None else mb
nb = n if nb is None else nb
mf = m if mf is None else mf
nf = n if nf is None else nf
# skin panels
p01 = Panel(group='skin', Nxx=Nxx_skin, x0=alow+defect, y0=ys+bb/2., a=aup, b=bleft, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu, rho_air=rho_air, speed_sound=speed_sound, Mach=Mach, V=air_speed, flow=flow)
p02 = Panel(group='skin', Nxx=Nxx_skin, x0=alow+defect, y0=ys-bb/2., a=aup, b=bb, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu, rho_air=rho_air, speed_sound=speed_sound, Mach=Mach, V=air_speed, flow=flow)
p03 = Panel(group='skin', Nxx=Nxx_skin, x0=alow+defect, y0=0, a=aup, b=bright, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu, rho_air=rho_air, speed_sound=speed_sound, Mach=Mach, V=air_speed, flow=flow)
# defect
p04 = Panel(group='skin', Nxx=Nxx_skin, x0=alow, y0=ys+bb/2., a=defect, b=bleft, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu, rho_air=rho_air, speed_sound=speed_sound, Mach=Mach, V=air_speed, flow=flow)
p05 = Panel(group='skin', Nxx=Nxx_skin, x0=alow, y0=ys-bb/2., a=defect, b=bb, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu, rho_air=rho_air, speed_sound=speed_sound, Mach=Mach, V=air_speed, flow=flow)
p06 = Panel(group='skin', Nxx=Nxx_skin, x0=alow, y0=0, a=defect, b=bright, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu, rho_air=rho_air, speed_sound=speed_sound, Mach=Mach, V=air_speed, flow=flow)
#
p07 = Panel(group='skin', Nxx=Nxx_skin, x0=0, y0=ys+bb/2., a=alow, b=bleft, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu, rho_air=rho_air, speed_sound=speed_sound, Mach=Mach, V=air_speed, flow=flow)
p08 = Panel(group='skin', Nxx=Nxx_skin, x0=0, y0=ys-bb/2., a=alow, b=bb, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu, rho_air=rho_air, speed_sound=speed_sound, Mach=Mach, V=air_speed, flow=flow)
p09 = Panel(group='skin', Nxx=Nxx_skin, x0=0, y0=0, a=alow, b=bright, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu, rho_air=rho_air, speed_sound=speed_sound, Mach=Mach, V=air_speed, flow=flow)
# stiffeners
p10 = Panel(group='base', Nxx=Nxx_base, x0=alow+defect, y0=ys-bb/2., a=aup, b=bb, r=r, m=mb, n=nb, plyt=plyt, stack=stack_base, laminaprop=laminaprop, mu=mu)
p11 = Panel(group='flange', Nxx=Nxx_flange, x0=alow+defect, y0=0, a=aup, b=bf, m=mf, n=nf, plyt=plyt, stack=stack_flange, laminaprop=laminaprop, mu=mu)
# defect
p12 = Panel(group='base', Nxx=Nxx_base, x0=alow, y0=ys-bb/2., a=defect, b=bb, r=r, m=mb, n=nb, plyt=plyt, stack=stack_base, laminaprop=laminaprop, mu=mu)
p13 = Panel(group='flange', Nxx=Nxx_flange, x0=alow, y0=0, a=defect, b=bf, m=mf, n=nf, plyt=plyt, stack=stack_flange, laminaprop=laminaprop, mu=mu)
#
p14 = Panel(group='base', Nxx=Nxx_base, x0=0, y0=ys-bb/2., a=alow, b=bb, r=r, m=mb, n=nb, plyt=plyt, stack=stack_base, laminaprop=laminaprop, mu=mu)
p15 = Panel(group='flange', Nxx=Nxx_flange, x0=0, y0=0, a=alow, b=bf, m=mf, n=nf, plyt=plyt, stack=stack_flange, laminaprop=laminaprop, mu=mu)
# boundary conditions
p01.u1tx = 1 ; p01.u1rx = 1 ; p01.u2tx = 0 ; p01.u2rx = 1
p01.v1tx = 1 ; p01.v1rx = 1 ; p01.v2tx = 0 ; p01.v2rx = 1
p01.w1tx = 1 ; p01.w1rx = 1 ; p01.w2tx = 0 ; p01.w2rx = 1
p01.u1ty = 1 ; p01.u1ry = 1 ; p01.u2ty = 1 ; p01.u2ry = 1
p01.v1ty = 1 ; p01.v1ry = 1 ; p01.v2ty = 0 ; p01.v2ry = 1
p01.w1ty = 1 ; p01.w1ry = 1 ; p01.w2ty = 0 ; p01.w2ry = 1
p02.u1tx = 1 ; p02.u1rx = 1 ; p02.u2tx = 0 ; p02.u2rx = 1
p02.v1tx = 1 ; p02.v1rx = 1 ; p02.v2tx = 0 ; p02.v2rx = 1
p02.w1tx = 1 ; p02.w1rx = 1 ; p02.w2tx = 0 ; p02.w2rx = 1
p02.u1ty = 1 ; p02.u1ry = 1 ; p02.u2ty = 1 ; p02.u2ry = 1
p02.v1ty = 1 ; p02.v1ry = 1 ; p02.v2ty = 1 ; p02.v2ry = 1
p02.w1ty = 1 ; p02.w1ry = 1 ; p02.w2ty = 1 ; p02.w2ry = 1
p03.u1tx = 1 ; p03.u1rx = 1 ; p03.u2tx = 0 ; p03.u2rx = 1
p03.v1tx = 1 ; p03.v1rx = 1 ; p03.v2tx = 0 ; p03.v2rx = 1
p03.w1tx = 1 ; p03.w1rx = 1 ; p03.w2tx = 0 ; p03.w2rx = 1
p03.u1ty = 1 ; p03.u1ry = 1 ; p03.u2ty = 1 ; p03.u2ry = 1
p03.v1ty = 0 ; p03.v1ry = 1 ; p03.v2ty = 1 ; p03.v2ry = 1
p03.w1ty = 0 ; p03.w1ry = 1 ; p03.w2ty = 1 ; p03.w2ry = 1
p04.u1tx = 1 ; p04.u1rx = 1 ; p04.u2tx = 1 ; p04.u2rx = 1
p04.v1tx = 1 ; p04.v1rx = 1 ; p04.v2tx = 1 ; p04.v2rx = 1
p04.w1tx = 1 ; p04.w1rx = 1 ; p04.w2tx = 1 ; p04.w2rx = 1
p04.u1ty = 1 ; p04.u1ry = 1 ; p04.u2ty = 1 ; p04.u2ry = 1
p04.v1ty = 1 ; p04.v1ry = 1 ; p04.v2ty = 0 ; p04.v2ry = 1
p04.w1ty = 1 ; p04.w1ry = 1 ; p04.w2ty = 0 ; p04.w2ry = 1
p05.u1tx = 1 ; p05.u1rx = 1 ; p05.u2tx = 1 ; p05.u2rx = 1
p05.v1tx = 1 ; p05.v1rx = 1 ; p05.v2tx = 1 ; p05.v2rx = 1
p05.w1tx = 1 ; p05.w1rx = 1 ; p05.w2tx = 1 ; p05.w2rx = 1
p05.u1ty = 1 ; p05.u1ry = 1 ; p05.u2ty = 1 ; p05.u2ry = 1
p05.v1ty = 1 ; p05.v1ry = 1 ; p05.v2ty = 1 ; p05.v2ry = 1
p05.w1ty = 1 ; p05.w1ry = 1 ; p05.w2ty = 1 ; p05.w2ry = 1
p06.u1tx = 1 ; p06.u1rx = 1 ; p06.u2tx = 1 ; p06.u2rx = 1
p06.v1tx = 1 ; p06.v1rx = 1 ; p06.v2tx = 1 ; p06.v2rx = 1
p06.w1tx = 1 ; p06.w1rx = 1 ; p06.w2tx = 1 ; p06.w2rx = 1
p06.u1ty = 1 ; p06.u1ry = 1 ; p06.u2ty = 1 ; p06.u2ry = 1
p06.v1ty = 0 ; p06.v1ry = 1 ; p06.v2ty = 1 ; p06.v2ry = 1
p06.w1ty = 0 ; p06.w1ry = 1 ; p06.w2ty = 1 ; p06.w2ry = 1
p07.u1tx = 1 ; p07.u1rx = 1 ; p07.u2tx = 1 ; p07.u2rx = 1
p07.v1tx = 0 ; p07.v1rx = 1 ; p07.v2tx = 1 ; p07.v2rx = 1
p07.w1tx = 0 ; p07.w1rx = 1 ; p07.w2tx = 1 ; p07.w2rx = 1
p07.u1ty = 1 ; p07.u1ry = 1 ; p07.u2ty = 1 ; p07.u2ry = 1
p07.v1ty = 1 ; p07.v1ry = 1 ; p07.v2ty = 0 ; p07.v2ry = 1
p07.w1ty = 1 ; p07.w1ry = 1 ; p07.w2ty = 0 ; p07.w2ry = 1
p08.u1tx = 1 ; p08.u1rx = 1 ; p08.u2tx = 1 ; p08.u2rx = 1
p08.v1tx = 0 ; p08.v1rx = 1 ; p08.v2tx = 1 ; p08.v2rx = 1
p08.w1tx = 0 ; p08.w1rx = 1 ; p08.w2tx = 1 ; p08.w2rx = 1
p08.u1ty = 1 ; p08.u1ry = 1 ; p08.u2ty = 1 ; p08.u2ry = 1
p08.v1ty = 1 ; p08.v1ry = 1 ; p08.v2ty = 1 ; p08.v2ry = 1
p08.w1ty = 1 ; p08.w1ry = 1 ; p08.w2ty = 1 ; p08.w2ry = 1
p09.u1tx = 1 ; p09.u1rx = 1 ; p09.u2tx = 1 ; p09.u2rx = 1
p09.v1tx = 0 ; p09.v1rx = 1 ; p09.v2tx = 1 ; p09.v2rx = 1
p09.w1tx = 0 ; p09.w1rx = 1 ; p09.w2tx = 1 ; p09.w2rx = 1
p09.u1ty = 1 ; p09.u1ry = 1 ; p09.u2ty = 1 ; p09.u2ry = 1
p09.v1ty = 0 ; p09.v1ry = 1 ; p09.v2ty = 1 ; p09.v2ry = 1
p09.w1ty = 0 ; p09.w1ry = 1 ; p09.w2ty = 1 ; p09.w2ry = 1
# base up
p10.u1tx = 1 ; p10.u1rx = 1 ; p10.u2tx = 1 ; p10.u2rx = 1
p10.v1tx = 1 ; p10.v1rx = 1 ; p10.v2tx = 1 ; p10.v2rx = 1
p10.w1tx = 1 ; p10.w1rx = 1 ; p10.w2tx = 1 ; p10.w2rx = 1
p10.u1ty = 1 ; p10.u1ry = 1 ; p10.u2ty = 1 ; p10.u2ry = 1
p10.v1ty = 1 ; p10.v1ry = 1 ; p10.v2ty = 1 ; p10.v2ry = 1
p10.w1ty = 1 ; p10.w1ry = 1 ; p10.w2ty = 1 ; p10.w2ry = 1
# flange up
p11.u1tx = 1 ; p11.u1rx = 1 ; p11.u2tx = 0 ; p11.u2rx = 1
p11.v1tx = 1 ; p11.v1rx = 1 ; p11.v2tx = 0 ; p11.v2rx = 1
p11.w1tx = 1 ; p11.w1rx = 1 ; p11.w2tx = 0 ; p11.w2rx = 1
p11.u1ty = 1 ; p11.u1ry = 1 ; p11.u2ty = 1 ; p11.u2ry = 1
p11.v1ty = 1 ; p11.v1ry = 1 ; p11.v2ty = 1 ; p11.v2ry = 1
p11.w1ty = 1 ; p11.w1ry = 1 ; p11.w2ty = 1 ; p11.w2ry = 1
# base mid
p12.u1tx = 1 ; p12.u1rx = 1 ; p12.u2tx = 1 ; p12.u2rx = 1
p12.v1tx = 1 ; p12.v1rx = 1 ; p12.v2tx = 1 ; p12.v2rx = 1
p12.w1tx = 1 ; p12.w1rx = 1 ; p12.w2tx = 1 ; p12.w2rx = 1
p12.u1ty = 1 ; p12.u1ry = 1 ; p12.u2ty = 1 ; p12.u2ry = 1
p12.v1ty = 1 ; p12.v1ry = 1 ; p12.v2ty = 1 ; p12.v2ry = 1
p12.w1ty = 1 ; p12.w1ry = 1 ; p12.w2ty = 1 ; p12.w2ry = 1
# flange mid
p13.u1tx = 1 ; p13.u1rx = 1 ; p13.u2tx = 1 ; p13.u2rx = 1
p13.v1tx = 1 ; p13.v1rx = 1 ; p13.v2tx = 1 ; p13.v2rx = 1
p13.w1tx = 1 ; p13.w1rx = 1 ; p13.w2tx = 1 ; p13.w2rx = 1
p13.u1ty = 1 ; p13.u1ry = 1 ; p13.u2ty = 1 ; p13.u2ry = 1
p13.v1ty = 1 ; p13.v1ry = 1 ; p13.v2ty = 1 ; p13.v2ry = 1
p13.w1ty = 1 ; p13.w1ry = 1 ; p13.w2ty = 1 ; p13.w2ry = 1
# base low
p14.u1tx = 1 ; p14.u1rx = 1 ; p14.u2tx = 1 ; p14.u2rx = 1
p14.v1tx = 1 ; p14.v1rx = 1 ; p14.v2tx = 1 ; p14.v2rx = 1
p14.w1tx = 1 ; p14.w1rx = 1 ; p14.w2tx = 1 ; p14.w2rx = 1
p14.u1ty = 1 ; p14.u1ry = 1 ; p14.u2ty = 1 ; p14.u2ry = 1
p14.v1ty = 1 ; p14.v1ry = 1 ; p14.v2ty = 1 ; p14.v2ry = 1
p14.w1ty = 1 ; p14.w1ry = 1 ; p14.w2ty = 1 ; p14.w2ry = 1
# flange low
p15.u1tx = 1 ; p15.u1rx = 1 ; p15.u2tx = 1 ; p15.u2rx = 1
p15.v1tx = 0 ; p15.v1rx = 1 ; p15.v2tx = 1 ; p15.v2rx = 1
p15.w1tx = 0 ; p15.w1rx = 1 ; p15.w2tx = 1 ; p15.w2rx = 1
p15.u1ty = 1 ; p15.u1ry = 1 ; p15.u2ty = 1 ; p15.u2ry = 1
p15.v1ty = 1 ; p15.v1ry = 1 ; p15.v2ty = 1 ; p15.v2ry = 1
p15.w1ty = 1 ; p15.w1ry = 1 ; p15.w2ty = 1 ; p15.w2ry = 1
conn = [
# skin-skin
dict(p1=p01, p2=p02, func='SSycte', ycte1=0, ycte2=p02.b),
dict(p1=p01, p2=p04, func='SSxcte', xcte1=0, xcte2=p04.a),
dict(p1=p02, p2=p03, func='SSycte', ycte1=0, ycte2=p03.b),
dict(p1=p02, p2=p05, func='SSxcte', xcte1=0, xcte2=p05.a),
dict(p1=p03, p2=p06, func='SSxcte', xcte1=0, xcte2=p06.a),
dict(p1=p04, p2=p05, func='SSycte', ycte1=0, ycte2=p05.b),
dict(p1=p04, p2=p07, func='SSxcte', xcte1=0, xcte2=p07.a),
dict(p1=p05, p2=p06, func='SSycte', ycte1=0, ycte2=p06.b),
dict(p1=p05, p2=p08, func='SSxcte', xcte1=0, xcte2=p08.a),
dict(p1=p06, p2=p09, func='SSxcte', xcte1=0, xcte2=p09.a),
dict(p1=p07, p2=p08, func='SSycte', ycte1=0, ycte2=p08.b),
dict(p1=p08, p2=p09, func='SSycte', ycte1=0, ycte2=p09.b),
# skin-base
dict(p1=p02, p2=p10, func='SB'),
dict(p1=p05, p2=p12, func='SB', has_defect=has_defect), # defect
dict(p1=p08, p2=p14, func='SB'),
# base-base
dict(p1=p10, p2=p12, func='SSxcte', xcte1=0, xcte2=p12.a),
dict(p1=p12, p2=p14, func='SSxcte', xcte1=0, xcte2=p14.a),
# base-flange
dict(p1=p10, p2=p11, func='BFycte', ycte1=p10.b/2., ycte2=0),
dict(p1=p12, p2=p13, func='BFycte', ycte1=p12.b/2., ycte2=0),
dict(p1=p14, p2=p15, func='BFycte', ycte1=p14.b/2., ycte2=0),
# flange-flange
dict(p1=p11, p2=p13, func='SSxcte', xcte1=0, xcte2=p13.a),
dict(p1=p13, p2=p15, func='SSxcte', xcte1=0, xcte2=p15.a),
]
panels = [p01, p02, p03, p04, p05, p06, p07, p08, p09,
p10, p11, p12, p13, p14, p15]
skin = [p01, p02, p03, p04, p05, p06, p07, p08, p09]
assy = PanelAssembly(panels)
size = assy.get_size()
valid_conn = []
for connecti in conn:
if connecti.get('has_defect'): # connecting if there is no defect
continue
valid_conn.append(connecti)
k0 = assy.calc_k0(valid_conn)
c = None
if (run_static_case and not
(Nxx_skin is None and Nxx_base is None and Nxx_flange is None)):
fext = np.zeros(size)
for p in [p07, p08, p09, p14, p15]:
Nforces = 100
fx = p.Nxx*p.b/(Nforces-1.)
for i in range(Nforces):
y = i*p.b/(Nforces-1.)
if i == 0 or i == (Nforces - 1):
p.add_force(0, y, fx/2., 0, 0)
else:
p.add_force(0, y, fx, 0, 0)
fext[p.col_start: p.col_end] = p.calc_fext(silent=True)
incs, cs = static(k0, -fext, silent=True)
c = cs[0]
kM = assy.calc_kM()
kG = assy.calc_kG0(c=c)
kA = 0
for p in skin:
# TODO the current approach has somewhat hiden settings
# check this strategy:
# - define module aerodynamics
# - function calc_kA inside a module piston_theory
# - pass piston_theory parameters and compute kA
kA += p.calc_kA(size=size, row0=p.row_start, col0=p.col_start, silent=True, finalize=False)
assert np.any(np.isnan(kA.data)) == False
assert np.any(np.isinf(kA.data)) == False
kA = csr_matrix(make_skew_symmetric(kA))
eigvals, eigvecs = freq((k0 + kG + kA), kM, tol=0, sparse_solver=True, silent=True,
sort=True, reduced_dof=False,
num_eigvalues=25, num_eigvalues_print=5)
if run_static_case:
return assy, c, eigvals, eigvecs
else:
return assy, eigvals, eigvecs
def tstiff2d_1stiff_freq(a,
b,
ys,
bb,
bf,
defect_a,
mu,
plyt,
laminaprop,
stack_skin,
stack_base,
stack_flange,
r=None,
m=8,
n=8,
mb=None,
nb=None,
mf=None,
nf=None):
r"""Frequency T-Stiffened Panel with possible defect at middle
For more details about each parameter and the aerodynamic formulation see
Ref. [castro2016FlutterPanel]_ .
For more details about the theory involved on the assembly of panels, see
[castro2017AssemblyModels]_.
The panel assembly looks like::
skin
_________ _____ _________
| | | |
| | | |
| p01 | p02 | p03 |
| | | |
|_________|_____|_________|
| p04 | p05 | p06 |
|_________|_____|_________|
| | | |
| | | |
| p07 | p08 | p09 |
| | | |
| | | |
|_________|_____|_________|
base flange
_____ _____
| | | |
| | | |
| p10 | | p11 |
| | | |
|_____| |_____|
| p12 | | p13 |
|_____| |_____|
| | | |
| | | |
| p14 | | p15 |
| | | |
| | | |
|_____| |_____|
Parameters
----------
a : float
Total length of the assembly (along `x`).
b : float
Total width of the assembly (along `y`).
ys : float
Position of the stiffener along `y`.
bb : float
Stiffener's base width.
bf : float
Stiffener's flange width.
defect_a : float
Debonding defect/assembly length ratio.
mu : float
Material density.
plyt : float
Ply thickness.
laminaprop : list or tuple
Orthotropic lamina properties: `E_1, E_2, \nu_{12}, G_{12}, G_{13}, G_{23}`.
stack_skin : list or tuple
Stacking sequence for the skin.
stack_base : list or tuple
Stacking sequence for the stiffener's base.
stack_flange : list or tuple
Stacking sequence for the stiffener's flange.
r : float or None, optional
Radius of the stiffened panel.
m, n : int, optional
Number of terms of the approximation function for the skin.
mb, nb : int, optional
Number of terms of the approximation function for the stiffener's base.
mf, nf : int, optional
Number of terms of the approximation function for the stiffener's
flange.
Examples
--------
The following example is one of the test cases:
.. literalinclude:: ../../../../../compmech/panel/assembly/tests/test_tstiff2d_assembly.py
:pyobject: test_tstiff2d_1stiff_freq
"""
defect = defect_a * a
has_defect = True if defect > 0 else False
defect = 0.33 * a if defect == 0 else defect # to avoid weird domains
aup = (a - defect) / 2.
alow = (a - defect) / 2.
bleft = b - ys - bb / 2.
bright = ys - bb / 2.
mb = m if mb is None else mb
nb = n if nb is None else nb
mf = m if mf is None else mf
nf = n if nf is None else nf
# skin panels
p01 = Panel(group='skin',
x0=alow + defect,
y0=ys + bb / 2.,
a=aup,
b=bleft,
r=r,
m=m,
n=n,
plyt=plyt,
stack=stack_skin,
laminaprop=laminaprop,
mu=mu)
p02 = Panel(group='skin',
x0=alow + defect,
y0=ys - bb / 2.,
a=aup,
b=bb,
r=r,
m=m,
n=n,
plyt=plyt,
stack=stack_skin,
laminaprop=laminaprop,
mu=mu)
p03 = Panel(group='skin',
x0=alow + defect,
y0=0,
a=aup,
b=bright,
r=r,
m=m,
n=n,
plyt=plyt,
stack=stack_skin,
laminaprop=laminaprop,
mu=mu)
# defect
p04 = Panel(group='skin',
x0=alow,
y0=ys + bb / 2.,
a=defect,
b=bleft,
r=r,
m=m,
n=n,
plyt=plyt,
stack=stack_skin,
laminaprop=laminaprop,
mu=mu)
p05 = Panel(group='skin',
x0=alow,
y0=ys - bb / 2.,
a=defect,
b=bb,
r=r,
m=m,
n=n,
plyt=plyt,
stack=stack_skin,
laminaprop=laminaprop,
mu=mu)
p06 = Panel(group='skin',
x0=alow,
y0=0,
a=defect,
b=bright,
r=r,
m=m,
n=n,
plyt=plyt,
stack=stack_skin,
laminaprop=laminaprop,
mu=mu)
#
p07 = Panel(group='skin',
x0=0,
y0=ys + bb / 2.,
a=alow,
b=bleft,
r=r,
m=m,
n=n,
plyt=plyt,
stack=stack_skin,
laminaprop=laminaprop,
mu=mu)
p08 = Panel(group='skin',
x0=0,
y0=ys - bb / 2.,
a=alow,
b=bb,
r=r,
m=m,
n=n,
plyt=plyt,
stack=stack_skin,
laminaprop=laminaprop,
mu=mu)
p09 = Panel(group='skin',
x0=0,
y0=0,
a=alow,
b=bright,
r=r,
m=m,
n=n,
plyt=plyt,
stack=stack_skin,
laminaprop=laminaprop,
mu=mu)
# stiffeners
p10 = Panel(group='base',
x0=alow + defect,
y0=ys - bb / 2.,
a=aup,
b=bb,
r=r,
m=mb,
n=nb,
plyt=plyt,
stack=stack_base,
laminaprop=laminaprop,
mu=mu)
p11 = Panel(group='flange',
x0=alow + defect,
y0=0,
a=aup,
b=bf,
m=mf,
n=nf,
plyt=plyt,
stack=stack_flange,
laminaprop=laminaprop,
mu=mu)
# defect
p12 = Panel(group='base',
x0=alow,
y0=ys - bb / 2.,
a=defect,
b=bb,
r=r,
m=mb,
n=nb,
plyt=plyt,
stack=stack_base,
laminaprop=laminaprop,
mu=mu)
p13 = Panel(group='flange',
x0=alow,
y0=0,
a=defect,
b=bf,
m=mf,
n=nf,
plyt=plyt,
stack=stack_flange,
laminaprop=laminaprop,
mu=mu)
#
p14 = Panel(group='base',
x0=0,
y0=ys - bb / 2.,
a=alow,
b=bb,
r=r,
m=mb,
n=nb,
plyt=plyt,
stack=stack_base,
laminaprop=laminaprop,
mu=mu)
p15 = Panel(group='flange',
x0=0,
y0=0,
a=alow,
b=bf,
m=mf,
n=nf,
plyt=plyt,
stack=stack_flange,
laminaprop=laminaprop,
mu=mu)
# boundary conditions
p01.u1tx = 1
p01.u1rx = 1
p01.u2tx = 0
p01.u2rx = 1
p01.v1tx = 1
p01.v1rx = 1
p01.v2tx = 0
p01.v2rx = 1
p01.w1tx = 1
p01.w1rx = 1
p01.w2tx = 0
p01.w2rx = 1
p01.u1ty = 1
p01.u1ry = 1
p01.u2ty = 0
p01.u2ry = 1
p01.v1ty = 1
p01.v1ry = 1
p01.v2ty = 0
p01.v2ry = 1
p01.w1ty = 1
p01.w1ry = 1
p01.w2ty = 0
p01.w2ry = 1
p02.u1tx = 1
p02.u1rx = 1
p02.u2tx = 0
p02.u2rx = 1
p02.v1tx = 1
p02.v1rx = 1
p02.v2tx = 0
p02.v2rx = 1
p02.w1tx = 1
p02.w1rx = 1
p02.w2tx = 0
p02.w2rx = 1
p02.u1ty = 1
p02.u1ry = 1
p02.u2ty = 1
p02.u2ry = 1
p02.v1ty = 1
p02.v1ry = 1
p02.v2ty = 1
p02.v2ry = 1
p02.w1ty = 1
p02.w1ry = 1
p02.w2ty = 1
p02.w2ry = 1
p03.u1tx = 1
p03.u1rx = 1
p03.u2tx = 0
p03.u2rx = 1
p03.v1tx = 1
p03.v1rx = 1
p03.v2tx = 0
p03.v2rx = 1
p03.w1tx = 1
p03.w1rx = 1
p03.w2tx = 0
p03.w2rx = 1
p03.u1ty = 0
p03.u1ry = 1
p03.u2ty = 1
p03.u2ry = 1
p03.v1ty = 0
p03.v1ry = 1
p03.v2ty = 1
p03.v2ry = 1
p03.w1ty = 0
p03.w1ry = 1
p03.w2ty = 1
p03.w2ry = 1
p04.u1tx = 1
p04.u1rx = 1
p04.u2tx = 1
p04.u2rx = 1
p04.v1tx = 1
p04.v1rx = 1
p04.v2tx = 1
p04.v2rx = 1
p04.w1tx = 1
p04.w1rx = 1
p04.w2tx = 1
p04.w2rx = 1
p04.u1ty = 1
p04.u1ry = 1
p04.u2ty = 0
p04.u2ry = 1
p04.v1ty = 1
p04.v1ry = 1
p04.v2ty = 0
p04.v2ry = 1
p04.w1ty = 1
p04.w1ry = 1
p04.w2ty = 0
p04.w2ry = 1
p05.u1tx = 1
p05.u1rx = 1
p05.u2tx = 1
p05.u2rx = 1
p05.v1tx = 1
p05.v1rx = 1
p05.v2tx = 1
p05.v2rx = 1
p05.w1tx = 1
p05.w1rx = 1
p05.w2tx = 1
p05.w2rx = 1
p05.u1ty = 1
p05.u1ry = 1
p05.u2ty = 1
p05.u2ry = 1
p05.v1ty = 1
p05.v1ry = 1
p05.v2ty = 1
p05.v2ry = 1
p05.w1ty = 1
p05.w1ry = 1
p05.w2ty = 1
p05.w2ry = 1
p06.u1tx = 1
p06.u1rx = 1
p06.u2tx = 1
p06.u2rx = 1
p06.v1tx = 1
p06.v1rx = 1
p06.v2tx = 1
p06.v2rx = 1
p06.w1tx = 1
p06.w1rx = 1
p06.w2tx = 1
p06.w2rx = 1
p06.u1ty = 0
p06.u1ry = 1
p06.u2ty = 1
p06.u2ry = 1
p06.v1ty = 0
p06.v1ry = 1
p06.v2ty = 1
p06.v2ry = 1
p06.w1ty = 0
p06.w1ry = 1
p06.w2ty = 1
p06.w2ry = 1
p07.u1tx = 0
p07.u1rx = 1
p07.u2tx = 1
p07.u2rx = 1
p07.v1tx = 0
p07.v1rx = 1
p07.v2tx = 1
p07.v2rx = 1
p07.w1tx = 0
p07.w1rx = 1
p07.w2tx = 1
p07.w2rx = 1
p07.u1ty = 1
p07.u1ry = 1
p07.u2ty = 0
p07.u2ry = 1
p07.v1ty = 1
p07.v1ry = 1
p07.v2ty = 0
p07.v2ry = 1
p07.w1ty = 1
p07.w1ry = 1
p07.w2ty = 0
p07.w2ry = 1
p08.u1tx = 0
p08.u1rx = 1
p08.u2tx = 1
p08.u2rx = 1
p08.v1tx = 0
p08.v1rx = 1
p08.v2tx = 1
p08.v2rx = 1
p08.w1tx = 0
p08.w1rx = 1
p08.w2tx = 1
p08.w2rx = 1
p08.u1ty = 1
p08.u1ry = 1
p08.u2ty = 1
p08.u2ry = 1
p08.v1ty = 1
p08.v1ry = 1
p08.v2ty = 1
p08.v2ry = 1
p08.w1ty = 1
p08.w1ry = 1
p08.w2ty = 1
p08.w2ry = 1
p09.u1tx = 0
p09.u1rx = 1
p09.u2tx = 1
p09.u2rx = 1
p09.v1tx = 0
p09.v1rx = 1
p09.v2tx = 1
p09.v2rx = 1
p09.w1tx = 0
p09.w1rx = 1
p09.w2tx = 1
p09.w2rx = 1
p09.u1ty = 0
p09.u1ry = 1
p09.u2ty = 1
p09.u2ry = 1
p09.v1ty = 0
p09.v1ry = 1
p09.v2ty = 1
p09.v2ry = 1
p09.w1ty = 0
p09.w1ry = 1
p09.w2ty = 1
p09.w2ry = 1
# base up
p10.u1tx = 1
p10.u1rx = 1
p10.u2tx = 1
p10.u2rx = 1
p10.v1tx = 1
p10.v1rx = 1
p10.v2tx = 1
p10.v2rx = 1
p10.w1tx = 1
p10.w1rx = 1
p10.w2tx = 1
p10.w2rx = 1
p10.u1ty = 1
p10.u1ry = 1
p10.u2ty = 1
p10.u2ry = 1
p10.v1ty = 1
p10.v1ry = 1
p10.v2ty = 1
p10.v2ry = 1
p10.w1ty = 1
p10.w1ry = 1
p10.w2ty = 1
p10.w2ry = 1
# flange up
p11.u1tx = 1
p11.u1rx = 1
p11.u2tx = 0
p11.u2rx = 1
p11.v1tx = 1
p11.v1rx = 1
p11.v2tx = 0
p11.v2rx = 1
p11.w1tx = 1
p11.w1rx = 1
p11.w2tx = 0
p11.w2rx = 1
p11.u1ty = 1
p11.u1ry = 1
p11.u2ty = 1
p11.u2ry = 1
p11.v1ty = 1
p11.v1ry = 1
p11.v2ty = 1
p11.v2ry = 1
p11.w1ty = 1
p11.w1ry = 1
p11.w2ty = 1
p11.w2ry = 1
# base mid
p12.u1tx = 1
p12.u1rx = 1
p12.u2tx = 1
p12.u2rx = 1
p12.v1tx = 1
p12.v1rx = 1
p12.v2tx = 1
p12.v2rx = 1
p12.w1tx = 1
p12.w1rx = 1
p12.w2tx = 1
p12.w2rx = 1
p12.u1ty = 1
p12.u1ry = 1
p12.u2ty = 1
p12.u2ry = 1
p12.v1ty = 1
p12.v1ry = 1
p12.v2ty = 1
p12.v2ry = 1
p12.w1ty = 1
p12.w1ry = 1
p12.w2ty = 1
p12.w2ry = 1
# flange mid
p13.u1tx = 1
p13.u1rx = 1
p13.u2tx = 1
p13.u2rx = 1
p13.v1tx = 1
p13.v1rx = 1
p13.v2tx = 1
p13.v2rx = 1
p13.w1tx = 1
p13.w1rx = 1
p13.w2tx = 1
p13.w2rx = 1
p13.u1ty = 1
p13.u1ry = 1
p13.u2ty = 1
p13.u2ry = 1
p13.v1ty = 1
p13.v1ry = 1
p13.v2ty = 1
p13.v2ry = 1
p13.w1ty = 1
p13.w1ry = 1
p13.w2ty = 1
p13.w2ry = 1
# base low
p14.u1tx = 1
p14.u1rx = 1
p14.u2tx = 1
p14.u2rx = 1
p14.v1tx = 1
p14.v1rx = 1
p14.v2tx = 1
p14.v2rx = 1
p14.w1tx = 1
p14.w1rx = 1
p14.w2tx = 1
p14.w2rx = 1
p14.u1ty = 1
p14.u1ry = 1
p14.u2ty = 1
p14.u2ry = 1
p14.v1ty = 1
p14.v1ry = 1
p14.v2ty = 1
p14.v2ry = 1
p14.w1ty = 1
p14.w1ry = 1
p14.w2ty = 1
p14.w2ry = 1
# flange low
p15.u1tx = 0
p15.u1rx = 1
p15.u2tx = 1
p15.u2rx = 1
p15.v1tx = 0
p15.v1rx = 1
p15.v2tx = 1
p15.v2rx = 1
p15.w1tx = 0
p15.w1rx = 1
p15.w2tx = 1
p15.w2rx = 1
p15.u1ty = 1
p15.u1ry = 1
p15.u2ty = 1
p15.u2ry = 1
p15.v1ty = 1
p15.v1ry = 1
p15.v2ty = 1
p15.v2ry = 1
p15.w1ty = 1
p15.w1ry = 1
p15.w2ty = 1
p15.w2ry = 1
conn = [
# skin-skin
dict(p1=p01, p2=p02, func='SSycte', ycte1=0, ycte2=p02.b),
dict(p1=p01, p2=p04, func='SSxcte', xcte1=0, xcte2=p04.a),
dict(p1=p02, p2=p03, func='SSycte', ycte1=0, ycte2=p03.b),
dict(p1=p02, p2=p05, func='SSxcte', xcte1=0, xcte2=p05.a),
dict(p1=p03, p2=p06, func='SSxcte', xcte1=0, xcte2=p06.a),
dict(p1=p04, p2=p05, func='SSycte', ycte1=0, ycte2=p05.b),
dict(p1=p04, p2=p07, func='SSxcte', xcte1=0, xcte2=p07.a),
dict(p1=p05, p2=p06, func='SSycte', ycte1=0, ycte2=p06.b),
dict(p1=p05, p2=p08, func='SSxcte', xcte1=0, xcte2=p08.a),
dict(p1=p06, p2=p09, func='SSxcte', xcte1=0, xcte2=p09.a),
dict(p1=p07, p2=p08, func='SSycte', ycte1=0, ycte2=p08.b),
dict(p1=p08, p2=p09, func='SSycte', ycte1=0, ycte2=p09.b),
# skin-base
dict(p1=p02, p2=p10, func='SB'),
dict(p1=p05, p2=p12, func='SB', has_defect=has_defect), # defect
dict(p1=p08, p2=p14, func='SB'),
# base-base
dict(p1=p10, p2=p12, func='SSxcte', xcte1=0, xcte2=p12.a),
dict(p1=p12, p2=p14, func='SSxcte', xcte1=0, xcte2=p14.a),
# base-flange
dict(p1=p10, p2=p11, func='BFycte', ycte1=p10.b / 2., ycte2=0),
dict(p1=p12, p2=p13, func='BFycte', ycte1=p12.b / 2., ycte2=0),
dict(p1=p14, p2=p15, func='BFycte', ycte1=p14.b / 2., ycte2=0),
# flange-flange
dict(p1=p11, p2=p13, func='SSxcte', xcte1=0, xcte2=p13.a),
dict(p1=p13, p2=p15, func='SSxcte', xcte1=0, xcte2=p15.a),
]
panels = [
p01, p02, p03, p04, p05, p06, p07, p08, p09, p10, p11, p12, p13, p14,
p15
]
skin = [p01, p02, p03, p04, p05, p06, p07, p08, p09]
base = [p10, p12, p14]
flange = [p11, p13, p15]
assy = PanelAssembly(panels)
size = assy.get_size()
valid_conn = []
for connecti in conn:
if connecti.get('has_defect'):
continue
valid_conn.append(connecti)
k0 = assy.calc_k0(conn=valid_conn)
kM = assy.calc_kM()
eigvals, eigvecs = freq(k0,
kM,
tol=0,
sparse_solver=True,
silent=True,
sort=True,
reduced_dof=False,
num_eigvalues=25,
num_eigvalues_print=5)
return assy, eigvals, eigvecs
def test_4panels_kt_kr():
"""Compare result of 4 assembled panels with single-domain results
The panel assembly looks like::
_________ _____
| | |
| | |
| p01 | p02 |
| | |
|_________|_____|
| p03 | p04 |
| | |
| | |
| | |
| | |
| | |
|_________|_____|
"""
print('Testing validity of the default kt and kr values')
plyt = 1.e-3 * 0.125
laminaprop = (142.5e9, 8.7e9, 0.28, 5.1e9, 5.1e9, 5.1e9)
stack = [0, 45, -45, 90, -45, 45, 0]
lam = laminate.read_stack(stack=stack, plyt=plyt, laminaprop=laminaprop)
mu = 1.3e3
r = 10.
m = 8
n = 8
a1 = 1.5
a2 = 1.5
a3 = 2.5
a4 = 2.5
b1 = 1.5
b2 = 0.5
b3 = 1.5
b4 = 0.5
A11 = lam.ABD[0, 0]
A22 = lam.ABD[1, 1]
D11 = lam.ABD[3, 3]
D22 = lam.ABD[4, 4]
p01 = Panel(group='panels',
x0=a3,
y0=b2,
a=a1,
b=b1,
r=r,
m=m,
n=n,
plyt=plyt,
stack=stack,
laminaprop=laminaprop,
mu=mu)
p02 = Panel(group='panels',
x0=a3,
y0=0,
a=a2,
b=b2,
r=r,
m=m,
n=n,
plyt=plyt,
stack=stack,
laminaprop=laminaprop,
mu=mu)
p03 = Panel(group='panels',
x0=0,
y0=b2,
a=a3,
b=b3,
r=r,
m=m,
n=n,
plyt=plyt,
stack=stack,
laminaprop=laminaprop,
mu=mu)
p04 = Panel(group='panels',
x0=0,
y0=0,
a=a4,
b=b4,
r=r,
m=m,
n=n,
plyt=plyt,
stack=stack,
laminaprop=laminaprop,
mu=mu)
kt13, kr13 = connections.calc_kt_kr(p01, p03, 'xcte')
kt24, kr24 = connections.calc_kt_kr(p02, p04, 'xcte')
kt12, kr12 = connections.calc_kt_kr(p01, p02, 'ycte')
kt34, kr34 = connections.calc_kt_kr(p03, p04, 'ycte')
# boundary conditions
p01.u1tx = 1
p01.u1rx = 1
p01.u2tx = 0
p01.u2rx = 1
p01.v1tx = 1
p01.v1rx = 1
p01.v2tx = 0
p01.v2rx = 1
p01.w1tx = 1
p01.w1rx = 1
p01.w2tx = 0
p01.w2rx = 1
p01.u1ty = 1
p01.u1ry = 1
p01.u2ty = 0
p01.u2ry = 1
p01.v1ty = 1
p01.v1ry = 1
p01.v2ty = 0
p01.v2ry = 1
p01.w1ty = 1
p01.w1ry = 1
p01.w2ty = 0
p01.w2ry = 1
p02.u1tx = 1
p02.u1rx = 1
p02.u2tx = 0
p02.u2rx = 1
p02.v1tx = 1
p02.v1rx = 1
p02.v2tx = 0
p02.v2rx = 1
p02.w1tx = 1
p02.w1rx = 1
p02.w2tx = 0
p02.w2rx = 1
p02.u1ty = 0
p02.u1ry = 1
p02.u2ty = 1
p02.u2ry = 1
p02.v1ty = 0
p02.v1ry = 1
p02.v2ty = 1
p02.v2ry = 1
p02.w1ty = 0
p02.w1ry = 1
p02.w2ty = 1
p02.w2ry = 1
p03.u1tx = 0
p03.u1rx = 1
p03.u2tx = 1
p03.u2rx = 1
p03.v1tx = 0
p03.v1rx = 1
p03.v2tx = 1
p03.v2rx = 1
p03.w1tx = 0
p03.w1rx = 1
p03.w2tx = 1
p03.w2rx = 1
p03.u1ty = 1
p03.u1ry = 1
p03.u2ty = 0
p03.u2ry = 1
p03.v1ty = 1
p03.v1ry = 1
p03.v2ty = 0
p03.v2ry = 1
p03.w1ty = 1
p03.w1ry = 1
p03.w2ty = 0
p03.w2ry = 1
p04.u1tx = 0
p04.u1rx = 1
p04.u2tx = 1
p04.u2rx = 1
p04.v1tx = 0
p04.v1rx = 1
p04.v2tx = 1
p04.v2rx = 1
p04.w1tx = 0
p04.w1rx = 1
p04.w2tx = 1
p04.w2rx = 1
p04.u1ty = 0
p04.u1ry = 1
p04.u2ty = 1
p04.u2ry = 1
p04.v1ty = 0
p04.v1ry = 1
p04.v2ty = 1
p04.v2ry = 1
p04.w1ty = 0
p04.w1ry = 1
p04.w2ty = 1
p04.w2ry = 1
conndict = [
dict(p1=p01,
p2=p02,
func='SSycte',
ycte1=0,
ycte2=p02.b,
kt=kt12,
kr=kr12),
dict(p1=p01,
p2=p03,
func='SSxcte',
xcte1=0,
xcte2=p03.a,
kt=kt13,
kr=kr13),
dict(p1=p02,
p2=p04,
func='SSxcte',
xcte1=0,
xcte2=p04.a,
kt=kt24,
kr=kr24),
dict(p1=p03,
p2=p04,
func='SSycte',
ycte1=0,
ycte2=p04.b,
kt=kt34,
kr=kr34),
]
panels = [p01, p02, p03, p04]
size = sum([3 * p.m * p.n for p in panels])
k0 = 0
kM = 0
row0 = 0
col0 = 0
for p in panels:
k0 += p.calc_k0(row0=row0,
col0=col0,
size=size,
silent=True,
finalize=False)
kM += p.calc_kM(row0=row0,
col0=col0,
size=size,
silent=True,
finalize=False)
p.row_start = row0
p.col_start = col0
row0 += 3 * p.m * p.n
col0 += 3 * p.m * p.n
p.row_end = row0
p.col_end = col0
for conn in conndict:
if conn.get('has_deffect'): # connecting if there is no deffect
continue
p1 = conn['p1']
p2 = conn['p2']
if conn['func'] == 'SSycte':
k0 += connections.kCSSycte.fkCSSycte11(conn['kt'],
conn['kr'],
p1,
conn['ycte1'],
size,
p1.row_start,
col0=p1.col_start)
k0 += connections.kCSSycte.fkCSSycte12(conn['kt'],
conn['kr'],
p1,
p2,
conn['ycte1'],
conn['ycte2'],
size,
p1.row_start,
col0=p2.col_start)
k0 += connections.kCSSycte.fkCSSycte22(conn['kt'],
conn['kr'],
p1,
p2,
conn['ycte2'],
size,
p2.row_start,
col0=p2.col_start)
elif conn['func'] == 'SSxcte':
k0 += connections.kCSSxcte.fkCSSxcte11(conn['kt'],
conn['kr'],
p1,
conn['xcte1'],
size,
p1.row_start,
col0=p1.col_start)
k0 += connections.kCSSxcte.fkCSSxcte12(conn['kt'],
conn['kr'],
p1,
p2,
conn['xcte1'],
conn['xcte2'],
size,
p1.row_start,
col0=p2.col_start)
k0 += connections.kCSSxcte.fkCSSxcte22(conn['kt'],
conn['kr'],
p1,
p2,
conn['xcte2'],
size,
p2.row_start,
col0=p2.col_start)
assert np.any(np.isnan(k0.data)) == False
assert np.any(np.isinf(k0.data)) == False
k0 = csr_matrix(make_symmetric(k0))
assert np.any(np.isnan(kM.data)) == False
assert np.any(np.isinf(kM.data)) == False
kM = csr_matrix(make_symmetric(kM))
eigvals, eigvecs = freq(k0,
kM,
tol=0,
sparse_solver=True,
silent=True,
sort=True,
reduced_dof=False,
num_eigvalues=25,
num_eigvalues_print=5)
# Results for single panel
m = 15
n = 15
singlepanel = Panel(a=(a1 + a3),
b=(b1 + b2),
r=r,
m=m,
n=n,
plyt=plyt,
stack=stack,
laminaprop=laminaprop,
mu=mu)
singlepanel.freq(silent=True)
assert np.isclose(eigvals[0], singlepanel.eigvals[0], atol=0.01, rtol=0.01)
def test_4panels_kt_kr():
"""Compare result of 4 assembled panels with single-domain results
The panel assembly looks like::
_________ _____
| | |
| | |
| p01 | p02 |
| | |
|_________|_____|
| p03 | p04 |
| | |
| | |
| | |
| | |
| | |
|_________|_____|
"""
print('Testing validity of the default kt and kr values')
plyt = 1.e-3 * 0.125
laminaprop=(142.5e9, 8.7e9, 0.28, 5.1e9, 5.1e9, 5.1e9)
stack=[0, 45, -45, 90, -45, 45, 0]
lam = laminate.read_stack(stack=stack, plyt=plyt, laminaprop=laminaprop)
mu=1.3e3
r = 10.
m = 8
n = 8
a1 = 1.5
a2 = 1.5
a3 = 2.5
a4 = 2.5
b1 = 1.5
b2 = 0.5
b3 = 1.5
b4 = 0.5
A11 = lam.ABD[0, 0]
A22 = lam.ABD[1, 1]
D11 = lam.ABD[3, 3]
D22 = lam.ABD[4, 4]
p01 = Panel(group='panels', x0=a3, y0=b2, a=a1, b=b1, r=r, m=m, n=n, plyt=plyt, stack=stack, laminaprop=laminaprop, mu=mu)
p02 = Panel(group='panels', x0=a3, y0=0, a=a2, b=b2, r=r, m=m, n=n, plyt=plyt, stack=stack, laminaprop=laminaprop, mu=mu)
p03 = Panel(group='panels', x0=0, y0=b2, a=a3, b=b3, r=r, m=m, n=n, plyt=plyt, stack=stack, laminaprop=laminaprop, mu=mu)
p04 = Panel(group='panels', x0=0, y0=0, a=a4, b=b4, r=r, m=m, n=n, plyt=plyt, stack=stack, laminaprop=laminaprop, mu=mu)
kt13, kr13 = connections.calc_kt_kr(p01, p03, 'xcte')
kt24, kr24 = connections.calc_kt_kr(p02, p04, 'xcte')
kt12, kr12 = connections.calc_kt_kr(p01, p02, 'ycte')
kt34, kr34 = connections.calc_kt_kr(p03, p04, 'ycte')
# boundary conditions
p01.u1tx = 1 ; p01.u1rx = 1 ; p01.u2tx = 0 ; p01.u2rx = 1
p01.v1tx = 1 ; p01.v1rx = 1 ; p01.v2tx = 0 ; p01.v2rx = 1
p01.w1tx = 1 ; p01.w1rx = 1 ; p01.w2tx = 0 ; p01.w2rx = 1
p01.u1ty = 1 ; p01.u1ry = 1 ; p01.u2ty = 0 ; p01.u2ry = 1
p01.v1ty = 1 ; p01.v1ry = 1 ; p01.v2ty = 0 ; p01.v2ry = 1
p01.w1ty = 1 ; p01.w1ry = 1 ; p01.w2ty = 0 ; p01.w2ry = 1
p02.u1tx = 1 ; p02.u1rx = 1 ; p02.u2tx = 0 ; p02.u2rx = 1
p02.v1tx = 1 ; p02.v1rx = 1 ; p02.v2tx = 0 ; p02.v2rx = 1
p02.w1tx = 1 ; p02.w1rx = 1 ; p02.w2tx = 0 ; p02.w2rx = 1
p02.u1ty = 0 ; p02.u1ry = 1 ; p02.u2ty = 1 ; p02.u2ry = 1
p02.v1ty = 0 ; p02.v1ry = 1 ; p02.v2ty = 1 ; p02.v2ry = 1
p02.w1ty = 0 ; p02.w1ry = 1 ; p02.w2ty = 1 ; p02.w2ry = 1
p03.u1tx = 0 ; p03.u1rx = 1 ; p03.u2tx = 1 ; p03.u2rx = 1
p03.v1tx = 0 ; p03.v1rx = 1 ; p03.v2tx = 1 ; p03.v2rx = 1
p03.w1tx = 0 ; p03.w1rx = 1 ; p03.w2tx = 1 ; p03.w2rx = 1
p03.u1ty = 1 ; p03.u1ry = 1 ; p03.u2ty = 0 ; p03.u2ry = 1
p03.v1ty = 1 ; p03.v1ry = 1 ; p03.v2ty = 0 ; p03.v2ry = 1
p03.w1ty = 1 ; p03.w1ry = 1 ; p03.w2ty = 0 ; p03.w2ry = 1
p04.u1tx = 0 ; p04.u1rx = 1 ; p04.u2tx = 1 ; p04.u2rx = 1
p04.v1tx = 0 ; p04.v1rx = 1 ; p04.v2tx = 1 ; p04.v2rx = 1
p04.w1tx = 0 ; p04.w1rx = 1 ; p04.w2tx = 1 ; p04.w2rx = 1
p04.u1ty = 0 ; p04.u1ry = 1 ; p04.u2ty = 1 ; p04.u2ry = 1
p04.v1ty = 0 ; p04.v1ry = 1 ; p04.v2ty = 1 ; p04.v2ry = 1
p04.w1ty = 0 ; p04.w1ry = 1 ; p04.w2ty = 1 ; p04.w2ry = 1
conndict = [
dict(p1=p01, p2=p02, func='SSycte', ycte1=0, ycte2=p02.b, kt=kt12, kr=kr12),
dict(p1=p01, p2=p03, func='SSxcte', xcte1=0, xcte2=p03.a, kt=kt13, kr=kr13),
dict(p1=p02, p2=p04, func='SSxcte', xcte1=0, xcte2=p04.a, kt=kt24, kr=kr24),
dict(p1=p03, p2=p04, func='SSycte', ycte1=0, ycte2=p04.b, kt=kt34, kr=kr34),
]
panels = [p01, p02, p03, p04]
size = sum([3*p.m*p.n for p in panels])
k0 = 0
kM = 0
row0 = 0
col0 = 0
for p in panels:
k0 += p.calc_k0(row0=row0, col0=col0, size=size, silent=True, finalize=False)
kM += p.calc_kM(row0=row0, col0=col0, size=size, silent=True, finalize=False)
p.row_start = row0
p.col_start = col0
row0 += 3*p.m*p.n
col0 += 3*p.m*p.n
p.row_end = row0
p.col_end = col0
for conn in conndict:
if conn.get('has_deffect'): # connecting if there is no deffect
continue
p1 = conn['p1']
p2 = conn['p2']
if conn['func'] == 'SSycte':
k0 += connections.kCSSycte.fkCSSycte11(
conn['kt'], conn['kr'], p1, conn['ycte1'],
size, p1.row_start, col0=p1.col_start)
k0 += connections.kCSSycte.fkCSSycte12(
conn['kt'], conn['kr'], p1, p2, conn['ycte1'], conn['ycte2'],
size, p1.row_start, col0=p2.col_start)
k0 += connections.kCSSycte.fkCSSycte22(
conn['kt'], conn['kr'], p1, p2, conn['ycte2'],
size, p2.row_start, col0=p2.col_start)
elif conn['func'] == 'SSxcte':
k0 += connections.kCSSxcte.fkCSSxcte11(
conn['kt'], conn['kr'], p1, conn['xcte1'],
size, p1.row_start, col0=p1.col_start)
k0 += connections.kCSSxcte.fkCSSxcte12(
conn['kt'], conn['kr'], p1, p2, conn['xcte1'], conn['xcte2'],
size, p1.row_start, col0=p2.col_start)
k0 += connections.kCSSxcte.fkCSSxcte22(
conn['kt'], conn['kr'], p1, p2, conn['xcte2'],
size, p2.row_start, col0=p2.col_start)
assert np.any(np.isnan(k0.data)) == False
assert np.any(np.isinf(k0.data)) == False
k0 = csr_matrix(make_symmetric(k0))
assert np.any(np.isnan(kM.data)) == False
assert np.any(np.isinf(kM.data)) == False
kM = csr_matrix(make_symmetric(kM))
eigvals, eigvecs = freq(k0, kM, tol=0, sparse_solver=True, silent=True,
sort=True, reduced_dof=False,
num_eigvalues=25, num_eigvalues_print=5)
# Results for single panel
m = 15
n = 15
singlepanel = Panel(a=(a1+a3), b=(b1+b2), r=r, m=m, n=n, plyt=plyt, stack=stack, laminaprop=laminaprop, mu=mu)
singlepanel.freq(silent=True)
assert np.isclose(eigvals[0], singlepanel.eigvals[0], atol=0.01, rtol=0.01)