def __init__(self, bay, mu, panel1, panel2, ys, bb, bf, bstack, bplyts,
blaminaprops, fstack, fplyts, flaminaprops,
model='tstiff2d_clt_donnell_bardell', mb=15, nb=12, mf=15, nf=12):
print('\n\nWARNING - TStiff2D no longer recommended!\n'
' There is a numerically unstable way to compute the\n'
' connection between the skin and stiffener\'s base, it is\n'
' recommended to use panel.assembly instead.\n'
' Module panel.assembly allows stable ways to perform\n'
' connection among panels, and avoids using sliced\n'
' integration intervals that were causing trouble in\n'
' TStiff2D\n\n')
self.bay = bay
self.panel1 = panel1
self.panel2 = panel2
self.model = model
if bstack is None:
raise ValueError('Base laminate must be defined!')
self.ys = ys
y1 = ys - bb/2.
y2 = ys + bb/2.
self.base = Panel(a=bay.a, b=bb, r=bay.r, alphadeg=bay.alphadeg,
stack=bstack, plyts=bplyts, laminaprops=blaminaprops,
mu=mu, m=mb, n=nb, offset=0.,
u1tx=1, u1rx=0, u2tx=1, u2rx=0,
v1tx=1, v1rx=0, v2tx=1, v2rx=0,
w1tx=1, w1rx=1, w2tx=1, w2rx=1,
u1ty=1, u1ry=0, u2ty=1, u2ry=0,
v1ty=1, v1ry=0, v2ty=1, v2ry=0,
w1ty=1, w1ry=1, w2ty=1, w2ry=1,
y1=y1, y2=y2)
self.base._rebuild()
if fstack is None:
raise ValueError('Flange laminate must be defined!')
self.flange = Panel(a=bay.a, b=bf, model='plate_clt_donnell_bardell',
stack=fstack, plyts=fplyts, laminaprops=flaminaprops,
mu=mu, m=mf, n=nf, offset=0.,
u1tx=0, u1rx=0, u2tx=0, u2rx=0,
v1tx=0, v1rx=0, v2tx=0, v2rx=0,
w1tx=0, w1rx=1, w2tx=0, w2rx=1,
u1ty=1, u1ry=0, u2ty=1, u2ry=0,
v1ty=1, v1ry=0, v2ty=1, v2ry=0,
w1ty=1, w1ry=1, w2ty=1, w2ry=1)
self.flange._rebuild()
self.eta_conn_base = 0.
self.eta_conn_flange = -1.
self.k0 = None
self.kM = None
self.kG0 = None
self._rebuild()
def _rebuild(self):
assert self.panel1.model == self.panel2.model
assert self.panel1.m == self.panel2.m
assert self.panel1.n == self.panel2.n
assert self.panel1.r == self.panel2.r
assert self.panel1.alphadeg == self.panel2.alphadeg
if self.fstack is not None:
self.hf = sum(self.fplyts)
self.Asf = self.bf*self.hf
self.flam = laminate.read_stack(self.fstack, plyts=self.fplyts,
laminaprops=self.flaminaprops)
self.flam.calc_equivalent_modulus()
h = 0.5*sum(self.panel1.plyts) + 0.5*sum(self.panel2.plyts)
hb = 0.
if self.bstack is not None:
hb = sum(self.bplyts)
y1 = self.ys - self.bb/2.
y2 = self.ys + self.bb/2.
self.base = Panel(a=bay.a, b=bay.b, r=bay.r, alphadeg=bay.alphadeg,
stack=self.bstack, plyts=self.bplyts,
mu=self.mu, m=bay.m, n=bay.n,
laminaprops=self.blaminaprops, offset=(-h/2.-hb/2.),
u1tx=bay.u1tx, u1rx=bay.u1rx, u2tx=bay.u2tx, u2rx=bay.u2rx,
v1tx=bay.v1tx, v1rx=bay.v1rx, v2tx=bay.v2tx, v2rx=bay.v2rx,
w1tx=bay.w1tx, w1rx=bay.w1rx, w2tx=bay.w2tx, w2rx=bay.w2rx,
u1ty=bay.u1ty, u1ry=bay.u1ry, u2ty=bay.u2ty, u2ry=bay.u2ry,
v1ty=bay.v1ty, v1ry=bay.v1ry, v2ty=bay.v2ty, v2ry=bay.v2ry,
w1ty=bay.w1ty, w1ry=bay.w1ry, w2ty=bay.w2ty, w2ry=bay.w2ry,
y1=y1, y2=y2)
self.Asb = self.bb*hb
#TODO check offset effect on curved panels
self.dbf = self.bf/2. + hb + h/2.
self.Iyy = self.hf*self.bf**3/12.
self.Jxx = self.hf*self.bf**3/12. + self.bf*self.hf**3/12.
Asb = self.Asb if self.Asb is not None else 0.
Asf = self.Asf if self.Asf is not None else 0.
self.As = Asb + Asf
if self.fstack is not None:
self.E1 = 0
#E3 = 0
self.S1 = 0
yply = self.flam.plies[0].t/2.
for i, ply in enumerate(self.flam.plies):
if i > 0:
yply += self.flam.plies[i-1].t/2. + self.flam.plies[i].t/2.
q = ply.QL
self.E1 += ply.t*(q[0,0] - q[0,1]**2/q[1,1])
#E3 += ply.t*(q[2,2] - q[1,2]**2/q[1,1])
self.S1 += -yply*ply.t*(q[0,2] - q[0,1]*q[1,2]/q[1,1])
self.F1 = self.bf**2/12.*self.E1
def __init__(self, bay, mu, panel1, panel2, ys, bb, bf, bstack, bplyts,
blaminaprops, fstack, fplyts, flaminaprops, mf=14, nf=11):
self.bay = bay
self.panel1 = panel1
self.panel2 = panel2
self.mu = mu
self.ys = ys
self.bb = bb
self.forces_flange = []
self.bstack = bstack
self.bplyts = bplyts
self.blaminaprops = blaminaprops
self.k0 = None
self.kM = None
self.kG0 = None
self.base = None
if bstack is not None:
y1 = self.ys - bb/2.
y2 = self.ys + bb/2.
h = 0.5*sum(self.panel1.plyts) + 0.5*sum(self.panel2.plyts)
hb = sum(self.bplyts)
self.base = Panel(a=bay.a, b=bay.b, r=bay.r, alphadeg=bay.alphadeg,
stack=bstack, plyts=bplyts, laminaprops=blaminaprops,
mu=mu, m=bay.m, n=bay.n, offset=(-h/2.-hb/2.),
u1tx=bay.u1tx, u1rx=bay.u1rx, u2tx=bay.u2tx, u2rx=bay.u2rx,
v1tx=bay.v1tx, v1rx=bay.v1rx, v2tx=bay.v2tx, v2rx=bay.v2rx,
w1tx=bay.w1tx, w1rx=bay.w1rx, w2tx=bay.w2tx, w2rx=bay.w2rx,
u1ty=bay.u1ty, u1ry=bay.u1ry, u2ty=bay.u2ty, u2ry=bay.u2ry,
v1ty=bay.v1ty, v1ry=bay.v1ry, v2ty=bay.v2ty, v2ry=bay.v2ry,
w1ty=bay.w1ty, w1ry=bay.w1ry, w2ty=bay.w2ty, w2ry=bay.w2ry,
y1=y1, y2=y2)
self.flange = None
if fstack is not None:
self.flange = Panel(m=mf, n=nf, a=bay.a, b=bf, mu=mu,
stack=fstack, plyts=fplyts, laminaprops=flaminaprops,
model='plate_clt_donnell_bardell',
u1tx=0., u1rx=0., u2tx=0., u2rx=0.,
v1tx=0., v1rx=0., v2tx=0., v2rx=0.,
w1tx=0., w1rx=1., w2tx=0., w2rx=1.,
u1ty=1., u1ry=0., u2ty=1., u2ry=0.,
v1ty=1., v1ry=0., v2ty=1., v2ry=0.,
w1ty=1., w1ry=1., w2ty=1., w2ry=1.)
self._rebuild()
class BladeStiff2D(object):
r"""Blade Stiffener using 2D Formulation for Flange
Blade-type of stiffener model using a 2D formulation for the flange and a
2D formulation for the base (padup)::
|| --> flange |
|| |-> stiffener
====== --> padup |
========================= --> panels
Panel1 Panel2
Both the flange and the base are optional. The stiffener's base is modeled
using the same approximation functions as the skin, with the proper
offset.
Each stiffener has a constant `y_s` coordinate.
"""
def __init__(self,
bay,
mu,
panel1,
panel2,
ys,
bb,
bf,
bstack,
bplyts,
blaminaprops,
fstack,
fplyts,
flaminaprops,
mf=14,
nf=11):
self.bay = bay
self.panel1 = panel1
self.panel2 = panel2
self.mu = mu
self.ys = ys
self.bb = bb
self.forces_flange = []
self.bstack = bstack
self.bplyts = bplyts
self.blaminaprops = blaminaprops
self.k0 = None
self.kM = None
self.kG0 = None
self.base = None
if bstack is not None:
y1 = self.ys - bb / 2.
y2 = self.ys + bb / 2.
h = 0.5 * sum(self.panel1.plyts) + 0.5 * sum(self.panel2.plyts)
hb = sum(self.bplyts)
self.base = Panel(a=bay.a,
b=bay.b,
r=bay.r,
alphadeg=bay.alphadeg,
stack=bstack,
plyts=bplyts,
laminaprops=blaminaprops,
mu=mu,
m=bay.m,
n=bay.n,
offset=(-h / 2. - hb / 2.),
u1tx=bay.u1tx,
u1rx=bay.u1rx,
u2tx=bay.u2tx,
u2rx=bay.u2rx,
v1tx=bay.v1tx,
v1rx=bay.v1rx,
v2tx=bay.v2tx,
v2rx=bay.v2rx,
w1tx=bay.w1tx,
w1rx=bay.w1rx,
w2tx=bay.w2tx,
w2rx=bay.w2rx,
u1ty=bay.u1ty,
u1ry=bay.u1ry,
u2ty=bay.u2ty,
u2ry=bay.u2ry,
v1ty=bay.v1ty,
v1ry=bay.v1ry,
v2ty=bay.v2ty,
v2ry=bay.v2ry,
w1ty=bay.w1ty,
w1ry=bay.w1ry,
w2ty=bay.w2ty,
w2ry=bay.w2ry,
y1=y1,
y2=y2)
self.flange = None
if fstack is not None:
self.flange = Panel(m=mf,
n=nf,
a=bay.a,
b=bf,
mu=mu,
stack=fstack,
plyts=fplyts,
laminaprops=flaminaprops,
model='plate_clt_donnell_bardell',
u1tx=0.,
u1rx=0.,
u2tx=0.,
u2rx=0.,
v1tx=0.,
v1rx=0.,
v2tx=0.,
v2rx=0.,
w1tx=0.,
w1rx=1.,
w2tx=0.,
w2rx=1.,
u1ty=1.,
u1ry=0.,
u2ty=1.,
u2ry=0.,
v1ty=1.,
v1ry=0.,
v2ty=1.,
v2ry=0.,
w1ty=1.,
w1ry=1.,
w2ty=1.,
w2ry=1.)
self._rebuild()
def _rebuild(self):
assert self.panel1.model == self.panel2.model
assert self.panel1.m == self.panel2.m
assert self.panel1.n == self.panel2.n
assert self.panel1.r == self.panel2.r
assert self.panel1.alphadeg == self.panel2.alphadeg
if self.flange is not None:
self.flange.lam = laminate.read_stack(
self.flange.stack,
plyts=self.flange.plyts,
laminaprops=self.flange.laminaprops)
self.flange.lam.calc_equivalent_modulus()
if self.base is not None:
h = 0.5 * sum(self.panel1.plyts) + 0.5 * sum(self.panel2.plyts)
hb = sum(self.bplyts)
self.dpb = h / 2. + hb / 2.
self.base.lam = laminate.read_stack(self.bstack,
plyts=self.bplyts,
laminaprops=self.blaminaprops,
offset=(-h / 2. - hb / 2.))
def calc_k0(self, size=None, row0=0, col0=0, silent=False, finalize=True):
"""Calculate the linear constitutive stiffness matrix
"""
self._rebuild()
msg('Calculating k0... ', level=2, silent=silent)
flangemod = panmodelDB.db[self.flange.model]['matrices']
bay = self.bay
a = bay.a
b = bay.b
m = bay.m
n = bay.n
k0 = 0.
if self.base is not None:
k0 += self.base.calc_k0(size=size,
row0=0,
col0=0,
silent=True,
finalize=False)
if self.flange is not None:
k0 += self.flange.calc_k0(size=size,
row0=row0,
col0=col0,
silent=True,
finalize=False)
# connectivity between stiffener'base and stiffener's flange
if self.base is None:
ktbf, krbf = calc_kt_kr(self.panel1, self.flange, 'ycte')
else:
ktbf, krbf = calc_kt_kr(self.base, self.flange, 'ycte')
mod = db['bladestiff2d_clt_donnell_bardell']['connections']
k0 += mod.fkCss(ktbf, krbf, self.ys, a, b, m, n, bay.u1tx,
bay.u1rx, bay.u2tx, bay.u2rx, bay.v1tx, bay.v1rx,
bay.v2tx, bay.v2rx, bay.w1tx, bay.w1rx, bay.w2tx,
bay.w2rx, bay.u1ty, bay.u1ry, bay.u2ty, bay.u2ry,
bay.v1ty, bay.v1ry, bay.v2ty, bay.v2ry, bay.w1ty,
bay.w1ry, bay.w2ty, bay.w2ry, size, 0, 0)
bf = self.flange.b
k0 += mod.fkCsf(
ktbf, krbf, self.ys, a, b, bf, m, n, self.flange.m,
self.flange.n, bay.u1tx, bay.u1rx, bay.u2tx, bay.u2rx,
bay.v1tx, bay.v1rx, bay.v2tx, bay.v2rx, bay.w1tx, bay.w1rx,
bay.w2tx, bay.w2rx, bay.u1ty, bay.u1ry, bay.u2ty, bay.u2ry,
bay.v1ty, bay.v1ry, bay.v2ty, bay.v2ry, bay.w1ty, bay.w1ry,
bay.w2ty, bay.w2ry, self.flange.u1tx, self.flange.u1rx,
self.flange.u2tx, self.flange.u2rx, self.flange.v1tx,
self.flange.v1rx, self.flange.v2tx, self.flange.v2rx,
self.flange.w1tx, self.flange.w1rx, self.flange.w2tx,
self.flange.w2rx, self.flange.u1ty, self.flange.u1ry,
self.flange.u2ty, self.flange.u2ry, self.flange.v1ty,
self.flange.v1ry, self.flange.v2ty, self.flange.v2ry,
self.flange.w1ty, self.flange.w1ry, self.flange.w2ty,
self.flange.w2ry, size, 0, col0)
k0 += mod.fkCff(
ktbf, krbf, a, bf, self.flange.m, self.flange.n,
self.flange.u1tx, self.flange.u1rx, self.flange.u2tx,
self.flange.u2rx, self.flange.v1tx, self.flange.v1rx,
self.flange.v2tx, self.flange.v2rx, self.flange.w1tx,
self.flange.w1rx, self.flange.w2tx, self.flange.w2rx,
self.flange.u1ty, self.flange.u1ry, self.flange.u2ty,
self.flange.u2ry, self.flange.v1ty, self.flange.v1ry,
self.flange.v2ty, self.flange.v2ry, self.flange.w1ty,
self.flange.w1ry, self.flange.w2ty, self.flange.w2ry, size,
row0, col0)
if finalize:
k0 = finalize_symmetric_matrix(k0)
self.k0 = k0
#NOTE forcing Python garbage collector to clean the memory
# it DOES make a difference! There is a memory leak not
# identified, probably in the csr_matrix process
gc.collect()
msg('finished!', level=2, silent=silent)
def calc_kG0(self,
size=None,
row0=0,
col0=0,
silent=False,
finalize=True,
c=None,
NLgeom=False):
"""Calculate the linear geometric stiffness matrix
"""
self._rebuild()
msg('Calculating kG0... ', level=2, silent=silent)
kG0 = 0.
if self.base is not None:
#TODO include kG0 for pad-up and Nxx load that arrives there
pass
if self.flange is not None:
kG0 += self.flange.calc_kG0(size=size,
row0=row0,
col0=col0,
silent=True,
finalize=False,
NLgeom=NLgeom)
if finalize:
kG0 = finalize_symmetric_matrix(kG0)
self.kG0 = kG0
#NOTE forcing Python garbage collector to clean the memory
# it DOES make a difference! There is a memory leak not
# identified, probably in the csr_matrix process
gc.collect()
msg('finished!', level=2, silent=silent)
def calc_kM(self, size=None, row0=0, col0=0, silent=False, finalize=True):
"""Calculate the mass matrix
"""
self._rebuild()
msg('Calculating kM... ', level=2, silent=silent)
kM = 0.
if self.base is not None:
kM += self.base.calc_kM(size=size,
row0=0,
col0=0,
silent=True,
finalize=False)
if self.flange is not None:
kM += self.flange.calc_kM(size=size,
row0=row0,
col0=col0,
silent=True,
finalize=False)
if finalize:
kM = finalize_symmetric_matrix(kM)
self.kM = kM
#NOTE forcing Python garbage collector to clean the memory
# it DOES make a difference! There is a memory leak not
# identified, probably in the csr_matrix process
gc.collect()
msg('finished!', level=2, silent=silent)
def test_fint():
m = 6
n = 6
for model in ['plate_clt_donnell_bardell',
'cpanel_clt_donnell_bardell'
]:
p = Panel()
p.model = model
p.w1tx = 0
p.w1rx = 1
p.u1tx = 1
p.u1ty = 1
p.u2ty = 1
p.a = 2.
p.b = 1.
p.r = 1.e5
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.nx = m
p.ny = n
p.m = m
p.n = n
P = 1000.
npts = 100
p.forces_inc = []
for y in np.linspace(0, p.b, npts):
p.forces_inc.append([0., y, P/(npts-1.), 0, 0])
p.forces_inc[0][2] /= 2.
p.forces_inc[-1][2] /= 2.
p.forces.append([p.a/2., p.b/2., 0, 0, 0.001])
p.static(NLgeom=True, silent=True)
c = p.analysis.cs[0]
p.plot(c, vec='w', filename='tmp_test_non_linear.png', colorbar=True)
p.uvw(p.analysis.cs[0])
assert np.isclose(p.w.max(), 0.000144768080125, rtol=0.001)
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)
class BladeStiff1D(object):
r"""Blade Stiffener using 1D Formulation for Flange
Blade-type of stiffener model using a 1D formulation for the flange and a
2D formulation for the padup (base)::
|| --> flange |
|| |-> stiffener
====== --> padup |
========================= --> panels
Panel1 Panel2
Both the flange and the padup are optional, but one must exist.
Each stiffener has a constant `y` coordinate.
"""
def __init__(self, bay, mu, panel1, panel2, ys, bb, bf, bstack, bplyts,
blaminaprops, fstack, fplyts, flaminaprops):
self.bay = bay
self.panel1 = panel1
self.panel2 = panel2
self.model = 'bladestiff1d_clt_donnell_bardell'
self.mu = mu
self.ys = ys
self.bb = bb
self.hb = 0.
self.bf = bf
self.hf = 0.
self.bstack = bstack
self.bplyts = bplyts
self.blaminaprops = blaminaprops
self.base = None
self.fstack = fstack
self.fplyts = fplyts
self.flaminaprops = flaminaprops
self.flam = None
self.As = None
self.Asb = None
self.Asf = None
self.Jxx = None
self.Iyy = None
self.Fx = None
self._rebuild()
def _rebuild(self):
assert self.panel1.model == self.panel2.model
assert self.panel1.m == self.panel2.m
assert self.panel1.n == self.panel2.n
assert self.panel1.r == self.panel2.r
assert self.panel1.alphadeg == self.panel2.alphadeg
if self.fstack is not None:
self.hf = sum(self.fplyts)
self.Asf = self.bf*self.hf
self.flam = laminate.read_stack(self.fstack, plyts=self.fplyts,
laminaprops=self.flaminaprops)
self.flam.calc_equivalent_modulus()
h = 0.5*sum(self.panel1.plyts) + 0.5*sum(self.panel2.plyts)
hb = 0.
if self.bstack is not None:
hb = sum(self.bplyts)
y1 = self.ys - self.bb/2.
y2 = self.ys + self.bb/2.
self.base = Panel(a=bay.a, b=bay.b, r=bay.r, alphadeg=bay.alphadeg,
stack=self.bstack, plyts=self.bplyts,
mu=self.mu, m=bay.m, n=bay.n,
laminaprops=self.blaminaprops, offset=(-h/2.-hb/2.),
u1tx=bay.u1tx, u1rx=bay.u1rx, u2tx=bay.u2tx, u2rx=bay.u2rx,
v1tx=bay.v1tx, v1rx=bay.v1rx, v2tx=bay.v2tx, v2rx=bay.v2rx,
w1tx=bay.w1tx, w1rx=bay.w1rx, w2tx=bay.w2tx, w2rx=bay.w2rx,
u1ty=bay.u1ty, u1ry=bay.u1ry, u2ty=bay.u2ty, u2ry=bay.u2ry,
v1ty=bay.v1ty, v1ry=bay.v1ry, v2ty=bay.v2ty, v2ry=bay.v2ry,
w1ty=bay.w1ty, w1ry=bay.w1ry, w2ty=bay.w2ty, w2ry=bay.w2ry,
y1=y1, y2=y2)
self.Asb = self.bb*hb
#TODO check offset effect on curved panels
self.dbf = self.bf/2. + hb + h/2.
self.Iyy = self.hf*self.bf**3/12.
self.Jxx = self.hf*self.bf**3/12. + self.bf*self.hf**3/12.
Asb = self.Asb if self.Asb is not None else 0.
Asf = self.Asf if self.Asf is not None else 0.
self.As = Asb + Asf
if self.fstack is not None:
self.E1 = 0
#E3 = 0
self.S1 = 0
yply = self.flam.plies[0].t/2.
for i, ply in enumerate(self.flam.plies):
if i > 0:
yply += self.flam.plies[i-1].t/2. + self.flam.plies[i].t/2.
q = ply.QL
self.E1 += ply.t*(q[0,0] - q[0,1]**2/q[1,1])
#E3 += ply.t*(q[2,2] - q[1,2]**2/q[1,1])
self.S1 += -yply*ply.t*(q[0,2] - q[0,1]*q[1,2]/q[1,1])
self.F1 = self.bf**2/12.*self.E1
def calc_k0(self, size=None, row0=0, col0=0, silent=False, finalize=True):
"""Calculate the linear constitutive stiffness matrix
"""
self._rebuild()
msg('Calculating k0... ', level=2, silent=silent)
k0 = 0.
if self.base is not None:
k0 += self.base.calc_k0(size=size, row0=row0, col0=col0,
silent=True, finalize=False)
if self.flam is not None:
mod = modelDB.db[self.model]['matrices']
bay = self.bay
k0 += mod.fk0f(self.ys, bay.a, bay.b, self.bf, self.dbf, self.E1, self.F1,
self.S1, self.Jxx, bay.m, bay.n,
bay.u1tx, bay.u1rx, bay.u2tx, bay.u2rx,
bay.w1tx, bay.w1rx, bay.w2tx, bay.w2rx,
bay.u1ty, bay.u1ry, bay.u2ty, bay.u2ry,
bay.w1ty, bay.w1ry, bay.w2ty, bay.w2ry,
size=size, row0=row0, col0=col0)
if finalize:
k0 = finalize_symmetric_matrix(k0)
self.k0 = k0
#NOTE forcing Python garbage collector to clean the memory
# it DOES make a difference! There is a memory leak not
# identified, probably in the csr_matrix process
gc.collect()
msg('finished!', level=2, silent=silent)
def calc_kG0(self, size=None, row0=0, col0=0, silent=False, finalize=True,
c=None):
"""Calculate the linear geometric stiffness matrix
"""
#TODO
if c is not None:
raise NotImplementedError('numerical kG0 not implemented')
self._rebuild()
msg('Calculating kG0... ', level=2, silent=silent)
kG0 = 0.
if self.base is not None:
# TODO include kG0 for padup
# now it is assumed that all the load goes to the flange
pass
if self.flam is not None:
Fx = self.Fx if self.Fx is not None else 0.
mod = modelDB.db[self.model]['matrices']
bay = self.bay
kG0 += mod.fkG0f(self.ys, Fx, bay.a, bay.b, self.bf, bay.m, bay.n,
bay.w1tx, bay.w1rx, bay.w2tx, bay.w2rx,
bay.w1ty, bay.w1ry, bay.w2ty, bay.w2ry,
size, row0, col0)
if finalize:
kG0 = finalize_symmetric_matrix(kG0)
self.kG0 = kG0
#NOTE forcing Python garbage collector to clean the memory
# it DOES make a difference! There is a memory leak not
# identified, probably in the csr_matrix process
gc.collect()
msg('finished!', level=2, silent=silent)
def calc_kM(self, size=None, row0=0, col0=0, silent=False, finalize=True):
"""Calculate the mass matrix
"""
self._rebuild()
msg('Calculating kM... ', level=2, silent=silent)
mod = modelDB.db[self.model]['matrices']
kM = 0.
if self.base is not None:
kM += self.base.calc_kM(size=size, row0=row0, col0=col0, silent=silent, finalize=False)
if self.flam is not None:
bay = self.bay
h = 0.5*sum(self.panel1.plyts) + 0.5*sum(self.panel2.plyts)
kM += mod.fkMf(self.ys, self.mu, h, self.hb, self.hf, bay.a, bay.b,
self.bf, self.dbf, bay.m, bay.n,
bay.u1tx, bay.u1rx, bay.u2tx, bay.u2rx,
bay.v1tx, bay.v1rx, bay.v2tx, bay.v2rx,
bay.w1tx, bay.w1rx, bay.w2tx, bay.w2rx,
bay.u1ty, bay.u1ry, bay.u2ty, bay.u2ry,
bay.v1ty, bay.v1ry, bay.v2ty, bay.v2ry,
bay.w1ty, bay.w1ry, bay.w2ty, bay.w2ry,
size=size, row0=row0, col0=col0)
if finalize:
kM = finalize_symmetric_matrix(kM)
self.kM = kM
#NOTE forcing Python garbage collector to clean the memory
# it DOES make a difference! There is a memory leak not
# identified, probably in the csr_matrix process
gc.collect()
msg('finished!', level=2, silent=silent)
def test_panel_aero():
for model in ['plate_clt_donnell_bardell',
'plate_clt_donnell_bardell_w',
'cpanel_clt_donnell_bardell']:
for atype in [1, 2]:
print('Flutter Analysis Piston Theory, atype={0}, model={1}'.
format(atype, 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
E2 = 8.7e9
p.laminaprop = (142.5e9, E2, 0.28, 5.1e9, 5.1e9, 5.1e9)
p.mu = 1.5e3
p.m = 8
p.n = 9
# pre-stress applied when atype == 1
p.Nxx = -60.
p.Nyy = -5.
# testing commong methodology based on betastar
if atype == 1:
betasstar = np.linspace(150, 350, 40)
elif atype == 2:
betasstar = np.linspace(670, 690, 40)
betas = betasstar/(p.a**3/E2/(len(p.stack)*p.plyt)**3)
p.beta = betas[0]
p.freq(atype=1, reduced_dof=False, sparse_solver=False,
silent=True)
out = np.zeros((len(betasstar), p.eigvals.shape[0]),
dtype=p.eigvals.dtype)
for i, beta in enumerate(betas):
p.beta = beta
p.freq(atype=2, reduced_dof=False, sparse_solver=False,
silent=True)
eigvals = p.eigvals*p.a**2/(np.pi**2*sum(p.plyts))*np.sqrt(p.mu/E2)
out[i, :] = eigvals
ind = np.where(np.any(out.imag != 0, axis=1))[0][0]
if atype == 1:
if not model.endswith('_w'):
assert np.isclose(betas[ind], 347.16346, atol=0.1, rtol=0)
else:
assert np.isclose(betas[ind], 174.27885, atol=0.1, rtol=0)
elif atype == 2:
if not model.endswith('_w'):
assert np.isclose(betas[ind], 728.625, atol=0.1, rtol=0)
else:
assert np.isclose(betas[ind], 728.625, atol=0.1, rtol=0)
def test_panel_fkG_num_Fnxny():
for model in ['plate_clt_donnell_bardell',
'cpanel_clt_donnell_bardell']:
print('Checking fkG_num for model {0}'.format(model))
# ssss
p = Panel()
p.a = 8.
p.b = 4.
p.r = 1.e8
p.stack = [0, 90, 90, 0, -45, +45]
p.plyt = 1e-3*0.125
p.laminaprop = (142.5e9, 8.7e9, 0.28, 5.1e9, 5.1e9, 5.1e9)
p.model = model
p.Nxx = -1.
p.m = 8
p.n = 9
p.u1ty = 1
p.u2ty = 1
p.u2tx = 1
p.v1tx = 0
p.v2tx = 1
p.v1ty = 1
p.v2ty = 1
num = 1000.
f = 0.
for i in range(int(num)):
if i == 0 or i == num - 2:
fx = p.Nxx*p.b/(num-1.)/2.
else:
fx = p.Nxx*p.b/(num-1.)
p.add_force(x=p.a, y=i*p.b/(num-1.), fx=fx, fy=0., fz=0.,
cte=True)
f += fx
p.static(silent=True)
c = p.analysis.cs[0]
p.lb(silent=True)
assert np.isclose(p.eigvals[0], 4.5290911349518801, atol=0.01, rtol=0)
nx = 9
ny = 9
Fnxny = p.F
p.lb(silent=True, c=c, Fnxny=Fnxny, nx=nx, ny=ny)
assert np.isclose(p.eigvals[0], 4.532851973656947, atol=0.01, rtol=0)
nx = 12
ny = 10
Fnxny = np.array([[p.F]*ny]*nx)
p.lb(silent=True, c=c, Fnxny=Fnxny, nx=nx, ny=ny)
assert np.isclose(p.eigvals[0], 4.532851973656947, atol=0.01, rtol=0)
def test_panel_aero():
for model in [
'plate_clt_donnell_bardell', 'plate_clt_donnell_bardell_w',
'cpanel_clt_donnell_bardell'
]:
for atype in [1, 2]:
print(
'Flutter Analysis Piston Theory, atype={0}, model={1}'.format(
atype, 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
E2 = 8.7e9
p.laminaprop = (142.5e9, E2, 0.28, 5.1e9, 5.1e9, 5.1e9)
p.mu = 1.5e3
p.m = 8
p.n = 9
# pre-stress applied when atype == 1
p.Nxx = -60.
p.Nyy = -5.
# testing commong methodology based on betastar
if atype == 1:
betasstar = np.linspace(150, 350, 40)
elif atype == 2:
betasstar = np.linspace(670, 690, 40)
betas = betasstar / (p.a**3 / E2 / (len(p.stack) * p.plyt)**3)
p.beta = betas[0]
p.freq(atype=1,
reduced_dof=False,
sparse_solver=False,
silent=True)
out = np.zeros((len(betasstar), p.eigvals.shape[0]),
dtype=p.eigvals.dtype)
for i, beta in enumerate(betas):
p.beta = beta
p.freq(atype=2,
reduced_dof=False,
sparse_solver=False,
silent=True)
eigvals = p.eigvals * p.a**2 / (
np.pi**2 * sum(p.plyts)) * np.sqrt(p.mu / E2)
out[i, :] = eigvals
ind = np.where(np.any(out.imag != 0, axis=1))[0][0]
if atype == 1:
if not model.endswith('_w'):
assert np.isclose(betas[ind], 347.16346, atol=0.1, rtol=0)
else:
assert np.isclose(betas[ind], 174.27885, atol=0.1, rtol=0)
elif atype == 2:
if not model.endswith('_w'):
assert np.isclose(betas[ind], 728.625, atol=0.1, rtol=0)
else:
assert np.isclose(betas[ind], 728.625, atol=0.1, rtol=0)
def test_fint():
m = 6
n = 6
for model in ['plate_clt_donnell_bardell', 'cpanel_clt_donnell_bardell']:
p = Panel()
p.model = model
p.w1tx = 0
p.w1rx = 1
p.u1tx = 1
p.u1ty = 1
p.u2ty = 1
p.a = 2.
p.b = 1.
p.r = 1.e5
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.nx = m
p.ny = n
p.m = m
p.n = n
P = 1000.
npts = 100
p.forces_inc = []
for y in np.linspace(0, p.b, npts):
p.forces_inc.append([0., y, P / (npts - 1.), 0, 0])
p.forces_inc[0][2] /= 2.
p.forces_inc[-1][2] /= 2.
p.forces.append([p.a / 2., p.b / 2., 0, 0, 0.001])
p.static(NLgeom=True, silent=True)
c = p.analysis.cs[0]
p.plot(c, vec='w', filename='tmp_test_non_linear.png', colorbar=True)
p.uvw(p.analysis.cs[0])
assert np.isclose(p.w.max(), 0.000144768080125, rtol=0.001)
def test_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.bc_ssss()
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
p.lb(silent=True)
if '_w' in model:
assert np.allclose(p.eigvals[0], 88.4769618837)
else:
assert np.allclose(p.eigvals[0], 85.2911727144)
p.Nxx = 0
p.Nyy = -1
p.lb(silent=True)
if '_w' in model:
assert np.allclose(p.eigvals[0], 26.4588171556)
else:
assert np.allclose(p.eigvals[0], 25.1756170679)
# ssfs
p = Panel()
p.bc_ssfs()
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
p.lb(silent=True)
if '_w' in model:
assert np.allclose(p.eigvals[0], 17.1442703121)
else:
assert np.allclose(p.eigvals[0], 15.8423562314)
p.bc_sfss()
p.Nxx = 0
p.Nyy = -1
p.lb(silent=True)
if '_w' in model:
assert np.allclose(p.eigvals[0], 15.8099861083)
else:
assert np.allclose(p.eigvals[0], 13.9421987614)
def test_freq():
for model in ['plate_clt_donnell_bardell',
'plate_clt_donnell_bardell_w',
'cpanel_clt_donnell_bardell',
'kpanel_clt_donnell_bardell']:
for atype in [3, 4]:
print('Frequency Analysis, atype={0}, model={1}'.format(
atype, model))
p = Panel()
p.model = model
p.bc_ssss()
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.
p.freq(sparse_solver=True, reduced_dof=False, silent=True,
atype=atype)
if atype == 3:
if '_w' in model:
assert np.allclose(p.eigvals[0], 19.9271684726)
else:
assert np.allclose(p.eigvals[0], 17.8587479369)
elif atype == 4:
if '_w' in model:
assert np.allclose(p.eigvals[0], 40.3728103572)
else:
assert np.allclose(p.eigvals[0], 39.3147553173)
def create_cylinder_assy(height,
r,
stack,
plyt,
laminaprop,
npanels,
m=8,
n=8):
r"""Cylinder Assembly
The panel assembly looks like::
B A
_______ _______ _______ _______
| | | | |
| | | | |
| | | | |
| p04 | p03 | p02 | p01 |
| | | | | /\ x
| | | | | |
|_______|_______|_______|_______| |
|
y <-------
where edges ``A`` and ``B`` are connected to produce the cyclic effect.
Parameters
----------
height : float
Cylinder height (along `x`).
r : float
Cylinder radius.
stack : list or tuple
Stacking sequence for the cylinder.
plyt : float
Ply thickness.
laminaprop : list or tuple
Orthotropic lamina properties: `E_1, E_2, \nu_{12}, G_{12}, G_{13}, G_{23}`.
npanels : int
The number of panels the cylinder perimiter.
m, n : int, optional
Number of approximation terms for each panel.
Returns
-------
assy, conns : tuple
A tuple containing the assembly and the default connectivity
list of dictionaries.
"""
if npanels < 2:
raise ValueError('At least two panels are needed')
skin = []
perimiter = 2 * np.pi * r
b_skin = perimiter / npanels
for i in range(npanels):
y0 = i * b_skin
panel = Panel(group='skin',
x0=0,
y0=y0,
a=height,
b=b_skin,
r=r,
m=m,
n=n,
plyt=plyt,
stack=stack,
laminaprop=laminaprop,
u1tx=0,
u1rx=1,
u2tx=0,
u2rx=1,
v1tx=0,
v1rx=1,
v2tx=0,
v2rx=1,
w1tx=0,
w1rx=1,
w2tx=0,
w2rx=1,
u1ty=1,
u1ry=1,
u2ty=1,
u2ry=1,
v1ty=1,
v1ry=1,
v2ty=1,
v2ry=1,
w1ty=1,
w1ry=1,
w2ty=1,
w2ry=1)
skin.append(panel)
conns = []
skin_loop = skin + [skin[0]]
for i in range(len(skin)):
if i != len(skin) - 1:
p01 = skin_loop[i]
p02 = skin_loop[i + 1]
conns.append(
dict(p1=p01, p2=p02, func='SSycte', ycte1=p01.b, ycte2=0))
else:
p01 = skin_loop[i + 1]
p02 = skin_loop[i]
conns.append(
dict(p1=p01, p2=p02, func='SSycte', ycte1=0, ycte2=p02.b))
assy = PanelAssembly(skin)
return assy, conns
class TStiff2D(object):
r"""T Stiffener using 2D Formulation for the Base and Flange
T-type of stiffener model using a 2D formulation for the flange and a
2D formulation for the base::
|| --> flange |
|| |-> stiffener
====== --> base |
========================= --> panels
Panel1 Panel2
The difference between this model and :class:'.BladeStiff2D' is that here
the stiffener's base has independent field variables allowing the
simulation of skin-stiffener debounding effects.
Each stiffener has a constant `y_s` coordinate.
"""
def __init__(self, bay, mu, panel1, panel2, ys, bb, bf, bstack, bplyts,
blaminaprops, fstack, fplyts, flaminaprops,
model='tstiff2d_clt_donnell_bardell', mb=15, nb=12, mf=15, nf=12):
print('\n\nWARNING - TStiff2D no longer recommended!\n'
' There is a numerically unstable way to compute the\n'
' connection between the skin and stiffener\'s base, it is\n'
' recommended to use panel.assembly instead.\n'
' Module panel.assembly allows stable ways to perform\n'
' connection among panels, and avoids using sliced\n'
' integration intervals that were causing trouble in\n'
' TStiff2D\n\n')
self.bay = bay
self.panel1 = panel1
self.panel2 = panel2
self.model = model
if bstack is None:
raise ValueError('Base laminate must be defined!')
self.ys = ys
y1 = ys - bb/2.
y2 = ys + bb/2.
self.base = Panel(a=bay.a, b=bb, r=bay.r, alphadeg=bay.alphadeg,
stack=bstack, plyts=bplyts, laminaprops=blaminaprops,
mu=mu, m=mb, n=nb, offset=0.,
u1tx=1, u1rx=0, u2tx=1, u2rx=0,
v1tx=1, v1rx=0, v2tx=1, v2rx=0,
w1tx=1, w1rx=1, w2tx=1, w2rx=1,
u1ty=1, u1ry=0, u2ty=1, u2ry=0,
v1ty=1, v1ry=0, v2ty=1, v2ry=0,
w1ty=1, w1ry=1, w2ty=1, w2ry=1,
y1=y1, y2=y2)
self.base._rebuild()
if fstack is None:
raise ValueError('Flange laminate must be defined!')
self.flange = Panel(a=bay.a, b=bf, model='plate_clt_donnell_bardell',
stack=fstack, plyts=fplyts, laminaprops=flaminaprops,
mu=mu, m=mf, n=nf, offset=0.,
u1tx=0, u1rx=0, u2tx=0, u2rx=0,
v1tx=0, v1rx=0, v2tx=0, v2rx=0,
w1tx=0, w1rx=1, w2tx=0, w2rx=1,
u1ty=1, u1ry=0, u2ty=1, u2ry=0,
v1ty=1, v1ry=0, v2ty=1, v2ry=0,
w1ty=1, w1ry=1, w2ty=1, w2ry=1)
self.flange._rebuild()
self.eta_conn_base = 0.
self.eta_conn_flange = -1.
self.k0 = None
self.kM = None
self.kG0 = None
self._rebuild()
def _rebuild(self):
assert self.panel1.model == self.panel2.model
assert self.panel1.r == self.panel2.r
assert self.panel1.alphadeg == self.panel2.alphadeg
a = None
b = None
if self.panel1 is not None:
a = self.panel1.a
b = self.panel1.b
elif self.panel2 is not None:
a = self.panel2.a
b = self.panel2.b
if a is not None and b is not None:
if a / b > 10.:
if self.base.m <= 15 and self.flange.m <= 15:
raise RuntimeError('For a/b > 10. use base.m and flange.m > 15')
else:
warn('For a/b > 10. be sure to check convergence for base.m and flange.m')
self.flange.lam = laminate.read_stack(self.flange.stack,
plyts=self.flange.plyts, laminaprops=self.flange.laminaprops)
#NOTE below offset is not needed since it is already considered in the
# connectivity matrices, using dpb
h = 0.5*sum(self.panel1.plyts) + 0.5*sum(self.panel2.plyts)
hb = sum(self.base.plyts)
self.dpb = h/2. + hb/2.
self.base.lam = laminate.read_stack(self.base.stack,
plyts=self.base.plyts, laminaprops=self.base.laminaprops,
offset=0.)
def calc_k0(self, size=None, row0=0, col0=0, silent=False, finalize=True):
"""Calculate the linear constitutive stiffness matrix
"""
self._rebuild()
msg('Calculating k0... ', level=2, silent=silent)
# NOTE
# row0 and col0 define where the stiffener's base matrix starts
# rowf and colf define where the stiffener's flange matrix starts
rowf = row0 + self.base.get_size()
colf = col0 + self.base.get_size()
k0 = 0.
k0 += self.base.calc_k0(size=size, row0=row0, col0=col0, silent=True, finalize=False)
k0 += self.flange.calc_k0(size=size, row0=rowf, col0=colf, silent=True, finalize=False)
# connectivity panel-base
conn = stiffmDB.db[self.model]['connections']
ktpb, krpb = calc_kt_kr(self.panel1, self.base, 'bot-top')
ktpb = min(1.e7, ktpb)
#TODO remove from Cython the capability to run with debonding defect
y1 = self.ys - self.base.b/2.
y2 = self.ys + self.base.b/2.
bay = self.bay
k0 += conn.fkCppy1y2(y1, y2,
ktpb, bay.a, bay.b, self.dpb, bay.m, bay.n,
bay.u1tx, bay.u1rx, bay.u2tx, bay.u2rx,
bay.v1tx, bay.v1rx, bay.v2tx, bay.v2rx,
bay.w1tx, bay.w1rx, bay.w2tx, bay.w2rx,
bay.u1ty, bay.u1ry, bay.u2ty, bay.u2ry,
bay.v1ty, bay.v1ry, bay.v2ty, bay.v2ry,
bay.w1ty, bay.w1ry, bay.w2ty, bay.w2ry,
size, 0, 0)
k0 += conn.fkCpby1y2(y1, y2,
ktpb, bay.a, bay.b, self.dpb,
bay.m, bay.n, self.base.m, self.base.n,
bay.u1tx, bay.u1rx, bay.u2tx, bay.u2rx,
bay.v1tx, bay.v1rx, bay.v2tx, bay.v2rx,
bay.w1tx, bay.w1rx, bay.w2tx, bay.w2rx,
bay.u1ty, bay.u1ry, bay.u2ty, bay.u2ry,
bay.v1ty, bay.v1ry, bay.v2ty, bay.v2ry,
bay.w1ty, bay.w1ry, bay.w2ty, bay.w2ry,
self.base.u1tx, self.base.u1rx, self.base.u2tx, self.base.u2rx,
self.base.v1tx, self.base.v1rx, self.base.v2tx, self.base.v2rx,
self.base.w1tx, self.base.w1rx, self.base.w2tx, self.base.w2rx,
self.base.u1ty, self.base.u1ry, self.base.u2ty, self.base.u2ry,
self.base.v1ty, self.base.v1ry, self.base.v2ty, self.base.v2ry,
self.base.w1ty, self.base.w1ry, self.base.w2ty, self.base.w2ry,
size, 0, col0)
k0 += conn.fkCbbpby1y2(y1, y2,
ktpb, bay.a, bay.b, self.base.m, self.base.n,
self.base.u1tx, self.base.u1rx, self.base.u2tx, self.base.u2rx,
self.base.v1tx, self.base.v1rx, self.base.v2tx, self.base.v2rx,
self.base.w1tx, self.base.w1rx, self.base.w2tx, self.base.w2rx,
self.base.u1ty, self.base.u1ry, self.base.u2ty, self.base.u2ry,
self.base.v1ty, self.base.v1ry, self.base.v2ty, self.base.v2ry,
self.base.w1ty, self.base.w1ry, self.base.w2ty, self.base.w2ry,
size, row0, col0)
# connectivity base-flange
ktbf, krbf = calc_kt_kr(self.base, self.flange, 'ycte')
ycte1 = (self.eta_conn_base + 1)/2. * self.base.b
ycte2 = (self.eta_conn_flange + 1)/2. * self.flange.b
k0 += fkCBFycte11(ktbf, krbf, self.base, ycte1, size, row0, col0)
k0 += fkCBFycte12(ktbf, krbf, self.base, self.flange, ycte1, ycte2, size, row0, colf)
k0 += fkCBFycte22(ktbf, krbf, self.base, self.flange, ycte2, size, rowf, colf)
if finalize:
k0 = finalize_symmetric_matrix(k0)
self.k0 = k0
#NOTE forcing Python garbage collector to clean the memory
# it DOES make a difference! There is a memory leak not
# identified, probably in the csr_matrix process
gc.collect()
msg('finished!', level=2, silent=silent)
def calc_kG0(self, size=None, row0=0, col0=0, silent=False, finalize=True,
c=None, NLgeom=False):
"""Calculate the linear geometric stiffness matrix
See :meth:`.Panel.calc_k0` for details on each parameter.
"""
self._rebuild()
if c is None:
msg('Calculating kG0... ', level=2, silent=silent)
else:
msg('Calculating kG... ', level=2, silent=silent)
# NOTE:
# - row0 and col0 define where the stiffener's base matrix starts
# - rowf and colf define where the stiffener's flange matrix starts
rowf = row0 + self.base.get_size()
colf = col0 + self.base.get_size()
kG0 = 0.
kG0 += self.base.calc_kG0(c=c, size=size, row0=row0, col0=col0, silent=True,
finalize=False, NLgeom=NLgeom)
kG0 += self.flange.calc_kG0(c=c, size=size, row0=rowf, col0=colf,
silent=True, finalize=False, NLgeom=NLgeom)
if finalize:
kG0 = finalize_symmetric_matrix(kG0)
self.kG0 = kG0
#NOTE forcing Python garbage collector to clean the memory
# it DOES make a difference! There is a memory leak not
# identified, probably in the csr_matrix process
gc.collect()
msg('finished!', level=2, silent=silent)
def calc_kM(self, size=None, row0=0, col0=0, silent=False, finalize=True):
"""Calculate the mass matrix
"""
self._rebuild()
msg('Calculating kM... ', level=2, silent=silent)
rowf = row0 + self.base.get_size()
colf = col0 + self.base.get_size()
kM = 0.
kM += self.base.calc_kM(size=size, row0=row0, col0=col0, silent=True,
finalize=False)
kM += self.flange.calc_kM(size=size, row0=rowf, col0=colf, silent=True,
finalize=False)
if finalize:
kM = finalize_symmetric_matrix(kM)
self.kM = kM
#NOTE forcing Python garbage collector to clean the memory
# it DOES make a difference! There is a memory leak not
# identified, probably in the csr_matrix process
gc.collect()
msg('finished!', level=2, silent=silent)
def __init__(self,
bay,
mu,
panel1,
panel2,
ys,
bb,
bf,
bstack,
bplyts,
blaminaprops,
fstack,
fplyts,
flaminaprops,
mf=14,
nf=11):
self.bay = bay
self.panel1 = panel1
self.panel2 = panel2
self.mu = mu
self.ys = ys
self.bb = bb
self.forces_flange = []
self.bstack = bstack
self.bplyts = bplyts
self.blaminaprops = blaminaprops
self.k0 = None
self.kM = None
self.kG0 = None
self.base = None
if bstack is not None:
y1 = self.ys - bb / 2.
y2 = self.ys + bb / 2.
h = 0.5 * sum(self.panel1.plyts) + 0.5 * sum(self.panel2.plyts)
hb = sum(self.bplyts)
self.base = Panel(a=bay.a,
b=bay.b,
r=bay.r,
alphadeg=bay.alphadeg,
stack=bstack,
plyts=bplyts,
laminaprops=blaminaprops,
mu=mu,
m=bay.m,
n=bay.n,
offset=(-h / 2. - hb / 2.),
u1tx=bay.u1tx,
u1rx=bay.u1rx,
u2tx=bay.u2tx,
u2rx=bay.u2rx,
v1tx=bay.v1tx,
v1rx=bay.v1rx,
v2tx=bay.v2tx,
v2rx=bay.v2rx,
w1tx=bay.w1tx,
w1rx=bay.w1rx,
w2tx=bay.w2tx,
w2rx=bay.w2rx,
u1ty=bay.u1ty,
u1ry=bay.u1ry,
u2ty=bay.u2ty,
u2ry=bay.u2ry,
v1ty=bay.v1ty,
v1ry=bay.v1ry,
v2ty=bay.v2ty,
v2ry=bay.v2ry,
w1ty=bay.w1ty,
w1ry=bay.w1ry,
w2ty=bay.w2ty,
w2ry=bay.w2ry,
y1=y1,
y2=y2)
self.flange = None
if fstack is not None:
self.flange = Panel(m=mf,
n=nf,
a=bay.a,
b=bf,
mu=mu,
stack=fstack,
plyts=fplyts,
laminaprops=flaminaprops,
model='plate_clt_donnell_bardell',
u1tx=0.,
u1rx=0.,
u2tx=0.,
u2rx=0.,
v1tx=0.,
v1rx=0.,
v2tx=0.,
v2rx=0.,
w1tx=0.,
w1rx=1.,
w2tx=0.,
w2rx=1.,
u1ty=1.,
u1ry=0.,
u2ty=1.,
u2ry=0.,
v1ty=1.,
v1ry=0.,
v2ty=1.,
v2ry=0.,
w1ty=1.,
w1ry=1.,
w2ty=1.,
w2ry=1.)
self._rebuild()
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_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 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 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_kT():
mns = [[4, 4], [4, 5], [4, 6], [5, 5], [5, 6], [6, 6], [8, 9], [9, 8]]
for m, n in mns:
for model in [
'plate_clt_donnell_bardell', 'cpanel_clt_donnell_bardell'
]:
p = Panel()
p.model = model
p.w1tx = 0
p.u1tx = 1
p.u1ty = 1
p.u2ty = 1
p.a = 2.
p.b = 0.5
p.r = 10
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.m = m
p.n = n
p.nx = m
p.ny = n
P = 1000.
npts = 5
p.forces_inc = []
for y in np.linspace(0, p.b, npts):
p.forces_inc.append([0., y, P / (npts - 1.), 0, 0])
p.forces_inc[0][2] /= 2.
p.forces_inc[-1][2] /= 2.
k0 = p.calc_k0(silent=True)
kT = p.calc_kT(c=np.zeros(p.get_size()), silent=True)
error = np.abs(kT - k0).sum()
assert error < 1.e-7
def create_cylinder_blade_stiffened(height, r, stack, stack_blades,
width_blades, plyt, laminaprop, npanels, m=8, n=8):
r"""Cylinder Assembly
The panel assembly looks like::
B A
_______ _______ _______ _______
| | | | |
| | | | |
| | | | |
| p04 | p03 | p02 | p01 |
| | | | |
| | | | |
|_______|_______|_______|_______|
Blade Blade Blade Blade
04 03 02 01
_ _ _ _
| | | | | | | |
| | | | | | | |
| | | | | | | |
| | | | | | | |
|_| |_| |_| |_|
x
/\
|
|
y <-------
where edges ``A`` and ``B`` are connected to produce the cyclic effect.
Parameters
----------
height : float
Cylinder height (along `x`).
r : float
Cylinder radius.
stack : array-like
Stacking sequence for the cylinder.
stack_blades : list of array-like
The stacking sequence for each blade (with length = npanels).
width_blades : array-like
The width for each blade (with length = npanels).
plyt : float
Ply thickness (assumed unique for the whole structure).
laminaprop : list or tuple
Orthotropic lamina properties: `E_1, E_2, \nu_{12}, G_{12}, G_{13}, G_{23}`.
npanels : int
The number of panels the cylinder perimiter.
m, n : int, optional
Number of approximation terms for each panel.
Returns
-------
assy, conns : tuple
A tuple containing the assembly and the default connectivity
list of dictionaries.
"""
if npanels < 2:
raise ValueError('At least two panels are needed')
if len(stack_blades) != npanels:
raise ValueError('stack_blades must have length = npanels')
if len(width_blades) != npanels:
raise ValueError('width_blades must have length = npanels')
skin = []
blades = []
perimiter = 2*np.pi*r
b_skin = perimiter / npanels
for i in range(npanels):
y0 = i*b_skin
panel = Panel(group='skin', x0=0, y0=y0, a=height, b=b_skin,
r=r, m=m, n=n, plyt=plyt, stack=stack, laminaprop=laminaprop,
u1tx=0, u1rx=1, u2tx=0, u2rx=1,
v1tx=0, v1rx=1, v2tx=0, v2rx=1,
w1tx=0, w1rx=1, w2tx=0, w2rx=1,
u1ty=1, u1ry=1, u2ty=1, u2ry=1,
v1ty=1, v1ry=1, v2ty=1, v2ry=1,
w1ty=1, w1ry=1, w2ty=1, w2ry=1)
skin.append(panel)
for i, panel in enumerate(skin):
y0 = i*b_skin
blade_name = 'blade_%02d' % i
blade = Panel(group=blade_name, x0=0, y0=y0, a=height,
b=width_blades[i], m=m, n=n, plyt=plyt,
stack=stack_blades[i], laminaprop=laminaprop,
u1tx=0, u1rx=1, u2tx=0, u2rx=1,
v1tx=0, v1rx=1, v2tx=0, v2rx=1,
w1tx=0, w1rx=1, w2tx=0, w2rx=1,
u1ty=1, u1ry=1, u2ty=1, u2ry=1,
v1ty=1, v1ry=1, v2ty=1, v2ry=1,
w1ty=1, w1ry=1, w2ty=1, w2ry=1)
blades.append(blade)
conns = []
skin_loop = skin + [skin[0]]
for i in range(len(skin)):
if i != len(skin) - 1:
p01 = skin_loop[i]
p02 = skin_loop[i+1]
conns.append(dict(p1=p01, p2=p02, func='SSycte', ycte1=p01.b, ycte2=0))
else:
p01 = skin_loop[i+1]
p02 = skin_loop[i]
conns.append(dict(p1=p01, p2=p02, func='SSycte', ycte1=0, ycte2=p02.b))
for panel, blade in zip(skin, blades):
conns.append(dict(p1=panel, p2=blade, func='BFycte', ycte1=0, ycte2=0))
assy = PanelAssembly(skin + blades)
return assy, conns
def test_panel_field_outputs():
m = 7
n = 6
#TODO implement for conical panels
strain_field = dict(exx=None, eyy=None, gxy=None, kxx=None, kyy=None, kxy=None)
stress_field = dict(Nxx=None, Nyy=None, Nxy=None, Mxx=None, Myy=None, Mxy=None)
for model in ['plate_clt_donnell_bardell',
'cpanel_clt_donnell_bardell']:
p = Panel()
p.model = model
p.u1tx = 1
p.u1ty = 1
p.u2ty = 1
p.v1tx = 0
p.v2tx = 0
p.v1ty = 0
p.v2ty = 0
p.a = 2.
p.b = 1.
p.r = 1.e5
p.stack = [0, -45, +45, 90, +45, -45, 0, 0]
p.plyt = 1e-3*0.125
p.laminaprop = (142.5e9, 8.7e9, 0.28, 5.1e9, 5.1e9, 5.1e9)
p.nx = m
p.ny = n
p.m = m
p.n = n
P = 1000.
npts = 100
p.forces_inc = []
for y in np.linspace(0, p.b, npts):
p.forces_inc.append([0., y, P/(npts-1.), 0, 0])
p.forces_inc[0][2] /= 2.
p.forces_inc[-1][2] /= 2.
p.static()
c = p.analysis.cs[0]
Ns = p.stress(c, gridx=50, gridy=50)
es = p.strain(c, gridx=50, gridy=50)
for k, v in strain_field.items():
if v is None:
strain_field[k] = es.get(k).min()
else:
assert np.isclose(strain_field[k], es.get(k).min(), rtol=0.05)
p.plot(c, vec=k, filename='tmp_test_panel_strain_field_%s.png' % k)
for k, v in stress_field.items():
if v is None:
stress_field[k] = Ns.get(k).min()
else:
assert np.isclose(stress_field[k], Ns.get(k).min(), rtol=0.05)
p.plot(c, vec=k, filename='tmp_test_panel_stress_field_%s.png' % k)
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 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_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 add_panel(self, y1, y2, stack=None, plyts=None, plyt=None,
laminaprops=None, laminaprop=None, model=None, mu=None, **kwargs):
"""Add a new panel to the current panel bay
Parameters
----------
y1 : float
Position of the first panel edge along `y`.
y2 : float
Position of the second panel edge along `y`.
stack : list, optional
Panel stacking sequence. If not given the stacking sequence of the
bay will be used.
plyts : list, optional
Thicknesses for each panel ply. If not supplied the bay ``plyts``
attribute will be used.
plyt : float, optional
Unique thickness to be used for all panel plies. If not supplied
the bay ``plyt`` attribute will be used.
laminaprops : list, optional
Lamina properties for each panel ply.
laminaprop : list, optional
Unique lamina properties for all panel plies.
model : str, optional
Not recommended to pass this parameter, but the user can use a
different model for each panel. It is recommended to defined
``model`` for the bay object.
mu : float, optional
Panel material density. If not given the bay density will be used.
Notes
-----
Additional parameters can be passed using the ``kwargs``.
"""
p = Panel()
p.m = self.m
p.n = self.n
p.a = self.a
p.b = self.b
p.r = self.r
p.y1 = y1
p.y2 = y2
p.d = 0.
p.model = model if model is not None else self.model
p.stack = stack if stack is not None else self.stack
p.plyt = plyt if plyt is not None else self.plyt
p.plyts = plyts if plyts is not None else self.plyts
p.laminaprop = laminaprop if laminaprop is not None else self.laminaprop
p.laminaprops = laminaprops if laminaprops is not None else self.laminaprops
p.mu = mu if mu is not None else self.mu
p.u1tx = self.u1tx
p.u1rx = self.u1rx
p.u2tx = self.u2tx
p.u2rx = self.u2rx
p.v1tx = self.v1tx
p.v1rx = self.v1rx
p.v2tx = self.v2tx
p.v2rx = self.v2rx
p.w1tx = self.w1tx
p.w1rx = self.w1rx
p.w2tx = self.w2tx
p.w2rx = self.w2rx
p.u1ty = self.u1ty
p.u1ry = self.u1ry
p.u2ty = self.u2ty
p.u2ry = self.u2ry
p.v1ty = self.v1ty
p.v1ry = self.v1ry
p.v2ty = self.v2ty
p.v2ry = self.v2ry
p.w1ty = self.w1ty
p.w1ry = self.w1ry
p.w2ty = self.w2ty
p.w2ry = self.w2ry
for k, v in kwargs.items():
setattr(p, k, v)
self.panels.append(p)
class BladeStiff2D(object):
r"""Blade Stiffener using 2D Formulation for Flange
Blade-type of stiffener model using a 2D formulation for the flange and a
2D formulation for the base (padup)::
|| --> flange |
|| |-> stiffener
====== --> padup |
========================= --> panels
Panel1 Panel2
Both the flange and the base are optional. The stiffener's base is modeled
using the same approximation functions as the skin, with the proper
offset.
Each stiffener has a constant `y_s` coordinate.
"""
def __init__(self, bay, mu, panel1, panel2, ys, bb, bf, bstack, bplyts,
blaminaprops, fstack, fplyts, flaminaprops, mf=14, nf=11):
self.bay = bay
self.panel1 = panel1
self.panel2 = panel2
self.mu = mu
self.ys = ys
self.bb = bb
self.forces_flange = []
self.bstack = bstack
self.bplyts = bplyts
self.blaminaprops = blaminaprops
self.k0 = None
self.kM = None
self.kG0 = None
self.base = None
if bstack is not None:
y1 = self.ys - bb/2.
y2 = self.ys + bb/2.
h = 0.5*sum(self.panel1.plyts) + 0.5*sum(self.panel2.plyts)
hb = sum(self.bplyts)
self.base = Panel(a=bay.a, b=bay.b, r=bay.r, alphadeg=bay.alphadeg,
stack=bstack, plyts=bplyts, laminaprops=blaminaprops,
mu=mu, m=bay.m, n=bay.n, offset=(-h/2.-hb/2.),
u1tx=bay.u1tx, u1rx=bay.u1rx, u2tx=bay.u2tx, u2rx=bay.u2rx,
v1tx=bay.v1tx, v1rx=bay.v1rx, v2tx=bay.v2tx, v2rx=bay.v2rx,
w1tx=bay.w1tx, w1rx=bay.w1rx, w2tx=bay.w2tx, w2rx=bay.w2rx,
u1ty=bay.u1ty, u1ry=bay.u1ry, u2ty=bay.u2ty, u2ry=bay.u2ry,
v1ty=bay.v1ty, v1ry=bay.v1ry, v2ty=bay.v2ty, v2ry=bay.v2ry,
w1ty=bay.w1ty, w1ry=bay.w1ry, w2ty=bay.w2ty, w2ry=bay.w2ry,
y1=y1, y2=y2)
self.flange = None
if fstack is not None:
self.flange = Panel(m=mf, n=nf, a=bay.a, b=bf, mu=mu,
stack=fstack, plyts=fplyts, laminaprops=flaminaprops,
model='plate_clt_donnell_bardell',
u1tx=0., u1rx=0., u2tx=0., u2rx=0.,
v1tx=0., v1rx=0., v2tx=0., v2rx=0.,
w1tx=0., w1rx=1., w2tx=0., w2rx=1.,
u1ty=1., u1ry=0., u2ty=1., u2ry=0.,
v1ty=1., v1ry=0., v2ty=1., v2ry=0.,
w1ty=1., w1ry=1., w2ty=1., w2ry=1.)
self._rebuild()
def _rebuild(self):
assert self.panel1.model == self.panel2.model
assert self.panel1.m == self.panel2.m
assert self.panel1.n == self.panel2.n
assert self.panel1.r == self.panel2.r
assert self.panel1.alphadeg == self.panel2.alphadeg
if self.flange is not None:
self.flange.lam = laminate.read_stack(self.flange.stack, plyts=self.flange.plyts,
laminaprops=self.flange.laminaprops)
self.flange.lam.calc_equivalent_modulus()
if self.base is not None:
h = 0.5*sum(self.panel1.plyts) + 0.5*sum(self.panel2.plyts)
hb = sum(self.bplyts)
self.dpb = h/2. + hb/2.
self.base.lam = laminate.read_stack(self.bstack, plyts=self.bplyts,
laminaprops=self.blaminaprops,
offset=(-h/2.-hb/2.))
def calc_k0(self, size=None, row0=0, col0=0, silent=False, finalize=True):
"""Calculate the linear constitutive stiffness matrix
"""
self._rebuild()
msg('Calculating k0... ', level=2, silent=silent)
flangemod = panmodelDB.db[self.flange.model]['matrices']
bay = self.bay
a = bay.a
b = bay.b
m = bay.m
n = bay.n
k0 = 0.
if self.base is not None:
k0 += self.base.calc_k0(size=size, row0=0, col0=0, silent=True,
finalize=False)
if self.flange is not None:
k0 += self.flange.calc_k0(size=size, row0=row0, col0=col0,
silent=True, finalize=False)
# connectivity between stiffener'base and stiffener's flange
if self.base is None:
ktbf, krbf = calc_kt_kr(self.panel1, self.flange, 'ycte')
else:
ktbf, krbf = calc_kt_kr(self.base, self.flange, 'ycte')
mod = db['bladestiff2d_clt_donnell_bardell']['connections']
k0 += mod.fkCss(ktbf, krbf, self.ys, a, b, m, n,
bay.u1tx, bay.u1rx, bay.u2tx, bay.u2rx,
bay.v1tx, bay.v1rx, bay.v2tx, bay.v2rx,
bay.w1tx, bay.w1rx, bay.w2tx, bay.w2rx,
bay.u1ty, bay.u1ry, bay.u2ty, bay.u2ry,
bay.v1ty, bay.v1ry, bay.v2ty, bay.v2ry,
bay.w1ty, bay.w1ry, bay.w2ty, bay.w2ry,
size, 0, 0)
bf = self.flange.b
k0 += mod.fkCsf(ktbf, krbf, self.ys, a, b, bf, m, n, self.flange.m, self.flange.n,
bay.u1tx, bay.u1rx, bay.u2tx, bay.u2rx,
bay.v1tx, bay.v1rx, bay.v2tx, bay.v2rx,
bay.w1tx, bay.w1rx, bay.w2tx, bay.w2rx,
bay.u1ty, bay.u1ry, bay.u2ty, bay.u2ry,
bay.v1ty, bay.v1ry, bay.v2ty, bay.v2ry,
bay.w1ty, bay.w1ry, bay.w2ty, bay.w2ry,
self.flange.u1tx, self.flange.u1rx, self.flange.u2tx, self.flange.u2rx,
self.flange.v1tx, self.flange.v1rx, self.flange.v2tx, self.flange.v2rx,
self.flange.w1tx, self.flange.w1rx, self.flange.w2tx, self.flange.w2rx,
self.flange.u1ty, self.flange.u1ry, self.flange.u2ty, self.flange.u2ry,
self.flange.v1ty, self.flange.v1ry, self.flange.v2ty, self.flange.v2ry,
self.flange.w1ty, self.flange.w1ry, self.flange.w2ty, self.flange.w2ry,
size, 0, col0)
k0 += mod.fkCff(ktbf, krbf, a, bf, self.flange.m, self.flange.n,
self.flange.u1tx, self.flange.u1rx, self.flange.u2tx, self.flange.u2rx,
self.flange.v1tx, self.flange.v1rx, self.flange.v2tx, self.flange.v2rx,
self.flange.w1tx, self.flange.w1rx, self.flange.w2tx, self.flange.w2rx,
self.flange.u1ty, self.flange.u1ry, self.flange.u2ty, self.flange.u2ry,
self.flange.v1ty, self.flange.v1ry, self.flange.v2ty, self.flange.v2ry,
self.flange.w1ty, self.flange.w1ry, self.flange.w2ty, self.flange.w2ry,
size, row0, col0)
if finalize:
k0 = finalize_symmetric_matrix(k0)
self.k0 = k0
#NOTE forcing Python garbage collector to clean the memory
# it DOES make a difference! There is a memory leak not
# identified, probably in the csr_matrix process
gc.collect()
msg('finished!', level=2, silent=silent)
def calc_kG0(self, size=None, row0=0, col0=0, silent=False, finalize=True,
c=None, NLgeom=False):
"""Calculate the linear geometric stiffness matrix
"""
self._rebuild()
msg('Calculating kG0... ', level=2, silent=silent)
kG0 = 0.
if self.base is not None:
#TODO include kG0 for pad-up and Nxx load that arrives there
pass
if self.flange is not None:
kG0 += self.flange.calc_kG0(size=size, row0=row0, col0=col0,
silent=True, finalize=False, NLgeom=NLgeom)
if finalize:
kG0 = finalize_symmetric_matrix(kG0)
self.kG0 = kG0
#NOTE forcing Python garbage collector to clean the memory
# it DOES make a difference! There is a memory leak not
# identified, probably in the csr_matrix process
gc.collect()
msg('finished!', level=2, silent=silent)
def calc_kM(self, size=None, row0=0, col0=0, silent=False, finalize=True):
"""Calculate the mass matrix
"""
self._rebuild()
msg('Calculating kM... ', level=2, silent=silent)
kM = 0.
if self.base is not None:
kM += self.base.calc_kM(size=size, row0=0, col0=0, silent=True, finalize=False)
if self.flange is not None:
kM += self.flange.calc_kM(size=size, row0=row0, col0=col0, silent=True, finalize=False)
if finalize:
kM = finalize_symmetric_matrix(kM)
self.kM = kM
#NOTE forcing Python garbage collector to clean the memory
# it DOES make a difference! There is a memory leak not
# identified, probably in the csr_matrix process
gc.collect()
msg('finished!', level=2, silent=silent)
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_panel_fkG_num_Fnxny():
for model in ['plate_clt_donnell_bardell', 'cpanel_clt_donnell_bardell']:
print('Checking fkG_num for model {0}'.format(model))
# ssss
p = Panel()
p.a = 8.
p.b = 4.
p.r = 1.e8
p.stack = [0, 90, 90, 0, -45, +45]
p.plyt = 1e-3 * 0.125
p.laminaprop = (142.5e9, 8.7e9, 0.28, 5.1e9, 5.1e9, 5.1e9)
p.model = model
p.Nxx = -1.
p.m = 8
p.n = 9
p.u1ty = 1
p.u2ty = 1
p.u2tx = 1
p.v1tx = 0
p.v2tx = 1
p.v1ty = 1
p.v2ty = 1
num = 1000.
f = 0.
for i in range(int(num)):
if i == 0 or i == num - 2:
fx = p.Nxx * p.b / (num - 1.) / 2.
else:
fx = p.Nxx * p.b / (num - 1.)
p.add_force(x=p.a,
y=i * p.b / (num - 1.),
fx=fx,
fy=0.,
fz=0.,
cte=True)
f += fx
p.static(silent=True)
c = p.analysis.cs[0]
p.lb(silent=True)
assert np.isclose(p.eigvals[0], 4.5290911349518801, atol=0.01, rtol=0)
nx = 9
ny = 9
Fnxny = p.F
p.lb(silent=True, c=c, Fnxny=Fnxny, nx=nx, ny=ny)
assert np.isclose(p.eigvals[0], 4.532851973656947, atol=0.01, rtol=0)
nx = 12
ny = 10
Fnxny = np.array([[p.F] * ny] * nx)
p.lb(silent=True, c=c, Fnxny=Fnxny, nx=nx, ny=ny)
assert np.isclose(p.eigvals[0], 4.532851973656947, atol=0.01, 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)
class TStiff2D(object):
r"""T Stiffener using 2D Formulation for the Base and Flange
T-type of stiffener model using a 2D formulation for the flange and a
2D formulation for the base::
|| --> flange |
|| |-> stiffener
====== --> base |
========================= --> panels
Panel1 Panel2
The difference between this model and :class:'.BladeStiff2D' is that here
the stiffener's base has independent field variables allowing the
simulation of skin-stiffener debounding effects.
Each stiffener has a constant `y_s` coordinate.
"""
def __init__(self,
bay,
mu,
panel1,
panel2,
ys,
bb,
bf,
bstack,
bplyts,
blaminaprops,
fstack,
fplyts,
flaminaprops,
model='tstiff2d_clt_donnell_bardell',
mb=15,
nb=12,
mf=15,
nf=12):
print(
'\n\nWARNING - TStiff2D no longer recommended!\n'
' There is a numerically unstable way to compute the\n'
' connection between the skin and stiffener\'s base, it is\n'
' recommended to use panel.assembly instead.\n'
' Module panel.assembly allows stable ways to perform\n'
' connection among panels, and avoids using sliced\n'
' integration intervals that were causing trouble in\n'
' TStiff2D\n\n')
self.bay = bay
self.panel1 = panel1
self.panel2 = panel2
self.model = model
if bstack is None:
raise ValueError('Base laminate must be defined!')
self.ys = ys
y1 = ys - bb / 2.
y2 = ys + bb / 2.
self.base = Panel(a=bay.a,
b=bb,
r=bay.r,
alphadeg=bay.alphadeg,
stack=bstack,
plyts=bplyts,
laminaprops=blaminaprops,
mu=mu,
m=mb,
n=nb,
offset=0.,
u1tx=1,
u1rx=0,
u2tx=1,
u2rx=0,
v1tx=1,
v1rx=0,
v2tx=1,
v2rx=0,
w1tx=1,
w1rx=1,
w2tx=1,
w2rx=1,
u1ty=1,
u1ry=0,
u2ty=1,
u2ry=0,
v1ty=1,
v1ry=0,
v2ty=1,
v2ry=0,
w1ty=1,
w1ry=1,
w2ty=1,
w2ry=1,
y1=y1,
y2=y2)
self.base._rebuild()
if fstack is None:
raise ValueError('Flange laminate must be defined!')
self.flange = Panel(a=bay.a,
b=bf,
model='plate_clt_donnell_bardell',
stack=fstack,
plyts=fplyts,
laminaprops=flaminaprops,
mu=mu,
m=mf,
n=nf,
offset=0.,
u1tx=0,
u1rx=0,
u2tx=0,
u2rx=0,
v1tx=0,
v1rx=0,
v2tx=0,
v2rx=0,
w1tx=0,
w1rx=1,
w2tx=0,
w2rx=1,
u1ty=1,
u1ry=0,
u2ty=1,
u2ry=0,
v1ty=1,
v1ry=0,
v2ty=1,
v2ry=0,
w1ty=1,
w1ry=1,
w2ty=1,
w2ry=1)
self.flange._rebuild()
self.eta_conn_base = 0.
self.eta_conn_flange = -1.
self.k0 = None
self.kM = None
self.kG0 = None
self._rebuild()
def _rebuild(self):
assert self.panel1.model == self.panel2.model
assert self.panel1.r == self.panel2.r
assert self.panel1.alphadeg == self.panel2.alphadeg
a = None
b = None
if self.panel1 is not None:
a = self.panel1.a
b = self.panel1.b
elif self.panel2 is not None:
a = self.panel2.a
b = self.panel2.b
if a is not None and b is not None:
if a / b > 10.:
if self.base.m <= 15 and self.flange.m <= 15:
raise RuntimeError(
'For a/b > 10. use base.m and flange.m > 15')
else:
warn(
'For a/b > 10. be sure to check convergence for base.m and flange.m'
)
self.flange.lam = laminate.read_stack(
self.flange.stack,
plyts=self.flange.plyts,
laminaprops=self.flange.laminaprops)
#NOTE below offset is not needed since it is already considered in the
# connectivity matrices, using dpb
h = 0.5 * sum(self.panel1.plyts) + 0.5 * sum(self.panel2.plyts)
hb = sum(self.base.plyts)
self.dpb = h / 2. + hb / 2.
self.base.lam = laminate.read_stack(self.base.stack,
plyts=self.base.plyts,
laminaprops=self.base.laminaprops,
offset=0.)
def calc_k0(self, size=None, row0=0, col0=0, silent=False, finalize=True):
"""Calculate the linear constitutive stiffness matrix
"""
self._rebuild()
msg('Calculating k0... ', level=2, silent=silent)
# NOTE
# row0 and col0 define where the stiffener's base matrix starts
# rowf and colf define where the stiffener's flange matrix starts
rowf = row0 + self.base.get_size()
colf = col0 + self.base.get_size()
k0 = 0.
k0 += self.base.calc_k0(size=size,
row0=row0,
col0=col0,
silent=True,
finalize=False)
k0 += self.flange.calc_k0(size=size,
row0=rowf,
col0=colf,
silent=True,
finalize=False)
# connectivity panel-base
conn = stiffmDB.db[self.model]['connections']
ktpb, krpb = calc_kt_kr(self.panel1, self.base, 'bot-top')
ktpb = min(1.e7, ktpb)
#TODO remove from Cython the capability to run with debonding defect
y1 = self.ys - self.base.b / 2.
y2 = self.ys + self.base.b / 2.
bay = self.bay
k0 += conn.fkCppy1y2(y1, y2, ktpb, bay.a, bay.b, self.dpb, bay.m,
bay.n, bay.u1tx, bay.u1rx, bay.u2tx, bay.u2rx,
bay.v1tx, bay.v1rx, bay.v2tx, bay.v2rx, bay.w1tx,
bay.w1rx, bay.w2tx, bay.w2rx, bay.u1ty, bay.u1ry,
bay.u2ty, bay.u2ry, bay.v1ty, bay.v1ry, bay.v2ty,
bay.v2ry, bay.w1ty, bay.w1ry, bay.w2ty, bay.w2ry,
size, 0, 0)
k0 += conn.fkCpby1y2(
y1, y2, ktpb, bay.a, bay.b, self.dpb, bay.m, bay.n, self.base.m,
self.base.n, bay.u1tx, bay.u1rx, bay.u2tx, bay.u2rx, bay.v1tx,
bay.v1rx, bay.v2tx, bay.v2rx, bay.w1tx, bay.w1rx, bay.w2tx,
bay.w2rx, bay.u1ty, bay.u1ry, bay.u2ty, bay.u2ry, bay.v1ty,
bay.v1ry, bay.v2ty, bay.v2ry, bay.w1ty, bay.w1ry, bay.w2ty,
bay.w2ry, self.base.u1tx, self.base.u1rx, self.base.u2tx,
self.base.u2rx, self.base.v1tx, self.base.v1rx, self.base.v2tx,
self.base.v2rx, self.base.w1tx, self.base.w1rx, self.base.w2tx,
self.base.w2rx, self.base.u1ty, self.base.u1ry, self.base.u2ty,
self.base.u2ry, self.base.v1ty, self.base.v1ry, self.base.v2ty,
self.base.v2ry, self.base.w1ty, self.base.w1ry, self.base.w2ty,
self.base.w2ry, size, 0, col0)
k0 += conn.fkCbbpby1y2(y1, y2, ktpb, bay.a, bay.b, self.base.m,
self.base.n, self.base.u1tx, self.base.u1rx,
self.base.u2tx, self.base.u2rx, self.base.v1tx,
self.base.v1rx, self.base.v2tx, self.base.v2rx,
self.base.w1tx, self.base.w1rx, self.base.w2tx,
self.base.w2rx, self.base.u1ty, self.base.u1ry,
self.base.u2ty, self.base.u2ry, self.base.v1ty,
self.base.v1ry, self.base.v2ty, self.base.v2ry,
self.base.w1ty, self.base.w1ry, self.base.w2ty,
self.base.w2ry, size, row0, col0)
# connectivity base-flange
ktbf, krbf = calc_kt_kr(self.base, self.flange, 'ycte')
ycte1 = (self.eta_conn_base + 1) / 2. * self.base.b
ycte2 = (self.eta_conn_flange + 1) / 2. * self.flange.b
k0 += fkCBFycte11(ktbf, krbf, self.base, ycte1, size, row0, col0)
k0 += fkCBFycte12(ktbf, krbf, self.base, self.flange, ycte1, ycte2,
size, row0, colf)
k0 += fkCBFycte22(ktbf, krbf, self.base, self.flange, ycte2, size,
rowf, colf)
if finalize:
k0 = finalize_symmetric_matrix(k0)
self.k0 = k0
#NOTE forcing Python garbage collector to clean the memory
# it DOES make a difference! There is a memory leak not
# identified, probably in the csr_matrix process
gc.collect()
msg('finished!', level=2, silent=silent)
def calc_kG0(self,
size=None,
row0=0,
col0=0,
silent=False,
finalize=True,
c=None,
NLgeom=False):
"""Calculate the linear geometric stiffness matrix
See :meth:`.Panel.calc_k0` for details on each parameter.
"""
self._rebuild()
if c is None:
msg('Calculating kG0... ', level=2, silent=silent)
else:
msg('Calculating kG... ', level=2, silent=silent)
# NOTE:
# - row0 and col0 define where the stiffener's base matrix starts
# - rowf and colf define where the stiffener's flange matrix starts
rowf = row0 + self.base.get_size()
colf = col0 + self.base.get_size()
kG0 = 0.
kG0 += self.base.calc_kG0(c=c,
size=size,
row0=row0,
col0=col0,
silent=True,
finalize=False,
NLgeom=NLgeom)
kG0 += self.flange.calc_kG0(c=c,
size=size,
row0=rowf,
col0=colf,
silent=True,
finalize=False,
NLgeom=NLgeom)
if finalize:
kG0 = finalize_symmetric_matrix(kG0)
self.kG0 = kG0
#NOTE forcing Python garbage collector to clean the memory
# it DOES make a difference! There is a memory leak not
# identified, probably in the csr_matrix process
gc.collect()
msg('finished!', level=2, silent=silent)
def calc_kM(self, size=None, row0=0, col0=0, silent=False, finalize=True):
"""Calculate the mass matrix
"""
self._rebuild()
msg('Calculating kM... ', level=2, silent=silent)
rowf = row0 + self.base.get_size()
colf = col0 + self.base.get_size()
kM = 0.
kM += self.base.calc_kM(size=size,
row0=row0,
col0=col0,
silent=True,
finalize=False)
kM += self.flange.calc_kM(size=size,
row0=rowf,
col0=colf,
silent=True,
finalize=False)
if finalize:
kM = finalize_symmetric_matrix(kM)
self.kM = kM
#NOTE forcing Python garbage collector to clean the memory
# it DOES make a difference! There is a memory leak not
# identified, probably in the csr_matrix process
gc.collect()
msg('finished!', level=2, silent=silent)
def __init__(self,
bay,
mu,
panel1,
panel2,
ys,
bb,
bf,
bstack,
bplyts,
blaminaprops,
fstack,
fplyts,
flaminaprops,
model='tstiff2d_clt_donnell_bardell',
mb=15,
nb=12,
mf=15,
nf=12):
print(
'\n\nWARNING - TStiff2D no longer recommended!\n'
' There is a numerically unstable way to compute the\n'
' connection between the skin and stiffener\'s base, it is\n'
' recommended to use panel.assembly instead.\n'
' Module panel.assembly allows stable ways to perform\n'
' connection among panels, and avoids using sliced\n'
' integration intervals that were causing trouble in\n'
' TStiff2D\n\n')
self.bay = bay
self.panel1 = panel1
self.panel2 = panel2
self.model = model
if bstack is None:
raise ValueError('Base laminate must be defined!')
self.ys = ys
y1 = ys - bb / 2.
y2 = ys + bb / 2.
self.base = Panel(a=bay.a,
b=bb,
r=bay.r,
alphadeg=bay.alphadeg,
stack=bstack,
plyts=bplyts,
laminaprops=blaminaprops,
mu=mu,
m=mb,
n=nb,
offset=0.,
u1tx=1,
u1rx=0,
u2tx=1,
u2rx=0,
v1tx=1,
v1rx=0,
v2tx=1,
v2rx=0,
w1tx=1,
w1rx=1,
w2tx=1,
w2rx=1,
u1ty=1,
u1ry=0,
u2ty=1,
u2ry=0,
v1ty=1,
v1ry=0,
v2ty=1,
v2ry=0,
w1ty=1,
w1ry=1,
w2ty=1,
w2ry=1,
y1=y1,
y2=y2)
self.base._rebuild()
if fstack is None:
raise ValueError('Flange laminate must be defined!')
self.flange = Panel(a=bay.a,
b=bf,
model='plate_clt_donnell_bardell',
stack=fstack,
plyts=fplyts,
laminaprops=flaminaprops,
mu=mu,
m=mf,
n=nf,
offset=0.,
u1tx=0,
u1rx=0,
u2tx=0,
u2rx=0,
v1tx=0,
v1rx=0,
v2tx=0,
v2rx=0,
w1tx=0,
w1rx=1,
w2tx=0,
w2rx=1,
u1ty=1,
u1ry=0,
u2ty=1,
u2ry=0,
v1ty=1,
v1ry=0,
v2ty=1,
v2ry=0,
w1ty=1,
w1ry=1,
w2ty=1,
w2ry=1)
self.flange._rebuild()
self.eta_conn_base = 0.
self.eta_conn_flange = -1.
self.k0 = None
self.kM = None
self.kG0 = None
self._rebuild()
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_kT():
mns = [[4, 4], [4, 5], [4, 6], [5, 5], [5, 6], [6, 6],
[8, 9], [9, 8]]
for m, n in mns:
for model in ['plate_clt_donnell_bardell',
'cpanel_clt_donnell_bardell']:
p = Panel()
p.model = model
p.w1tx = 0
p.u1tx = 1
p.u1ty = 1
p.u2ty = 1
p.a = 2.
p.b = 0.5
p.r = 10
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.m = m
p.n = n
p.nx = m
p.ny = n
P = 1000.
npts = 5
p.forces_inc = []
for y in np.linspace(0, p.b, npts):
p.forces_inc.append([0., y, P/(npts-1.), 0, 0])
p.forces_inc[0][2] /= 2.
p.forces_inc[-1][2] /= 2.
k0 = p.calc_k0(silent=True)
kT = p.calc_kT(c=np.zeros(p.get_size()), silent=True)
error = np.abs(kT-k0).sum()
assert error < 1.e-7
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
