def calc_kA(self, silent=False):
self._rebuild()
msg('Calculating kA... ', level=2, silent=silent)
model = self.model
a = self.a
b = self.b
r = self.r
m = self.m
n = self.n
num = panmDB.db[self.model]['num']
size = self.get_size()
if self.beta is None:
if self.Mach < 1:
raise ValueError('Mach number must be >= 1')
elif self.Mach == 1:
self.Mach = 1.0001
M = self.Mach
beta = self.rho_air * self.V**2 / (M**2 - 1)**0.5
gamma = beta*1./(2.*self.r*(M**2 - 1)**0.5)
ainf = self.speed_sound
aeromu = beta/(M*ainf)*(M**2 - 2)/(M**2 - 1)
else:
beta = self.beta
gamma = self.gamma if self.gamma is not None else 0.
aeromu = self.aeromu if self.aeromu is not None else 0.
# contributions from panels
#TODO summing up coo_matrix objects may be slow!
p = self.panels[0]
#TODO if the initialization of panel is correct, the line below is
# unnecessary
p.flow = self.flow
p.calc_kA(silent=silent, finalize=False)
kA = p.kA
assert np.any(np.isnan(kA.data)) == False
assert np.any(np.isinf(kA.data)) == False
kA = csr_matrix(make_skew_symmetric(kA))
self.kA = kA
#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_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 calc_linear_matrices(self, combined_load_case=None, silent=False,
calc_kG0=True, calc_kA=True, calc_kM=True):
self._rebuild()
msg('Calculating linear matrices... ', level=2, silent=silent)
fk0, fkG0, fkA, fkM, k0edges = modelDB.get_linear_matrices(self)
model = self.model
a = self.a
b = self.b
m1 = self.m1
n1 = self.n1
laminaprops = self.laminaprops
plyts = self.plyts
h = sum(plyts)
stack = self.stack
mu = self.mu
if calc_kA and self.beta is None:
if self.M < 1:
raise ValueError('Mach number must be >= 1')
elif self.M == 1:
self.M = 1.0001
self.beta = self.rho * self.V**2 / (self.M**2 - 1)**0.5
beta = self.beta
if stack != []:
lam = laminate.read_stack(stack, plyts=plyts,
laminaprops=laminaprops)
if 'clpt' in model:
if lam is not None:
F = lam.ABD
elif 'fsdt' in model:
if lam is not None:
F = lam.ABDE
F[6:, 6:] *= self.K
if self.force_orthotropic_laminate:
msg('')
msg('Forcing orthotropic laminate...', level=2)
F[0, 2] = 0. # A16
F[1, 2] = 0. # A26
F[2, 0] = 0. # A61
F[2, 1] = 0. # A62
F[0, 5] = 0. # B16
F[5, 0] = 0. # B61
F[1, 5] = 0. # B26
F[5, 1] = 0. # B62
F[3, 2] = 0. # B16
F[2, 3] = 0. # B61
F[4, 2] = 0. # B26
F[2, 4] = 0. # B62
F[3, 5] = 0. # D16
F[4, 5] = 0. # D26
F[5, 3] = 0. # D61
F[5, 4] = 0. # D62
if F.shape[0] == 8:
F[6, 7] = 0. # A45
F[7, 6] = 0. # A54
self.lam = lam
self.F = F
k0 = fk0(a, b, F, m1, n1)
if calc_kA:
kA = fkA(beta, a, b, m1, n1)
if calc_kM:
kM = fkM(mu, h, a, b, m1, n1)
if calc_kG0:
Fx = self.Fx if self.Fx is not None else 0.
Fy = self.Fy if self.Fy is not None else 0.
Fxy = self.Fxy if self.Fxy is not None else 0.
Fyx = self.Fyx if self.Fyx is not None else 0.
if not combined_load_case:
kG0 = fkG0(Fx, Fy, Fxy, Fyx, a, b, m1, n1)
else:
kG0_Fx = fkG0(Fx, 0, 0, 0, a, b, m1, n1)
kG0_Fy = fkG0(0, Fy, 0, 0, a, b, m1, n1)
kG0_Fxy = fkG0(0, 0, Fxy, 0, a, b, m1, n1)
kG0_Fyx = fkG0(0, 0, 0, Fyx, a, b, m1, n1)
# performing checks for the linear stiffness matrices
assert np.any(np.isnan(k0.data)) == False
assert np.any(np.isnan(k0.data)) == False
if calc_kA:
assert np.any(np.isinf(kA.data)) == False
assert np.any(np.isinf(kA.data)) == False
if calc_kM:
assert np.any(np.isinf(kM.data)) == False
assert np.any(np.isinf(kM.data)) == False
k0 = csr_matrix(make_symmetric(k0))
if calc_kA:
kA = csr_matrix(make_skew_symmetric(kA))
if calc_kM:
kM = csr_matrix(make_symmetric(kM))
if k0edges is not None:
assert np.any((np.isnan(k0edges.data)
| np.isinf(k0edges.data))) == False
k0edges = csr_matrix(make_symmetric(k0edges))
if k0edges is not None:
k0 = k0 + k0edges
self.k0 = k0
if calc_kA:
self.kA = kA
if calc_kM:
self.kM = kM
if calc_kG0:
if not combined_load_case:
assert np.any((np.isnan(kG0.data) | np.isinf(kG0.data))) == False
kG0 = csr_matrix(make_symmetric(kG0))
self.kG0 = kG0
else:
assert np.any((np.isnan(kG0_Fx.data)
| np.isinf(kG0_Fx.data))) == False
assert np.any((np.isnan(kG0_Fy.data)
| np.isinf(kG0_Fy.data))) == False
assert np.any((np.isnan(kG0_Fxy.data)
| np.isinf(kG0_Fxy.data))) == False
assert np.any((np.isnan(kG0_Fyx.data)
| np.isinf(kG0_Fyx.data))) == False
kG0_Fx = csr_matrix(make_symmetric(kG0_Fx))
kG0_Fy = csr_matrix(make_symmetric(kG0_Fy))
kG0_Fxy = csr_matrix(make_symmetric(kG0_Fxy))
kG0_Fyx = csr_matrix(make_symmetric(kG0_Fyx))
self.kG0_Fx = kG0_Fx
self.kG0_Fy = kG0_Fy
self.kG0_Fxy = kG0_Fxy
self.kG0_Fyx = kG0_Fyx
#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_linear_matrices(self, combined_load_case=None, silent=False,
calc_kG0=True, calc_kA=True, calc_kM=True):
self._rebuild()
msg('Calculating linear matrices... ', level=2, silent=silent)
fk0, fkG0, fkAx, fkAy, fcA, fkM, fk0edges, fk0sb, fk0sf, fk0sf2, fkMsb, fkMsf = \
modelDB.get_linear_matrices(self)
model = self.model
a = self.a
b = self.b
r = self.r
m1 = self.m1
n1 = self.n1
laminaprops = self.laminaprops
plyts = self.plyts
h = sum(plyts)
stack = self.stack
mu = self.mu
if calc_kA and self.beta is None:
if self.Mach < 1:
raise ValueError('Mach number must be >= 1')
elif self.Mach == 1:
self.Mach = 1.0001
M = self.Mach
beta = self.rho_air * self.V**2 / (M**2 - 1)**0.5
gamma = beta*1./(2.*r*(M**2 - 1)**0.5)
ainf = self.speed_sound
aeromu = beta/(M*ainf)*(M**2 - 2)/(M**2 - 1)
elif calc_kA and self.beta is not None:
beta = self.beta
gamma = self.gamma if self.gamma is not None else 0.
aeromu = self.aeromu if self.aeromu is not None else 0.
elif not calc_kA:
pass
else:
raise NotImplementedError('check here')
if stack != []:
lam = laminate.read_stack(stack, plyts=plyts,
laminaprops=laminaprops)
if 'clpt' in model:
if lam is not None:
F = lam.ABD
elif 'fsdt' in model:
if lam is not None:
F = lam.ABDE
F[6:, 6:] *= self.K
self.lam = lam
self.F = F
k0 = fk0(a, b, r, F, m1, n1)
if (self.model == 'clpt_donnell_bc1'
or self.model == 'clpt_sanders_bc1'):
k0edges = fk0edges(m1, n1, a, b,
self.kphixBot, self.kphixTop,
self.kphiyLeft, self.kphiyRight)
elif self.model == 'fsdt_donnell_bc1':
k0edges = fk0edges(m1, n1, a, b,
self.kphixBot, self.kphixTop,
self.kphiyBot, self.kphiyTop,
self.kphixLeft, self.kphixRight,
self.kphiyLeft, self.kphiyRight)
else:
raise
if calc_kA:
if self.flow == 'x':
kA = fkAx(beta, gamma, a, b, m1, n1)
elif self.flow == 'y':
kA = fkAy(beta, a, b, m1, n1)
if fcA is None:
cA = None
else:
cA = fcA(aeromu, a, b, m1, n1)
cA = cA*(0+1j)
if calc_kM:
if self.model == 'fsdt_donnell_bc1':
raise NotImplementedError('There is a bug with kM for model %s'
% self.model)
kM = fkM(mu, h, a, b, m1, n1)
if calc_kG0:
Fx = self.Fx if self.Fx is not None else 0.
Fy = self.Fy if self.Fy is not None else 0.
Fxy = self.Fxy if self.Fxy is not None else 0.
Fyx = self.Fyx if self.Fyx is not None else 0.
if not combined_load_case:
kG0 = fkG0(Fx, Fy, Fxy, Fyx, a, b, r, m1, n1)
else:
kG0_Fx = fkG0(Fx, 0, 0, 0, a, b, r, m1, n1)
kG0_Fy = fkG0(0, Fy, 0, 0, a, b, r, m1, n1)
kG0_Fxy = fkG0(0, 0, Fxy, 0, a, b, r, m1, n1)
kG0_Fyx = fkG0(0, 0, 0, Fyx, a, b, r, m1, n1)
# contributions from stiffeners
#TODO summing up coo_matrix objects may be very slow!
for s in self.stiffeners:
if s.blam is not None:
Fsb = s.blam.ABD
k0 += fk0sb(s.ys, s.bb, a, b, r, m1, n1, Fsb)
if s.flange_formulation == 1:
k0 += fk0sf(s.ys, a, b, r, m1, n1, s.Exx, s.Gxy, s.Jxx, s.Iyy)
elif s.flange_formulation == 2:
k0 += fk0sf2(s.bf, s.df, s.ys, a, b, r, m1, n1, s.E1, s.F1,
s.S1, s.Jxx)
if s.blam is not None:
kM += fkMsb(s.mu, s.ys, s.db, s.hb, a, b, m1, n1)
kM += fkMsf(s.mu, s.ys, s.df, s.Asf, a, b, s.Iyy, s.Jxx, m1, n1)
# performing checks for the linear stiffness matrices
assert np.any(np.isnan(k0.data)) == False
assert np.any(np.isinf(k0.data)) == False
if calc_kA:
assert np.any(np.isnan(kA.data)) == False
assert np.any(np.isinf(kA.data)) == False
if cA is not None:
assert np.any(np.isnan(cA.data)) == False
assert np.any(np.isinf(cA.data)) == False
if calc_kM:
assert np.any(np.isnan(kM.data)) == False
assert np.any(np.isinf(kM.data)) == False
k0 = csr_matrix(make_symmetric(k0))
if calc_kA:
kA = csr_matrix(make_skew_symmetric(kA))
if cA is not None:
cA = csr_matrix(make_symmetric(cA))
if calc_kM:
kM = csr_matrix(make_symmetric(kM))
assert np.any(np.isnan(k0edges.data)) == False
assert np.any(np.isinf(k0edges.data)) == False
k0edges = csr_matrix(make_symmetric(k0edges))
k0 = k0 + k0edges
self.k0 = k0
if calc_kA:
self.kA = kA
self.cA = cA
if calc_kM:
self.kM = kM
if calc_kG0:
if not combined_load_case:
assert np.any((np.isnan(kG0.data) | np.isinf(kG0.data))) == False
kG0 = csr_matrix(make_symmetric(kG0))
self.kG0 = kG0
else:
assert np.any((np.isnan(kG0_Fx.data)
| np.isinf(kG0_Fx.data))) == False
assert np.any((np.isnan(kG0_Fy.data)
| np.isinf(kG0_Fy.data))) == False
assert np.any((np.isnan(kG0_Fxy.data)
| np.isinf(kG0_Fxy.data))) == False
assert np.any((np.isnan(kG0_Fyx.data)
| np.isinf(kG0_Fyx.data))) == False
kG0_Fx = csr_matrix(make_symmetric(kG0_Fx))
kG0_Fy = csr_matrix(make_symmetric(kG0_Fy))
kG0_Fxy = csr_matrix(make_symmetric(kG0_Fxy))
kG0_Fyx = csr_matrix(make_symmetric(kG0_Fyx))
self.kG0_Fx = kG0_Fx
self.kG0_Fy = kG0_Fy
self.kG0_Fxy = kG0_Fxy
self.kG0_Fyx = kG0_Fyx
#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)
