def test_lb_Stiffener2D():
print('Testing linear buckling 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 = 15
spb.n = 16
spb.add_panel(y1=0, y2=spb.b / 2., plyt=spb.plyt, Nxx=-1.)
spb.add_panel(y1=spb.b / 2., y2=spb.b, plyt=spb.plyt, Nxx_cte=1000.)
spb.add_bladestiff2d(ys=spb.b / 2.,
m1=14,
n1=11,
bf=0.05,
fstack=[0, 90, 90, 0],
fplyt=spb.plyt,
flaminaprop=spb.laminaprop)
k0 = spb.calc_k0(silent=True)
kG = spb.calc_kG0(silent=True)
eigvals, eigvecs = lb(k0, kG, silent=True)
assert np.isclose(eigvals[0].real, 301.0825234, atol=0.1, rtol=0)
def test_lb_Stiffener2D():
print('Testing linear buckling 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 = 15
spb.n = 16
spb.add_panel(y1=0, y2=spb.b/2., plyt=spb.plyt, Nxx=-1.)
spb.add_panel(y1=spb.b/2., y2=spb.b, plyt=spb.plyt, Nxx_cte=1000.)
spb.add_bladestiff2d(ys=spb.b/2., m1=14, n1=11, bf=0.05,
fstack=[0, 90, 90, 0],
fplyt=spb.plyt, flaminaprop=spb.laminaprop)
k0 = spb.calc_k0(silent=True)
kG = spb.calc_kG0(silent=True)
eigvals, eigvecs = lb(k0, kG, silent=True)
assert np.isclose(eigvals[0].real, 301.0825234, atol=0.1, rtol=0)
def cylinder_compression_lb_Nxx_cte(height,
r,
stack,
plyt,
laminaprop,
npanels,
Nxxs,
m=8,
n=8,
num_eigvalues=20):
"""Linear buckling analysis with a constant Nxx for each panel
See :func:`.create_cylinder_assy` for most parameters.
Parameters
----------
Nxxs : list
A Nxx for each panel.
num_eigvalues : int
Number of eigenvalues to be extracted.
Returns
-------
assy, eigvals, eigvecs : tuple
Assembly, eigenvalues and eigenvectors.
Examples
--------
The following example is one of the test cases:
.. literalinclude:: ../../../../../compmech/panel/assembly/tests/test_cylinder.py
:pyobject: test_cylinder_compression_lb_Nxx_cte
"""
assy, conns = create_cylinder_assy(height=height,
r=r,
stack=stack,
plyt=plyt,
laminaprop=laminaprop,
npanels=npanels,
m=m,
n=n)
if len(Nxxs) != npanels:
raise ValueError('The length of "Nxxs" must be the same as "npanels"')
for i, p in enumerate(assy.panels):
p.Nxx = Nxxs[i]
k0 = assy.calc_k0(conns, silent=True)
kG = assy.calc_kG0(silent=True)
eigvals, eigvecs = lb(k0,
kG,
tol=0,
sparse_solver=True,
silent=True,
num_eigvalues=num_eigvalues,
num_eigvalues_print=5)
return assy, eigvals, eigvecs
def test_bladestiff2d_lb():
print('Testing linear buckling with BladeStiff2D')
spb = StiffPanelBay()
spb.a = 2.
spb.b = 1.
spb.stack = [0, +45, -45, 90, -45, +45]
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 = 17
spb.n = 16
Nxx = -50.
spb.add_panel(y1=0, y2=spb.b / 2., plyt=spb.plyt, Nxx=Nxx)
spb.add_panel(y1=spb.b / 2., y2=spb.b, plyt=spb.plyt, Nxx=Nxx)
bb = spb.b / 5.
bf = bb
stiff = spb.add_bladestiff2d(ys=spb.b / 2.,
bf=bf,
bb=bb,
fstack=[0, 90, 90, 0] * 8,
fplyt=spb.plyt * 1.,
flaminaprop=spb.laminaprop,
bstack=[0, 90, 90, 0] * 4,
bplyt=spb.plyt * 1.,
blaminaprop=spb.laminaprop,
mf=17,
nf=16)
spb.calc_k0()
spb.calc_kG0()
eigvals, eigvecs = lb(spb.k0, spb.kG0, silent=True)
spb.plot_skin(eigvecs[:, 0],
filename='tmp_test_bladestiff2d_lb_skin.png',
colorbar=True)
spb.plot_stiffener(eigvecs[:, 0],
si=0,
region='flange',
filename='tmp_test_bladestiff2d_lb_stiff_flange.png',
colorbar=True)
calc = eigvals[0] * Nxx
spb.plot_skin(eigvecs[:, 0],
filename='tmp_test_bladestiff2d_lb_skin.png',
colorbar=True,
vec='w',
clean=False)
assert np.isclose(calc, -759.05689868085778, atol=0.0001, rtol=0.001)
def cylinder_blade_stiffened_compression_lb_Nxx_cte(height, r, stack, stack_blades,
width_blades, plyt, laminaprop,
npanels, Nxxs_skin, Nxxs_blade, m=8, n=8, num_eigvalues=20):
"""Linear buckling analysis with a constant Nxx for each panel
See :func:`.create_cylinder_blade_stiffened` for most parameters.
Parameters
----------
Nxxs_skin : list
A Nxx for each skin panel.
Nxxs_blade : list
A Nxx for each blade stiffener.
num_eigvalues : int
Number of eigenvalues to be extracted.
Returns
-------
assy, eigvals, eigvecs : tuple
Assembly, eigenvalues and eigenvectors.
Examples
--------
The following example is one of the test cases:
.. literalinclude:: ../../../../../compmech/panel/assembly/tests/test_cylinder_blade_stiffened.py
:pyobject: test_cylinder_blade_stiffened_compression_lb_Nxx_cte
"""
assy, conns = create_cylinder_blade_stiffened(height=height, r=r,
stack=stack, stack_blades=stack_blades, width_blades=width_blades,
plyt=plyt, laminaprop=laminaprop, npanels=npanels, m=m, n=n)
if len(Nxxs_skin) != npanels:
raise ValueError('The length of "Nxxs_skin" must be the same as "npanels"')
if len(Nxxs_blade) != npanels:
raise ValueError('The length of "Nxxs_blade" must be the same as "npanels"')
i_skin = -1
i_blade = -1
for p in assy.panels:
if 'skin' in p.group:
i_skin += 1
p.Nxx = Nxxs_skin[i_skin]
elif 'blade' in p.group:
i_blade += 1
p.Nxx = Nxxs_blade[i_blade]
k0 = assy.calc_k0(conns, silent=True)
kG = assy.calc_kG0(silent=True)
eigvals, eigvecs = lb(k0, kG, tol=0, sparse_solver=True, silent=True,
num_eigvalues=num_eigvalues, num_eigvalues_print=5)
return assy, eigvals, eigvecs
def test_tstiff2d_lb():
#NOTE reference values taken from
# compmech.panel.assembly.tstiff2d_1stiff_compression
a_b_list = [0.5, 2., 10.]
ref_values = [-152.607275551, -80.15391295315146, -79.39137361313862]
for a_b, ref_value in zip(a_b_list, ref_values):
print('Testing linear buckling')
spb = StiffPanelBay()
spb.b = 1.
spb.a = spb.b * a_b
spb.stack = [0, +45, -45, 90, -45, +45]
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
Nxx = -10.
spb.add_panel(y1=0, y2=spb.b / 2., plyt=spb.plyt, Nxx=Nxx)
spb.add_panel(y1=spb.b / 2., y2=spb.b, plyt=spb.plyt, Nxx=Nxx)
bb = spb.b / 5.
if False:
stiff = spb.add_tstiff2d(ys=spb.b / 2.,
bf=bb / 2,
bb=bb,
fstack=[0, 90, 90, 0] * 8,
fplyt=spb.plyt * 1.,
flaminaprop=spb.laminaprop,
bstack=[0, 90, 90, 0] * 4,
bplyt=spb.plyt * 1.,
blaminaprop=spb.laminaprop,
mb=13,
nb=12,
mf=13,
nf=12,
Nxxf=Nxx)
spb.calc_k0()
spb.calc_kG0()
eigvals, eigvecs = lb(spb.k0, spb.kG0, silent=True)
calc = eigvals[0] * Nxx
assert np.isclose(calc, ref_value, rtol=0.05)
def test_tstiff2d_lb():
#NOTE reference values taken from
# compmech.panel.assembly.tstiff2d_1stiff_compression
a_b_list = [0.5, 2., 10.]
ref_values = [-152.607275551, -80.15391295315146, -79.39137361313862]
for a_b, ref_value in zip(a_b_list, ref_values):
print('Testing linear buckling')
spb = StiffPanelBay()
spb.b = 1.
spb.a = spb.b * a_b
spb.stack = [0, +45, -45, 90, -45, +45]
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
Nxx = -10.
spb.add_panel(y1=0, y2=spb.b/2., plyt=spb.plyt, Nxx=Nxx)
spb.add_panel(y1=spb.b/2., y2=spb.b, plyt=spb.plyt, Nxx=Nxx)
bb = spb.b/5.
if False:
stiff = spb.add_tstiff2d(ys=spb.b/2., bf=bb/2, bb=bb,
fstack=[0, 90, 90, 0]*8,
fplyt=spb.plyt*1., flaminaprop=spb.laminaprop,
bstack=[0, 90, 90, 0]*4,
bplyt=spb.plyt*1., blaminaprop=spb.laminaprop,
mb=13, nb=12, mf=13, nf=12, Nxxf=Nxx)
spb.calc_k0()
spb.calc_kG0()
eigvals, eigvecs = lb(spb.k0, spb.kG0, silent=True)
calc = eigvals[0]*Nxx
assert np.isclose(calc, ref_value, rtol=0.05)
def test_panel_lb():
for model in [
'plate_clt_donnell_bardell', 'plate_clt_donnell_bardell_w',
'cpanel_clt_donnell_bardell', 'kpanel_clt_donnell_bardell'
]:
print('Linear buckling for model {0}'.format(model))
# ssss
p = Panel()
p.m = 12
p.n = 13
p.stack = [0, 90, -45, +45]
p.plyt = 0.125e-3
p.laminaprop = (142.5e9, 8.7e9, 0.28, 5.1e9, 5.1e9, 5.1e9)
p.model = model
p.a = 1.
p.b = 0.5
p.r = 1.e8
p.alphadeg = 0.
p.Nxx = -1
k0 = p.calc_k0(silent=True)
kG0 = p.calc_kG0(silent=True)
eigvals, eigvecs = lb(k0, kG0, silent=True)
if '_w' in model:
assert np.isclose(eigvals[0], 88.47696, atol=0.1, rtol=0)
else:
assert np.isclose(eigvals[0], 85.2912, atol=0.1, rtol=0)
p.Nxx = 0
p.Nyy = -1
k0 = p.calc_k0(silent=True)
kG0 = p.calc_kG0(silent=True)
eigvals, eigvecs = lb(k0, kG0, silent=True)
if '_w' in model:
assert np.isclose(eigvals[0], 26.45882, atol=0.1, rtol=0)
else:
assert np.isclose(eigvals[0], 25.17562, atol=0.1, rtol=0)
# ssfs
p = Panel()
p.u2ty = 1
p.v2ty = 1
p.w2ty = 1
p.u2ry = 1
p.v2ry = 1
p.m = 12
p.n = 13
p.stack = [0, 90, -45, +45]
p.plyt = 0.125e-3
p.laminaprop = (142.5e9, 8.7e9, 0.28, 5.1e9, 5.1e9, 5.1e9)
p.model = model
p.a = 1.
p.b = 0.5
p.r = 1.e8
p.alphadeg = 0.
p.Nxx = -1
k0 = p.calc_k0(silent=True)
kG0 = p.calc_kG0(silent=True)
eigvals, eigvecs = lb(k0, kG0, silent=True)
if '_w' in model:
assert np.isclose(eigvals[0], 17.14427, atol=0.1, rtol=0)
else:
assert np.isclose(eigvals[0], 15.842356, atol=0.1, rtol=0)
p.u2tx = 1
p.v2tx = 1
p.w2tx = 1
p.u2rx = 1
p.v2rx = 1
p.u2ty = 0
p.v2ty = 0
p.w2ty = 0
p.u2ry = 0
p.v2ry = 0
p.Nxx = 0
p.Nyy = -1
k0 = p.calc_k0(silent=True)
kG0 = p.calc_kG0(silent=True)
eigvals, eigvecs = lb(k0, kG0, silent=True)
if '_w' in model:
assert np.isclose(eigvals[0], 15.809986, atol=0.1, rtol=0)
else:
assert np.isclose(eigvals[0], 13.9421988, atol=0.1, rtol=0)
def cylinder_blade_stiffened_compression_lb_Nxx_from_static(height, r, stack,
stack_blades, width_blades, plyt, laminaprop, npanels, Nxxs_skin,
Nxxs_blade, m=8, n=8,
num_eigvalues=20):
"""Linear buckling analysis with a Nxx calculated using static analysis
See :func:`.create_cylinder_blade_stiffened` for most parameters.
Parameters
----------
Nxxs_skin : list
A Nxx for each skin panel.
Nxxs_blade : list
A Nxx for each blade stiffener.
num_eigvalues : int
Number of eigenvalues to be extracted.
Returns
-------
assy, c, eigvals, eigvecs : tuple
Assembly, static results, eigenvalues and eigenvectors.
Examples
--------
The following example is one of the test cases:
.. literalinclude:: ../../../../../compmech/panel/assembly/tests/test_cylinder.py
:pyobject: test_cylinder_blade_stiffened_compression_lb_Nxx_from_static
"""
assy, conns = create_cylinder_blade_stiffened(height=height, r=r,
stack=stack, stack_blades=stack_blades, width_blades=width_blades,
plyt=plyt, laminaprop=laminaprop, npanels=npanels, m=m, n=n)
if len(Nxxs_skin) != npanels:
raise ValueError('The length of "Nxxs_skin" must be the same as "npanels"')
if len(Nxxs_blade) != npanels:
raise ValueError('The length of "Nxxs_blade" must be the same as "npanels"')
i_skin = -1
i_blade = -1
for p in assy.panels:
p.u2tx = 1
if 'skin' in p.group:
i_skin += 1
p.Nxx = Nxxs_skin[i_skin]
elif 'blade' in p.group:
i_blade += 1
p.Nxx = Nxxs_blade[i_blade]
#TODO improve application of distributed loads
for p in assy.panels:
Nforces = 1000
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):
fx_applied = fx/2.
else:
fx_applied = fx
p.add_force(p.a, y, fx_applied, 0, 0)
fext = assy.calc_fext(silent=True)
k0 = assy.calc_k0(conns, silent=True)
incs, cs = static(k0, fext, silent=True)
c = cs[0]
kG = assy.calc_kG0(c=c, silent=True)
eigvals = eigvecs = None
eigvals, eigvecs = lb(k0, kG, tol=0, sparse_solver=True, silent=True,
num_eigvalues=num_eigvalues, num_eigvalues_print=5)
return assy, c, eigvals, eigvecs
def tstiff2d_1stiff_compression(a, b, ys, bb, bf, defect_a, mu, plyt,
laminaprop, stack_skin, stack_base, stack_flange,
Nxx_skin, Nxx_base, Nxx_flange, run_static_case=True,
r=None, m=8, n=8, mb=None, nb=None, mf=None, nf=None,
nx=None, ny=None, nxb=None, nyb=None, nxf=None, nyf=None):
r"""Linear Buckling of T-Stiffened panel with debonding defect
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
For more details about the theory involved, see
[castro2017AssemblyModels]_.
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.
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.
nx, ny, nxb, nyb, nxf, nyf : int, optional
Define of integration points used for skin, stiffener's base or flange;
along x and y. Keeping ``None`` will use the default (see
:class:`.Panel`).
Examples
--------
The following example is one of the test cases:
.. literalinclude:: ../../../../../compmech/panel/assembly/tests/test_tstiff2d_assembly.py
:pyobject: test_tstiff2d_1stiff_compression
"""
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
nx = m if nx is None else nx
ny = n if ny is None else ny
nxb = mb if nxb is None else nxb
nyb = nb if nyb is None else nyb
nxf = mf if nxf is None else nxf
nyf = nf if nyf is None else nyf
# 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, nx=nx, ny=ny)
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, nx=nx, ny=ny)
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, nx=nx, ny=ny)
# 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, nx=nx, ny=ny)
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, nx=nx, ny=ny)
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, nx=nx, ny=ny)
#
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, nx=nx, ny=ny)
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, nx=nx, ny=ny)
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, nx=nx, ny=ny)
# 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, nx=nxb, ny=nyb)
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, nx=nxf, ny=nyf)
# 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, nx=nxb, ny=nyb)
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, nx=nxf, ny=nyf)
#
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, nx=nxb, ny=nyb)
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, nx=nxf, ny=nyf)
# 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
if run_static_case:
p07.u1tx = 1 ; p07.u1rx = 1 ; p07.u2tx = 1 ; p07.u2rx = 1
else:
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 = 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
if run_static_case:
p08.u1tx = 1 ; p08.u1rx = 1 ; p08.u2tx = 1 ; p08.u2rx = 1
else:
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
if run_static_case:
p09.u1tx = 1 ; p09.u1rx = 1 ; p09.u2tx = 1 ; p09.u2rx = 1
else:
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 = 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
if run_static_case:
p15.u1tx = 1 ; p15.u1rx = 1 ; p15.u2tx = 1 ; p15.u2rx = 1
else:
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]
assy = PanelAssembly(panels)
size = sum([3*p.m*p.n for p in panels])
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:
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]
kG = assy.calc_kG0(c=c)
eigvals = eigvecs = None
eigvals, eigvecs = lb(k0, kG, tol=0, sparse_solver=True, silent=True,
num_eigvalues=25, num_eigvalues_print=5)
if run_static_case:
return assy, c, eigvals, eigvecs
else:
return assy, eigvals, eigvecs
def test_panel_lb():
for model in ['plate_clt_donnell_bardell',
'plate_clt_donnell_bardell_w',
'cpanel_clt_donnell_bardell',
'kpanel_clt_donnell_bardell']:
print('Linear buckling for model {0}'.format(model))
# ssss
p = Panel()
p.m = 12
p.n = 13
p.stack = [0, 90, -45, +45]
p.plyt = 0.125e-3
p.laminaprop = (142.5e9, 8.7e9, 0.28, 5.1e9, 5.1e9, 5.1e9)
p.model = model
p.a = 1.
p.b = 0.5
p.r = 1.e8
p.alphadeg = 0.
p.Nxx = -1
k0 = p.calc_k0(silent=True)
kG0 = p.calc_kG0(silent=True)
eigvals, eigvecs = lb(k0, kG0, silent=True)
if '_w' in model:
assert np.isclose(eigvals[0], 88.47696, atol=0.1, rtol=0)
else:
assert np.isclose(eigvals[0], 85.2912, atol=0.1, rtol=0)
p.Nxx = 0
p.Nyy = -1
k0 = p.calc_k0(silent=True)
kG0 = p.calc_kG0(silent=True)
eigvals, eigvecs = lb(k0, kG0, silent=True)
if '_w' in model:
assert np.isclose(eigvals[0], 26.45882, atol=0.1, rtol=0)
else:
assert np.isclose(eigvals[0], 25.17562, atol=0.1, rtol=0)
# ssfs
p = Panel()
p.u2ty = 1
p.v2ty = 1
p.w2ty = 1
p.u2ry = 1
p.v2ry = 1
p.m = 12
p.n = 13
p.stack = [0, 90, -45, +45]
p.plyt = 0.125e-3
p.laminaprop = (142.5e9, 8.7e9, 0.28, 5.1e9, 5.1e9, 5.1e9)
p.model = model
p.a = 1.
p.b = 0.5
p.r = 1.e8
p.alphadeg = 0.
p.Nxx = -1
k0 = p.calc_k0(silent=True)
kG0 = p.calc_kG0(silent=True)
eigvals, eigvecs = lb(k0, kG0, silent=True)
if '_w' in model:
assert np.isclose(eigvals[0], 17.14427, atol=0.1, rtol=0)
else:
assert np.isclose(eigvals[0], 15.842356, atol=0.1, rtol=0)
p.u2tx = 1
p.v2tx = 1
p.w2tx = 1
p.u2rx = 1
p.v2rx = 1
p.u2ty = 0
p.v2ty = 0
p.w2ty = 0
p.u2ry = 0
p.v2ry = 0
p.Nxx = 0
p.Nyy = -1
k0 = p.calc_k0(silent=True)
kG0 = p.calc_kG0(silent=True)
eigvals, eigvecs = lb(k0, kG0, silent=True)
if '_w' in model:
assert np.isclose(eigvals[0], 15.809986, atol=0.1, rtol=0)
else:
assert np.isclose(eigvals[0], 13.9421988, atol=0.1, rtol=0)
