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)
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 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_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, 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_kT(self, c=None, silent=False, finalize=True, inc=None):
msg('Calculating kT for assembly...', level=2, silent=silent)
size = self.get_size()
kT = 0
#TODO use multiprocessing.Pool here
for p in self.panels:
if p.row_start is None or p.col_start is None:
raise ValueError(
'Panel attributes "row_start" and "col_start" must be defined!'
)
kT += p.calc_k0(c=c,
size=size,
row0=p.row_start,
col0=p.col_start,
silent=True,
finalize=False,
inc=inc,
NLgeom=True)
kT += p.calc_kG0(c=c,
size=size,
row0=p.row_start,
col0=p.col_start,
silent=True,
finalize=False,
NLgeom=True)
if finalize:
kT = finalize_symmetric_matrix(kT)
k0_conn = self.get_k0_conn()
kT += k0_conn
self.kT = kT
msg('finished!', level=2, silent=silent)
return kT
def static(K, fext, silent=False):
"""Static Analyses
Parameters
----------
K : sparse_matrix
Stiffness matrix. Should include initial stress stiffness matrix,
aerodynamic matrix and so forth when applicable.
fext : array-like
Vector of external loads.
silent : bool, optional
A boolean to tell whether the log messages should be printed.
"""
increments = []
cs = []
NLgeom=False
if NLgeom:
raise NotImplementedError('Independent static function not ready for NLgeom')
else:
msg('Started Linear Static Analysis', silent=silent)
c = solve(K, fext, silent=silent)
increments.append(1.)
cs.append(c)
msg('Finished Linear Static Analysis', silent=silent)
return increments, cs
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 static(K, fext, silent=False):
"""Static Analyses
Parameters
----------
K : sparse_matrix
Stiffness matrix. Should include initial stress stiffness matrix,
aerodynamic matrix and so forth when applicable.
fext : array-like
Vector of external loads.
silent : bool, optional
A boolean to tell whether the log messages should be printed.
"""
increments = []
cs = []
NLgeom = False
if NLgeom:
raise NotImplementedError(
'Independent static function not ready for NLgeom')
else:
msg('Started Linear Static Analysis', silent=silent)
c = solve(K, fext, silent=silent)
increments.append(1.)
cs.append(c)
msg('Finished Linear Static Analysis', silent=silent)
return increments, cs
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 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)
panmod = panmodelDB.db[self.panel1.model]['matrices']
mod = modelDB.db[self.model]['matrices']
bay = self.bay
a = bay.a
b = bay.b
m = bay.m
n = bay.n
m1 = self.m1
n1 = self.n1
bf = self.bf
kM = 0.
if self.blam is not None:
# stiffener pad-up
y1 = self.ys - self.bb/2.
y2 = self.ys + self.bb/2.
kM += panmod.fkMy1y2(y1, y2, self.mu, self.db, self.hb, 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)
if self.flam is not None:
kM += mod.fkMf(self.mu, self.hf, a, bf, 0., m1, n1,
self.u1txf, self.u1rxf, self.u2txf, self.u2rxf,
self.v1txf, self.v1rxf, self.v2txf, self.v2rxf,
self.w1txf, self.w1rxf, self.w2txf, self.w2rxf,
self.u1tyf, self.u1ryf, self.u2tyf, self.u2ryf,
self.v1tyf, self.v1ryf, self.v2tyf, self.v2ryf,
self.w1tyf, self.w1ryf, self.w2tyf, self.w2ryf,
size, row0, col0)
if finalize:
assert np.any(np.isnan(kM.data)) == False
assert np.any(np.isinf(kM.data)) == False
kM = csr_matrix(make_symmetric(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 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)
panmod = panmodelDB.db[self.panel1.model]['matrices']
mod = modelDB.db[self.model]['matrices']
bay = self.bay
ys = self.ys
a = bay.a
b = bay.b
m = self.panel1.m
n = self.panel1.n
r = self.panel1.r
alphadeg = self.panel1.alphadeg
alphadeg = alphadeg if alphadeg is not None else 0.
alpharad = deg2rad(alphadeg)
k0 = 0.
if self.blam is not None:
Fsb = self.blam.ABD
y1 = ys - self.bb/2.
y2 = ys + self.bb/2.
k0 += panmod.fk0y1y2(y1, y2, a, b, r, alpharad, Fsb, 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=size, row0=row0, col0=col0)
if self.flam is not None:
k0 += mod.fk0f(ys, a, b, self.bf, self.df, self.E1, self.F1,
self.S1, self.Jxx, m, 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:
assert np.any(np.isnan(k0.data)) == False
assert np.any(np.isinf(k0.data)) == False
k0 = csr_matrix(make_symmetric(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_k0(self, silent=False):
self._rebuild()
msg('Calculating k0... ', 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()
k0 = 0.
# contributions from panels
for p in self.panels:
p.calc_k0(size=size, row0=0, col0=0, silent=True,
finalize=False)
#TODO summing up coo_matrix objects may be slow!
k0 += p.k0
# contributions from bladestiff1ds
for s in self.bladestiff1ds:
s.calc_k0(size=size, row0=0, col0=0, silent=True,
finalize=False)
#TODO summing up coo_matrix objects may be slow!
k0 += s.k0
# contributions from bladestiff2ds
row0 = num*m*n
col0 = num*m*n
for i, s in enumerate(self.bladestiff2ds):
num1 = stiffmDB.db[s.model]['num1']
if i > 0:
s_1 = bay.bladestiff2ds[i-1]
row0 += num1*s_1.m1*s_1.n1
col0 += num1*s_1.m1*s_1.n1
s.calc_k0(size=size, row0=row0, col0=col0, silent=True,
finalize=False)
#TODO summing up coo_matrix objects may be slow!
k0 += s.k0
# performing checks for the stiffness matrices
assert np.any(np.isnan(k0.data)) == False
assert np.any(np.isinf(k0.data)) == False
k0 = csr_matrix(make_symmetric(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_fext(self, inc=1., silent=False):
msg('Calculating external forces for assembly...', level=2, silent=silent)
size = self.get_size()
fext = 0
for p in self.panels:
if p.col_start is None:
raise ValueError('Panel attributes "col_start" must be defined!')
fext += p.calc_fext(inc=inc, size=size, col0=p.col_start, silent=True)
self.fext = fext
msg('finished!', level=2, silent=silent)
return fext
def calc_fint(self, c, silent=False, inc=1.):
msg('Calculating internal forces for assembly...', level=2, silent=silent)
size = self.get_size()
fint = 0
for p in self.panels:
if p.col_start is None:
raise ValueError('Panel attributes "col_start" must be defined!')
fint += p.calc_fint(c=c, size=size, col0=p.col_start, silent=True)
k0_conn = self.get_k0_conn()
fint += k0_conn*c
self.fint = fint
msg('finished!', level=2, silent=silent)
return fint
def calc_kM(self, silent=False, finalize=True):
msg('Calculating kM for assembly...', level=2, silent=silent)
size = self.get_size()
kM = 0
for p in self.panels:
if p.row_start is None or p.col_start is None:
raise ValueError('Panel attributes "row_start" and "col_start" must be defined!')
kM += p.calc_kM(row0=p.row_start, col0=p.col_start, size=size, silent=True, finalize=False)
if finalize:
kM = finalize_symmetric_matrix(kM)
self.kM = kM
msg('finished!', level=2, silent=silent)
return kM
def calc_fext(self, silent=False):
"""Calculates the external force vector `\{F_{ext}\}`
Parameters
----------
silent : bool, optional
A boolean to tell whether the msg messages should be printed.
Returns
-------
fext : np.ndarray
The external force vector
"""
msg('Calculating external forces...', level=2, silent=silent)
num = panmDB.db[self.model]['num']
fg = panmDB.db[self.model]['field'].fg
# punctual forces on skin
size = num*self.m*self.n
g = np.zeros((3, size), dtype=DOUBLE)
fext_skin = np.zeros(size, dtype=DOUBLE)
for i, force in enumerate(self.forces_skin):
x, y, fx, fy, fz = force
fg(g, self.m, self.n, x, y, self.a, self.b)
fpt = np.array([[fx, fy, fz]])
fext_skin += fpt.dot(g).ravel()
fext = fext_skin
# punctual forces on stiffener
for s in self.bladestiff2ds:
num1 = stiffmDB.db[s.model]['num1']
m1 = s.m1
n1 = s.n1
bf = s.bf
size = num1*m1*n1
g_stiffener = np.zeros((3, size), dtype=DOUBLE)
fext_stiffener = np.zeros(size, dtype=DOUBLE)
for i, force in enumerate(s.forces):
xf, yf, fx, fy, fz = force
fg(g_stiffener, m1, n1, xf, yf, self.a, bf)
fpt = np.array([[fx, fy, fz]])
fext_stiffener += fpt.dot(g_stiffener).ravel()
fext = np.concatenate((fext, fext_stiffener))
msg('finished!', level=2, silent=silent)
return fext
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 calc_fint(self, c, silent=False, inc=1.):
msg('Calculating internal forces for assembly...',
level=2,
silent=silent)
size = self.get_size()
fint = 0
for p in self.panels:
if p.col_start is None:
raise ValueError(
'Panel attributes "col_start" must be defined!')
fint += p.calc_fint(c=c, size=size, col0=p.col_start, silent=True)
k0_conn = self.get_k0_conn()
fint += k0_conn * c
self.fint = fint
msg('finished!', level=2, silent=silent)
return fint
def save(self):
"""Save the ``AeroPistonPlate`` object using ``cPickle``
Notes
-----
The pickled file will have the name stored in ``AeroPistonPlate.name``
followed by a ``'.AeroPistonPlate'`` extension.
"""
name = self.name + '.AeroPistonPlate'
msg('Saving AeroPistonPlate to {}'.format(name))
self._clear_matrices()
with open(name, 'wb') as f:
cPickle.dump(self, f, protocol=cPickle.HIGHEST_PROTOCOL)
def save(self):
"""Save the :class:`StiffPanelBay` object using ``cPickle``
Notes
-----
The pickled file will have the name stored in
:property:`.StiffPanelBay.name` followed by a
``'.StiffPanelBay'`` extension.
"""
name = self.name + '.StiffPanelBay'
msg('Saving StiffPanelBay to {0}'.format(name))
self._clear_matrices()
with open(name, 'wb') as f:
cPickle.dump(self, f, protocol=cPickle.HIGHEST_PROTOCOL)
def calc_fext(self, inc=1., silent=False):
msg('Calculating external forces for assembly...',
level=2,
silent=silent)
size = self.get_size()
fext = 0
for p in self.panels:
if p.col_start is None:
raise ValueError(
'Panel attributes "col_start" must be defined!')
fext += p.calc_fext(inc=inc,
size=size,
col0=p.col_start,
silent=True)
self.fext = fext
msg('finished!', level=2, silent=silent)
return fext
def calc_cA(self, silent=False):
self._rebuild()
msg('Calculating cA... ', 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
p = self.panels[0]
p.calc_cA(size=size, row0=0, col0=0, silent=silent)
cA = p.cA
assert np.any(np.isnan(cA.data)) == False
assert np.any(np.isinf(cA.data)) == False
cA = csr_matrix(make_symmetric(cA))
self.cA = cA
#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):
"""Calculate the linear geometric stiffness matrix
"""
self._rebuild()
msg('Calculating kG0... ', level=2, silent=silent)
panmod = panmodelDB.db[self.panel1.model]['matrices']
mod = modelDB.db[self.model]['matrices']
bay = self.bay
ys = self.ys
m = bay.m
n = bay.n
mu = self.mu
kG0 = 0.
if self.blam is not None:
Fsb = self.blam.ABD
y1 = ys - self.bb/2.
y2 = ys + self.bb/2.
# TODO include kG0 for padup
# now it is assumed that all the load goes to the flange
if self.flam is not None:
Fx = self.Fx if self.Fx is not None else 0.
kG0 += mod.fkG0f(ys, Fx, bay.a, bay.b, self.bf, m, n,
bay.w1tx, bay.w1rx, bay.w2tx, bay.w2rx,
bay.w1ty, bay.w1ry, bay.w2ty, bay.w2ry,
size, row0, col0)
if finalize:
assert np.any((np.isnan(kG0.data) | np.isinf(kG0.data))) == False
kG0 = csr_matrix(make_symmetric(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_kT(self, c=None, silent=False, finalize=True, inc=None):
msg('Calculating kT for assembly...', level=2, silent=silent)
size = self.get_size()
kT = 0
#TODO use multiprocessing.Pool here
for p in self.panels:
if p.row_start is None or p.col_start is None:
raise ValueError('Panel attributes "row_start" and "col_start" must be defined!')
kT += p.calc_k0(c=c, size=size, row0=p.row_start, col0=p.col_start,
silent=True, finalize=False, inc=inc, NLgeom=True)
kT += p.calc_kG0(c=c, size=size, row0=p.row_start,
col0=p.col_start, silent=True, finalize=False, NLgeom=True)
if finalize:
kT = finalize_symmetric_matrix(kT)
k0_conn = self.get_k0_conn()
kT += k0_conn
self.kT = kT
msg('finished!', level=2, silent=silent)
return kT
def calc_kM(self, silent=False, finalize=True):
msg('Calculating kM for assembly...', level=2, silent=silent)
size = self.get_size()
kM = 0
for p in self.panels:
if p.row_start is None or p.col_start is None:
raise ValueError(
'Panel attributes "row_start" and "col_start" must be defined!'
)
kM += p.calc_kM(row0=p.row_start,
col0=p.col_start,
size=size,
silent=True,
finalize=False)
if finalize:
kM = finalize_symmetric_matrix(kM)
self.kM = kM
msg('finished!', level=2, silent=silent)
return kM
def calc_kG0(self, size=None, row0=0, col0=0, silent=False, finalize=True):
"""Calculate the linear geometric stiffness matrix
"""
self._rebuild()
msg('Calculating kG0... ', level=2, silent=silent)
mod = modelDB.db[self.model]['matrices']
bay = self.bay
a = bay.a
kG0 = 0.
if self.blam is not None:
# stiffener pad-up
#TODO include kG0 for pad-up (Nxx load that arrives there)
pass
if self.flam is not None:
F = self.flam.ABD
# stiffener flange
Nxx = self.Nxx if self.Nxx is not None else 0.
Nxy = self.Nxy if self.Nxy is not None else 0.
kG0 += mod.fkG0f(Nxx, 0., Nxy, a, self.bf, self.m1, self.n1,
self.w1txf, self.w1rxf, self.w2txf, self.w2rxf,
self.w1tyf, self.w1ryf, self.w2tyf, self.w2ryf,
size, row0, col0)
if finalize:
assert np.any((np.isnan(kG0.data) | np.isinf(kG0.data))) == False
kG0 = csr_matrix(make_symmetric(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_kG0(self, c=None, silent=False, finalize=True):
"""Calculate the geometric stiffness matrix of the assembly
Parameters
----------
c : array-like or None, optional
This must be the result of a static analysis, used to compute
non-linear terms based on the actual displacement field.
silent : bool, optional
A boolean to tell whether the log messages should be printed.
finalize : bool, optional
Asserts validity of output data and makes the output matrix
symmetric, should be ``False`` when assemblying.
"""
size = self.get_size()
if c is None:
msg('Calculating kG0 for assembly...', level=2, silent=silent)
else:
check_c(c, size)
msg('Calculating kG for assembly...', level=2, silent=silent)
kG0 = 0.
for p in self.panels:
if p.row_start is None or p.col_start is None:
raise ValueError('Panel attributes "row_start" and "col_start" must be defined!')
kG0 += p.calc_kG0(c=c, row0=p.row_start, col0=p.col_start, size=size,
silent=True, finalize=False)
if finalize:
kG0 = finalize_symmetric_matrix(kG0)
self.kG0 = kG0
msg('finished!', level=2, silent=silent)
return kG0
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 static(self, NLgeom=False, silent=False):
"""General solver for static analyses
Selects the specific solver based on the ``NL_method`` parameter.
"""
self.increments = []
self.cs = []
if NLgeom:
self.maxInc = max(self.initialInc, self.maxInc)
msg('Started Non-Linear Static Analysis', silent=silent)
if self.NL_method is 'NR':
_solver_NR(self)
elif self.NL_method is 'arc_length':
_solver_arc_length(self)
else:
raise ValueError('{0} is an invalid NL_method')
else:
msg('Started Linear Static Analysis', silent=silent)
fext = self.calc_fext()
k0 = self.calc_k0()
if self.calc_k0_bc is not None:
k0_bc = self.calc_k0_bc()
k0max = k0.max()
k0 /= k0max
fextmax = fext.max()
fext /= fextmax
k0 = k0 + k0_bc
c = solve(k0, fext)
if self.calc_k0_bc is not None:
k0 *= k0max
fext *= fextmax
c /= k0max
c *= fextmax
self.cs.append(c)
self.increments.append(1.)
msg('Finished Linear Static Analysis', silent=silent)
self.last_analysis = 'static'
return self.increments, self.cs
def calc_k0(self, conn=None, c=None, silent=False, finalize=True, inc=1.):
"""Calculate the constitutive stiffness matrix of the assembly
Parameters
----------
conn : dict, optional
A connectivity dictionary. Optional if already defined for the
assembly.
c : array-like or None, optional
This must be the result of a static analysis, used to compute
non-linear terms based on the actual displacement field.
silent : bool, optional
A boolean to tell whether the log messages should be printed.
finalize : bool, optional
Asserts validity of output data and makes the output matrix
symmetric, should be ``False`` when assemblying.
inc : float, optional
Dummy argument needed for non-linear analyses.
"""
size = self.get_size()
if c is None:
msg('Calculating k0 for assembly...', level=2, silent=silent)
else:
check_c(c, size)
msg('Calculating kL for assembly...', level=2, silent=silent)
k0 = 0.
for p in self.panels:
if p.row_start is None or p.col_start is None:
raise ValueError(
'Panel attributes "row_start" and "col_start" must be defined!'
)
k0 += p.calc_k0(c=c,
row0=p.row_start,
col0=p.col_start,
size=size,
silent=True,
finalize=False)
if finalize:
k0 = finalize_symmetric_matrix(k0)
k0_conn = self.get_k0_conn(conn=conn)
k0 += self.k0_conn
self.k0 = k0
msg('finished!', level=2, silent=silent)
return k0
def calc_k0(self, conn=None, c=None, silent=False, finalize=True, inc=1.):
"""Calculate the constitutive stiffness matrix of the assembly
Parameters
----------
conn : dict, optional
A connectivity dictionary. Optional if already defined for the
assembly.
c : array-like or None, optional
This must be the result of a static analysis, used to compute
non-linear terms based on the actual displacement field.
silent : bool, optional
A boolean to tell whether the log messages should be printed.
finalize : bool, optional
Asserts validity of output data and makes the output matrix
symmetric, should be ``False`` when assemblying.
inc : float, optional
Dummy argument needed for non-linear analyses.
"""
size = self.get_size()
if c is None:
msg('Calculating k0 for assembly...', level=2, silent=silent)
else:
check_c(c, size)
msg('Calculating kL for assembly...', level=2, silent=silent)
k0 = 0.
for p in self.panels:
if p.row_start is None or p.col_start is None:
raise ValueError('Panel attributes "row_start" and "col_start" must be defined!')
k0 += p.calc_k0(c=c, row0=p.row_start, col0=p.col_start, size=size,
silent=True, finalize=False)
if finalize:
k0 = finalize_symmetric_matrix(k0)
k0_conn = self.get_k0_conn(conn=conn)
k0 += self.k0_conn
self.k0 = k0
msg('finished!', level=2, silent=silent)
return k0
def static(self, NLgeom=False, silent=False):
"""General solver for static analyses
Selects the specific solver based on the ``NL_method`` parameter.
Parameters
----------
NLgeom : bool
Flag to indicate whether a linear or a non-linear analysis is to
be performed.
silent : bool, optional
A boolean to tell whether the log messages should be printed.
"""
self.increments = []
self.cs = []
if NLgeom:
self.maxInc = max(self.initialInc, self.maxInc)
msg('Started Non-Linear Static Analysis', silent=silent)
if self.NL_method is 'NR':
_solver_NR(self, silent=silent)
elif self.NL_method is 'arc_length':
_solver_arc_length(self)
else:
raise ValueError('{0} is an invalid NL_method')
else:
msg('Started Linear Static Analysis', silent=silent)
fext = self.calc_fext(silent=silent)
k0 = self.calc_k0(silent=silent)
c = solve(k0, fext, silent=silent)
self.cs.append(c)
self.increments.append(1.)
msg('Finished Linear Static Analysis', silent=silent)
self.last_analysis = 'static'
return self.increments, self.cs
def static(self, NLgeom=False, silent=False):
"""General solver for static analyses
Selects the specific solver based on the ``NL_method`` parameter.
Parameters
----------
NLgeom : bool
Flag to indicate whether a linear or a non-linear analysis is to
be performed.
silent : bool, optional
A boolean to tell whether the log messages should be printed.
"""
self.increments = []
self.cs = []
if NLgeom:
self.maxInc = max(self.initialInc, self.maxInc)
msg('Started Non-Linear Static Analysis', silent=silent)
if self.NL_method is 'NR':
_solver_NR(self, silent=silent)
elif self.NL_method is 'arc_length':
_solver_arc_length(self)
else:
raise ValueError('{0} is an invalid NL_method')
else:
msg('Started Linear Static Analysis', silent=silent)
fext = self.calc_fext(silent=silent)
k0 = self.calc_k0(silent=silent)
c = solve(k0, fext, silent=silent)
self.cs.append(c)
self.increments.append(1.)
msg('Finished Linear Static Analysis', silent=silent)
self.last_analysis = 'static'
return self.increments, self.cs
def calc_kG0(self, c=None, silent=False, finalize=True):
"""Calculate the geometric stiffness matrix of the assembly
Parameters
----------
c : array-like or None, optional
This must be the result of a static analysis, used to compute
non-linear terms based on the actual displacement field.
silent : bool, optional
A boolean to tell whether the log messages should be printed.
finalize : bool, optional
Asserts validity of output data and makes the output matrix
symmetric, should be ``False`` when assemblying.
"""
size = self.get_size()
if c is None:
msg('Calculating kG0 for assembly...', level=2, silent=silent)
else:
check_c(c, size)
msg('Calculating kG for assembly...', level=2, silent=silent)
kG0 = 0.
for p in self.panels:
if p.row_start is None or p.col_start is None:
raise ValueError(
'Panel attributes "row_start" and "col_start" must be defined!'
)
kG0 += p.calc_kG0(c=c,
row0=p.row_start,
col0=p.col_start,
size=size,
silent=True,
finalize=False)
if finalize:
kG0 = finalize_symmetric_matrix(kG0)
self.kG0 = kG0
msg('finished!', level=2, silent=silent)
return kG0
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_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 plot(self, c, group, invert_y=False, vec='w', filename='', ax=None,
figsize=(3.5, 2.), save=True, title='', identify=False,
show_boundaries=False, boundary_line='--k', boundary_linewidth=1.,
colorbar=False, cbar_nticks=2, cbar_format=None, cbar_title='',
cbar_fontsize=10, colormap='jet', aspect='equal', clean=True,
dpi=400, texts=[], xs=None, ys=None, gridx=50, gridy=50,
num_levels=400, vecmin=None, vecmax=None, calc_data_only=False):
r"""Contour plot for a Ritz constants vector.
Parameters
----------
c : np.ndarray
The Ritz constants that will be used to compute the field contour.
group : str
A group to plot. Each panel in ``panels`` should contain an
attribute ``group``, which is used to identify which entities
should be plotted together.
vec : str, optional
Can be one of the components:
- Displacement: ``'u'``, ``'v'``, ``'w'``, ``'phix'``, ``'phiy'``
- Strain: ``'exx'``, ``'eyy'``, ``'gxy'``, ``'kxx'``, ``'kyy'``,
``'kxy'``, ``'gyz'``, ``'gxz'``
- Stress: ``'Nxx'``, ``'Nyy'``, ``'Nxy'``, ``'Mxx'``, ``'Myy'``,
``'Mxy'``, ``'Qy'``, ``'Qx'``
invert_y : bool, optional
Inverts the `y` axis of the plot.
save : bool, optional
Flag telling whether the contour should be saved to an image file.
dpi : int, optional
Resolution of the saved file in dots per inch.
filename : str, optional
The file name for the generated image file. If no value is given,
the `name` parameter of the ``Panel`` object will be used.
ax : AxesSubplot, optional
When ``ax`` is given, the contour plot will be created inside it.
figsize : tuple, optional
The figure size given by ``(width, height)``.
title : str, optional
If any string is given a title is added to the contour plot.
indentify : bool, optional
If domains should be identified. If yes, the name of each panel is
used.
show_boundaries : bool, optional
If boundaries between domains should be drawn.
boundary_line : str, optional
Matplotlib string to define line type and color.
boundary_linewidth : float, optional
Matplotlib float to define line width.
colorbar : bool, optional
If a colorbar should be added to the contour plot.
cbar_nticks : int, optional
Number of ticks added to the colorbar.
cbar_format : [ None | format string | Formatter object ], optional
See the ``matplotlib.pyplot.colorbar`` documentation.
cbar_title : str, optional
Colorbar title. If ``cbar_title == ''`` no title is added.
cbar_fontsize : int, optional
Fontsize of the colorbar labels.
colormap : string, optional
Name of a matplotlib available colormap.
aspect : str, optional
String that will be passed to the ``AxesSubplot.set_aspect()``
method.
clean : bool, optional
Clean axes ticks, grids, spines etc.
xs : np.ndarray, optional
The `x` positions where to calculate the displacement field.
Default is ``None`` and the method ``_default_field`` is used.
ys : np.ndarray, optional
The ``y`` positions where to calculate the displacement field.
Default is ``None`` and the method ``_default_field`` is used.
gridx : int, optional
Number of points along the `x` axis where to calculate the
displacement field.
gridy : int, optional
Number of points along the `y` where to calculate the
displacement field.
num_levels : int, optional
Number of contour levels (higher values make the contour smoother).
vecmin : float, optional
Minimum value for the contour scale (useful to compare with other
results). If not specified it will be taken from the calculated
field.
vecmax : float, optional
Maximum value for the contour scale.
calc_data_only : bool, optional
If only calculated data should be returned.
Returns
-------
ax : matplotlib.axes.Axes
The Matplotlib object that can be used to modify the current plot
if needed.
data : dict
Data calculated during the plotting procedure.
"""
msg('Plotting contour...')
import matplotlib
if platform.system().lower() == 'linux':
matplotlib.use('Agg')
import matplotlib.pyplot as plt
msg('Computing field variables...', level=1)
displs = ['u', 'v', 'w', 'phix', 'phiy']
strains = ['exx', 'eyy', 'gxy', 'kxx', 'kyy', 'kxy', 'gyz', 'gxz']
stresses = ['Nxx', 'Nyy', 'Nxy', 'Mxx', 'Myy', 'Mxy', 'Qy', 'Qx']
if vec in displs:
res = self.uvw(c, group, gridx=gridx, gridy=gridy)
elif vec in strains:
res = self.strain(c, group, gridx=gridx, gridy=gridy)
elif vec in stresses:
res = self.stress(c, group, gridx=gridx, gridy=gridy)
else:
raise ValueError(
'{0} is not a valid vec parameter value!'.format(vec))
field = np.array(res[vec])
msg('Finished!', level=1)
if vecmin is None:
vecmin = field.min()
if vecmax is None:
vecmax = field.max()
data = dict(vecmin=vecmin, vecmax=vecmax)
if calc_data_only:
return None, data
levels = linspace(vecmin, vecmax, num_levels)
if ax is None:
fig = plt.figure(figsize=figsize)
ax = fig.add_subplot(111)
else:
if isinstance(ax, matplotlib.axes.Axes):
ax = ax
fig = ax.figure
save = False
else:
raise ValueError('ax must be an Axes object')
if invert_y == True:
ax.invert_yaxis()
ax.invert_xaxis()
colormap_obj = getattr(cm, colormap, None)
if colormap_obj is None:
warn('Invalid colormap, using "jet"', level=1)
colormap_obj = cm.jet
count = -1
for i, panel in enumerate(self.panels):
if panel.group != group:
continue
count += 1
xplot = res['y'][count] + panel.y0
yplot = res['x'][count] + panel.x0
field = res[vec][count]
contour = ax.contourf(xplot, yplot, field, levels=levels,
cmap=colormap_obj)
if identify:
ax.text(xplot.mean(), yplot.mean(), 'P {0:02d}'.format(i+1),
transform=ax.transData, ha='center')
if show_boundaries:
x1, x2 = xplot.min(), xplot.max()
y1, y2 = yplot.min(), yplot.max()
ax.plot((x1, x2), (y1, y1), boundary_line, lw=boundary_linewidth)
ax.plot((x1, x2), (y2, y2), boundary_line, lw=boundary_linewidth)
ax.plot((x1, x1), (y1, y2), boundary_line, lw=boundary_linewidth)
ax.plot((x2, x2), (y1, y2), boundary_line, lw=boundary_linewidth)
if colorbar:
from mpl_toolkits.axes_grid1 import make_axes_locatable
fsize = cbar_fontsize
divider = make_axes_locatable(ax)
cax = divider.append_axes('right', size='5%', pad=0.05)
cbarticks = linspace(vecmin, vecmax, cbar_nticks)
cbar = plt.colorbar(contour, ticks=cbarticks, format=cbar_format,
cax=cax)
if cbar_title:
cax.text(0.5, 1.05, cbar_title, horizontalalignment='center',
verticalalignment='bottom', fontsize=fsize)
cbar.outline.remove()
cbar.ax.tick_params(labelsize=fsize, pad=0., tick2On=False)
if title != '':
ax.set_title(str(title))
fig.tight_layout()
ax.set_aspect(aspect)
ax.grid(False)
ax.set_frame_on(False)
if clean:
ax.xaxis.set_ticks_position('none')
ax.yaxis.set_ticks_position('none')
ax.xaxis.set_ticklabels([])
ax.yaxis.set_ticklabels([])
else:
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
for kwargs in texts:
ax.text(transform=ax.transAxes, **kwargs)
if save:
if not filename:
filename = group + '.png'
fig.savefig(filename, transparent=True,
bbox_inches='tight', pad_inches=0.05, dpi=dpi)
plt.close()
msg('finished!')
return ax, data
def plot(self,
c,
group,
invert_y=False,
vec='w',
filename='',
ax=None,
figsize=(3.5, 2.),
save=True,
title='',
identify=False,
show_boundaries=False,
boundary_line='--k',
boundary_linewidth=1.,
colorbar=False,
cbar_nticks=2,
cbar_format=None,
cbar_title='',
cbar_fontsize=10,
colormap='jet',
aspect='equal',
clean=True,
dpi=400,
texts=[],
xs=None,
ys=None,
gridx=50,
gridy=50,
num_levels=400,
vecmin=None,
vecmax=None,
calc_data_only=False):
r"""Contour plot for a Ritz constants vector.
Parameters
----------
c : np.ndarray
The Ritz constants that will be used to compute the field contour.
group : str
A group to plot. Each panel in ``panels`` should contain an
attribute ``group``, which is used to identify which entities
should be plotted together.
vec : str, optional
Can be one of the components:
- Displacement: ``'u'``, ``'v'``, ``'w'``, ``'phix'``, ``'phiy'``
- Strain: ``'exx'``, ``'eyy'``, ``'gxy'``, ``'kxx'``, ``'kyy'``,
``'kxy'``, ``'gyz'``, ``'gxz'``
- Stress: ``'Nxx'``, ``'Nyy'``, ``'Nxy'``, ``'Mxx'``, ``'Myy'``,
``'Mxy'``, ``'Qy'``, ``'Qx'``
invert_y : bool, optional
Inverts the `y` axis of the plot.
save : bool, optional
Flag telling whether the contour should be saved to an image file.
dpi : int, optional
Resolution of the saved file in dots per inch.
filename : str, optional
The file name for the generated image file. If no value is given,
the `name` parameter of the ``Panel`` object will be used.
ax : AxesSubplot, optional
When ``ax`` is given, the contour plot will be created inside it.
figsize : tuple, optional
The figure size given by ``(width, height)``.
title : str, optional
If any string is given a title is added to the contour plot.
indentify : bool, optional
If domains should be identified. If yes, the name of each panel is
used.
show_boundaries : bool, optional
If boundaries between domains should be drawn.
boundary_line : str, optional
Matplotlib string to define line type and color.
boundary_linewidth : float, optional
Matplotlib float to define line width.
colorbar : bool, optional
If a colorbar should be added to the contour plot.
cbar_nticks : int, optional
Number of ticks added to the colorbar.
cbar_format : [ None | format string | Formatter object ], optional
See the ``matplotlib.pyplot.colorbar`` documentation.
cbar_title : str, optional
Colorbar title. If ``cbar_title == ''`` no title is added.
cbar_fontsize : int, optional
Fontsize of the colorbar labels.
colormap : string, optional
Name of a matplotlib available colormap.
aspect : str, optional
String that will be passed to the ``AxesSubplot.set_aspect()``
method.
clean : bool, optional
Clean axes ticks, grids, spines etc.
xs : np.ndarray, optional
The `x` positions where to calculate the displacement field.
Default is ``None`` and the method ``_default_field`` is used.
ys : np.ndarray, optional
The ``y`` positions where to calculate the displacement field.
Default is ``None`` and the method ``_default_field`` is used.
gridx : int, optional
Number of points along the `x` axis where to calculate the
displacement field.
gridy : int, optional
Number of points along the `y` where to calculate the
displacement field.
num_levels : int, optional
Number of contour levels (higher values make the contour smoother).
vecmin : float, optional
Minimum value for the contour scale (useful to compare with other
results). If not specified it will be taken from the calculated
field.
vecmax : float, optional
Maximum value for the contour scale.
calc_data_only : bool, optional
If only calculated data should be returned.
Returns
-------
ax : matplotlib.axes.Axes
The Matplotlib object that can be used to modify the current plot
if needed.
data : dict
Data calculated during the plotting procedure.
"""
msg('Plotting contour...')
import matplotlib
if platform.system().lower() == 'linux':
matplotlib.use('Agg')
import matplotlib.pyplot as plt
msg('Computing field variables...', level=1)
displs = ['u', 'v', 'w', 'phix', 'phiy']
strains = ['exx', 'eyy', 'gxy', 'kxx', 'kyy', 'kxy', 'gyz', 'gxz']
stresses = ['Nxx', 'Nyy', 'Nxy', 'Mxx', 'Myy', 'Mxy', 'Qy', 'Qx']
if vec in displs:
res = self.uvw(c, group, gridx=gridx, gridy=gridy)
elif vec in strains:
res = self.strain(c, group, gridx=gridx, gridy=gridy)
elif vec in stresses:
res = self.stress(c, group, gridx=gridx, gridy=gridy)
else:
raise ValueError(
'{0} is not a valid vec parameter value!'.format(vec))
field = np.array(res[vec])
msg('Finished!', level=1)
if vecmin is None:
vecmin = field.min()
if vecmax is None:
vecmax = field.max()
data = dict(vecmin=vecmin, vecmax=vecmax)
if calc_data_only:
return None, data
levels = linspace(vecmin, vecmax, num_levels)
if ax is None:
fig = plt.figure(figsize=figsize)
ax = fig.add_subplot(111)
else:
if isinstance(ax, matplotlib.axes.Axes):
ax = ax
fig = ax.figure
save = False
else:
raise ValueError('ax must be an Axes object')
if invert_y == True:
ax.invert_yaxis()
ax.invert_xaxis()
colormap_obj = getattr(cm, colormap, None)
if colormap_obj is None:
warn('Invalid colormap, using "jet"', level=1)
colormap_obj = cm.jet
count = -1
for i, panel in enumerate(self.panels):
if panel.group != group:
continue
count += 1
xplot = res['y'][count] + panel.y0
yplot = res['x'][count] + panel.x0
field = res[vec][count]
contour = ax.contourf(xplot,
yplot,
field,
levels=levels,
cmap=colormap_obj)
if identify:
ax.text(xplot.mean(),
yplot.mean(),
'P {0:02d}'.format(i + 1),
transform=ax.transData,
ha='center')
if show_boundaries:
x1, x2 = xplot.min(), xplot.max()
y1, y2 = yplot.min(), yplot.max()
ax.plot((x1, x2), (y1, y1),
boundary_line,
lw=boundary_linewidth)
ax.plot((x1, x2), (y2, y2),
boundary_line,
lw=boundary_linewidth)
ax.plot((x1, x1), (y1, y2),
boundary_line,
lw=boundary_linewidth)
ax.plot((x2, x2), (y1, y2),
boundary_line,
lw=boundary_linewidth)
if colorbar:
from mpl_toolkits.axes_grid1 import make_axes_locatable
fsize = cbar_fontsize
divider = make_axes_locatable(ax)
cax = divider.append_axes('right', size='5%', pad=0.05)
cbarticks = linspace(vecmin, vecmax, cbar_nticks)
cbar = plt.colorbar(contour,
ticks=cbarticks,
format=cbar_format,
cax=cax)
if cbar_title:
cax.text(0.5,
1.05,
cbar_title,
horizontalalignment='center',
verticalalignment='bottom',
fontsize=fsize)
cbar.outline.remove()
cbar.ax.tick_params(labelsize=fsize, pad=0., tick2On=False)
if title != '':
ax.set_title(str(title))
fig.tight_layout()
ax.set_aspect(aspect)
ax.grid(False)
ax.set_frame_on(False)
if clean:
ax.xaxis.set_ticks_position('none')
ax.yaxis.set_ticks_position('none')
ax.xaxis.set_ticklabels([])
ax.yaxis.set_ticklabels([])
else:
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
for kwargs in texts:
ax.text(transform=ax.transAxes, **kwargs)
if save:
if not filename:
filename = group + '.png'
fig.savefig(filename,
transparent=True,
bbox_inches='tight',
pad_inches=0.05,
dpi=dpi)
plt.close()
msg('finished!')
return ax, data
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_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_Vf(self, rho=None, M=None, modes=(0, 1, 2, 3, 4, 5), num=10,
silent=False):
r"""Calculate the flutter speed
If ``rho`` and ``M`` are not supplied, ``beta`` will be returned.
Parameters
----------
rho : float, optional
Air density.
M : float, optional
Mach number.
modes : tuple, optional
The modes that should be monitored.
num : int, optional
Number of points to search for each iteration.
Returns
-------
lambdacr : float
The critical ``beta``.
"""
#TODO
# - use a linear or parabolic interpolation to estimate new_lim1
msg('Flutter calculation...', level=1, silent=silent)
lim1 = 0.1
lim2 = 100.
new_lim1 = 1e6
new_lim2 = -1e6
eigvals_imag = np.zeros((num, len(modes)))
if max(modes) > self.num_eigvalues-1:
self.num_eigvalues = max(modes)+1
count = 0
while True:
count += 1
betas = np.linspace(lim1, lim2, num)
msg('iteration %d:' % count, level=2, silent=silent)
msg('lambda_min: %1.3f' % lim1, level=3, silent=silent)
msg('lambda_max: %1.3f' % lim2, level=3, silent=silent)
for i, beta in enumerate(betas):
self.beta = beta
self.freq(atype=1, sparse_solver=False, silent=True)
for j, mode in enumerate(modes):
eigvals_imag[i, j] = self.eigvals[mode].imag
check = np.where(eigvals_imag != 0.)
if not np.any(check):
continue
if np.abs(eigvals_imag[check]).min() < 0.01:
break
if 0 in check[0]:
new_lim1 = min(new_lim1, 0.5*betas[check[0][0]])
new_lim2 = max(new_lim2, 1.5*betas[check[0][-1]])
elif check[0].min() > 0:
new_lim1 = betas[check[0][0]-1]
new_lim2 = betas[check[0][0]]
else:
new_lim1 = min(new_lim1, lim1/2.)
new_lim2 = max(new_lim2, 2*lim2)
lim1 = new_lim1
lim2 = new_lim2
msg('finished!', level=1)
msg('Number of analyses = %d' % (count*num), level=1)
return lim1
def freq(K, M, tol=0, sparse_solver=True, silent=False,
sort=True, reduced_dof=False,
num_eigvalues=25, num_eigvalues_print=5):
"""Frequency Analysis
Parameters
----------
K : sparse_matrix
Stiffness matrix. Should include initial stress stiffness matrix,
aerodynamic matrix and so forth when applicable.
M : sparse_matrix
Mass matrix.
tol : float, optional
A tolerance value passed to ``scipy.sparse.linalg.eigs``.
sparse_solver : bool, optional
Tells if solver :func:`scipy.linalg.eig` or
:func:`scipy.sparse.linalg.eigs` should be used.
.. note:: It is recommended ``sparse_solver=False``, because it
was verified that the sparse solver becomes unstable
for some cases, though the sparse solver is faster.
silent : bool, optional
A boolean to tell whether the log messages should be printed.
sort : bool, optional
Sort the output eigenvalues and eigenmodes.
reduced_dof : bool, optional
Considers only the contributions of `v` and `w` to the stiffness
matrix and accelerates the run. Only effective when
``sparse_solver=False``.
num_eigvalues : int, optional
Number of calculated eigenvalues.
num_eigvalues_print : int, optional
Number of eigenvalues to print.
Returns
-------
The extracted eigenvalues are stored in the ``eigvals`` parameter and
the `i^{th}` eigenvector in the ``eigvecs[:, i-1]`` parameter.
"""
msg('Running frequency analysis...', silent=silent)
msg('Eigenvalue solver... ', level=2, silent=silent)
k = min(num_eigvalues, M.shape[0]-2)
if sparse_solver:
msg('eigs() solver...', level=3, silent=silent)
sizebkp = M.shape[0]
K, M, used_cols = remove_null_cols(K, M, silent=silent,
level=3)
#NOTE Looking for better performance with symmetric matrices, I tried
# using compmech.sparse.is_symmetric and eigsh, but it seems not
# to improve speed (I did not try passing only half of the sparse
# matrices to the solver)
eigvals, peigvecs = eigs(A=K, k=k, which='LM', M=M, tol=tol,
sigma=-1.)
eigvecs = np.zeros((sizebkp, num_eigvalues), dtype=peigvecs.dtype)
eigvecs[used_cols, :] = peigvecs
eigvals = np.sqrt(eigvals) # omega^2 to omega, in rad/s
else:
msg('eig() solver...', level=3, silent=silent)
M = M.toarray()
K = K.toarray()
sizebkp = M.shape[0]
col_sum = M.sum(axis=0)
check = col_sum != 0
used_cols = np.arange(M.shape[0])[check]
M = M[:, check][check, :]
K = K[:, check][check, :]
if reduced_dof:
i = np.arange(M.shape[0])
take = np.column_stack((i[1::3], i[2::3])).flatten()
M = M[:, take][take, :]
K = K[:, take][take, :]
#TODO did not try using eigh when input is symmetric to see if there
# will be speed improvements
eigvals, peigvecs = eig(a=-M, b=K)
eigvecs = np.zeros((sizebkp, K.shape[0]),
dtype=peigvecs.dtype)
eigvecs[check, :] = peigvecs
eigvals = np.sqrt(-1./eigvals) # -1/omega^2 to omega, in rad/s
eigvals = eigvals
msg('finished!', level=3, silent=silent)
if sort:
sort_ind = np.lexsort((np.round(eigvals.imag, 1),
np.round(eigvals.real, 1)))
eigvals = eigvals[sort_ind]
eigvecs = eigvecs[:, sort_ind]
higher_zero = eigvals.real > 1e-6
eigvals = eigvals[higher_zero]
eigvecs = eigvecs[:, higher_zero]
if not sparse_solver and reduced_dof:
new_eigvecs = np.zeros((3*eigvecs.shape[0]//2, eigvecs.shape[1]),
dtype=eigvecs.dtype)
new_eigvecs[take, :] = eigvecs
eigvecs = new_eigvecs
msg('finished!', level=2, silent=silent)
msg('first {0} eigenvalues:'.format(num_eigvalues_print), level=1,
silent=silent)
for eigval in eigvals[:num_eigvalues_print]:
msg('{0} rad/s'.format(eigval), level=2, silent=silent)
return eigvals, eigvecs
def _solver_NR(run, silent=False):
"""Newton-Raphson solver
"""
msg('Initialization...', level=1, silent=silent)
modified_NR = run.modified_NR
inc = run.initialInc
total = inc
once_at_total = False
max_total = 0.
fext = run.calc_fext(inc=inc, silent=silent)
k0 = run.calc_k0(silent=silent)
c = solve(k0, fext, silent=silent)
kT_last = k0
if modified_NR:
compute_kT = False
else:
compute_kT = True
step_num = 1
while True:
msg('Started Load Step {} - '.format(step_num) +
'Attempting time = {0}'.format(total),
level=1,
silent=silent)
# TODO maybe for pdC=True, pdT the fext must be calculated with
# the last kT available...
absERR = 1.e6
relERR = 1.e6
min_Rmax = 1.e6
prev_Rmax = 1.e6
last_min_Rmax = 1.e6
iteration = 0
converged = False
kT = kT_last
fext = run.calc_fext(inc=total, silent=silent)
iter_NR = 0
while True:
iteration += 1
msg('Iteration: {}'.format(iteration), level=2, silent=silent)
if iteration > run.maxNumIter:
warn('Maximum number of iterations achieved!',
level=2,
silent=silent)
break
if compute_kT or (run.kT_initial_state and step_num == 1
and iteration
== 1) or iter_NR == (run.compute_every_n - 1):
iter_NR = 0
kT = run.calc_kT(c=c, inc=total, silent=silent)
else:
iter_NR += 1
if not modified_NR:
compute_kT = True
fint = run.calc_fint(c=c, inc=total, silent=silent)
R = fext - fint
# convergence criteria:
# - maximum residual force Rmax
Rmax = np.abs(R).max()
msg('Rmax = {0}'.format(Rmax), level=3, silent=silent)
if iteration >= 2 and Rmax < run.absTOL:
converged = True
break
if (Rmax > prev_Rmax and Rmax > min_Rmax and iteration > 2):
warn('Diverged!', level=2, silent=silent)
break
else:
min_Rmax = min(min_Rmax, Rmax)
change_rate_Rmax = abs(prev_Rmax - Rmax) / abs(prev_Rmax)
if (iteration > 2 and change_rate_Rmax < run.too_slow_TOL):
warn('Diverged! (convergence too slow)',
level=2,
silent=silent)
break
prev_Rmax = Rmax
msg('Solving... ', level=2, silent=silent)
delta_c = solve(kT, R, silent=silent)
msg('finished!', level=2, silent=silent)
eta1 = 0.
eta2 = 1.
if run.line_search:
msg('Performing line-search... ', level=2, silent=silent)
iter_line_search = 0
while True:
c1 = c + eta1 * delta_c
c2 = c + eta2 * delta_c
fint1 = run.calc_fint(c=c1, inc=total, silent=silent)
fint2 = run.calc_fint(c=c2, inc=total, silent=silent)
R1 = fext - fint1
R2 = fext - fint2
s1 = delta_c.dot(R1)
s2 = delta_c.dot(R2)
eta_new = (eta2 - eta1) * (-s1 / (s2 - s1)) + eta1
eta1 = eta2
eta2 = eta_new
eta2 = min(max(eta2, 0.2), 10.)
if abs(eta2 - eta1) < 0.01:
break
iter_line_search += 1
if iter_line_search == run.max_iter_line_search:
eta2 = 1.
warn('maxinum number of iterations',
level=3,
silent=silent)
break
msg('finished!', level=2, silent=silent)
c = c + eta2 * delta_c
if converged:
msg('Finished Load Step {} at'.format(step_num) +
' time = {0}'.format(total),
level=1,
silent=silent)
run.increments.append(total)
run.cs.append(c.copy()) #NOTE copy required
finished = False
if abs(total - 1) < 1e-3:
finished = True
else:
factor = 1.1
if once_at_total:
inc_new = min(factor * inc, run.maxInc, (1. - total) / 2)
else:
inc_new = min(factor * inc, run.maxInc, 1. - total)
msg('Changing time increment from {0:1.9f} to {1:1.9f}'.format(
inc, inc_new),
level=1,
silent=silent)
inc = inc_new
total += inc
total = min(1, total)
step_num += 1
if finished:
break
if modified_NR:
msg('Updating kT...', level=1, silent=silent)
kT = run.calc_kT(c=c, inc=total, silent=silent)
msg('kT updated!', level=1, silent=silent)
compute_kT = False
kT_last = kT
else:
max_total = max(max_total, total)
while True:
factor = 0.3
msg('Bisecting time increment from {0} to {1}'.format(
inc, inc * factor),
level=1,
silent=silent)
if abs(total - 1) < 1e-3:
once_at_total = True
total -= inc
inc *= factor
if inc < run.minInc:
msg('Minimum step size achieved!', level=1, silent=silent)
break
total += inc
if total >= max_total:
continue
else:
break
if inc < run.minInc:
msg('Stopping solver: minimum step size achieved!',
level=1,
silent=silent)
break
if len(run.cs) > 0:
c = run.cs[-1].copy() #NOTE copy required
else:
# means that run bisection must be done in initialInc
fext = run.calc_fext(inc=inc, silent=silent)
c = solve(k0, fext, silent=silent)
msg('Finished Non-Linear Static Analysis', silent=silent)
msg('at time {0}'.format(total), level=1, silent=silent)
def plot_skin(self, c, invert_y=False, plot_type=1, vec='w',
deform_u=False, deform_u_sf=100.,
filename='',
ax=None, figsize=(3.5, 2.), save=True,
add_title=False, title='',
colorbar=False, cbar_nticks=2, cbar_format=None,
cbar_title='', cbar_fontsize=10,
aspect='equal', clean=True, dpi=400,
texts=[], xs=None, ys=None, gridx=300, gridy=300,
num_levels=400, vecmin=None, vecmax=None):
r"""Contour plot for a Ritz constants vector.
Parameters
----------
c : np.ndarray
The Ritz constants that will be used to compute the field contour.
vec : str, optional
Can be one of the components:
- Displacement: ``'u'``, ``'v'``, ``'w'``, ``'phix'``, ``'phiy'``
- Strain: ``'exx'``, ``'eyy'``, ``'gxy'``, ``'kxx'``, ``'kyy'``,
``'kxy'``, ``'gyz'``, ``'gxz'``
- Stress: ``'Nxx'``, ``'Nyy'``, ``'Nxy'``, ``'Mxx'``, ``'Myy'``,
``'Mxy'``, ``'Qy'``, ``'Qx'``
deform_u : bool, optional
If ``True`` the contour plot will look deformed.
deform_u_sf : float, optional
The scaling factor used to deform the contour.
invert_y : bool, optional
Inverts the `y` axis of the plot. It may be used to match
the coordinate system of the finite element models created
using the ``desicos.abaqus`` module.
plot_type : int, optional
For cylinders only ``4`` and ``5`` are valid.
For cones all the following types can be used:
- ``1``: concave up (with ``invert_y=False``) (default)
- ``2``: concave down (with ``invert_y=False``)
- ``3``: stretched closed
- ``4``: stretched opened (`r \times y` vs. `a`)
- ``5``: stretched opened (`y` vs. `a`)
save : bool, optional
Flag telling whether the contour should be saved to an image file.
dpi : int, optional
Resolution of the saved file in dots per inch.
filename : str, optional
The file name for the generated image file. If no value is given,
the `name` parameter of the :class:`StiffPanelBay` object
will be used.
ax : AxesSubplot, optional
When ``ax`` is given, the contour plot will be created inside it.
figsize : tuple, optional
The figure size given by ``(width, height)``.
add_title : bool, optional
If a title should be added to the figure.
title : str, optional
If any string is given ``add_title`` will be ignored and the given
title added to the contour plot.
colorbar : bool, optional
If a colorbar should be added to the contour plot.
cbar_nticks : int, optional
Number of ticks added to the colorbar.
cbar_format : [ None | format string | Formatter object ], optional
See the ``matplotlib.pyplot.colorbar`` documentation.
cbar_fontsize : int, optional
Fontsize of the colorbar labels.
cbar_title : str, optional
Colorbar title. If ``cbar_title == ''`` no title is added.
aspect : str, optional
String that will be passed to the ``AxesSubplot.set_aspect()``
method.
clean : bool, optional
Clean axes ticks, grids, spines etc.
xs : np.ndarray, optional
The `x` positions where to calculate the displacement field.
Default is ``None`` and the method ``_default_field`` is used.
ys : np.ndarray, optional
The ``y`` positions where to calculate the displacement field.
Default is ``None`` and the method ``_default_field`` is used.
gridx : int, optional
Number of points along the `x` axis where to calculate the
displacement field.
gridy : int, optional
Number of points along the `y` where to calculate the
displacement field.
num_levels : int, optional
Number of contour levels (higher values make the contour smoother).
vecmin : float, optional
Minimum value for the contour scale (useful to compare with other
results). If not specified it will be taken from the calculated
field.
vecmax : float, optional
Maximum value for the contour scale.
Returns
-------
ax : matplotlib.axes.Axes
The Matplotlib object that can be used to modify the current plot
if needed.
"""
msg('Plotting contour...')
ubkp, vbkp, wbkp, phixbkp, phiybkp = (self.u, self.v, self.w,
self.phix, self.phiy)
import matplotlib.pyplot as plt
import matplotlib
msg('Computing field variables...', level=1)
displs = ['u', 'v', 'w', 'phix', 'phiy']
if vec in displs:
self.uvw_skin(c, xs=xs, ys=ys, gridx=gridx, gridy=gridy)
field = getattr(self, vec)
else:
raise ValueError(
'{0} is not a valid vec parameter value!'.format(vec))
msg('Finished!', level=1)
Xs = self.Xs
Ys = self.Ys
if vecmin is None:
vecmin = field.min()
if vecmax is None:
vecmax = field.max()
levels = linspace(vecmin, vecmax, num_levels)
if ax is None:
fig = plt.figure(figsize=figsize)
ax = fig.add_subplot(111)
else:
if isinstance(ax, matplotlib.axes.Axes):
ax = ax
fig = ax.figure
save = False
else:
raise ValueError('ax must be an Axes object')
x = Ys
y = Xs
if deform_u:
if vec in displs:
pass
else:
self.uvw_skin(c, xs=xs, ys=ys, gridx=gridx, gridy=gridy)
field_u = self.u
field_v = self.v
y -= deform_u_sf*field_u
x += deform_u_sf*field_v
contour = ax.contourf(x, y, field, levels=levels)
if colorbar:
from mpl_toolkits.axes_grid1 import make_axes_locatable
fsize = cbar_fontsize
divider = make_axes_locatable(ax)
cax = divider.append_axes('right', size='5%', pad=0.05)
cbarticks = linspace(vecmin, vecmax, cbar_nticks)
cbar = plt.colorbar(contour, ticks=cbarticks, format=cbar_format,
cax=cax)
if cbar_title:
cax.text(0.5, 1.05, cbar_title, horizontalalignment='center',
verticalalignment='bottom', fontsize=fsize)
cbar.outline.remove()
cbar.ax.tick_params(labelsize=fsize, pad=0., tick2On=False)
if invert_y == True:
ax.invert_yaxis()
ax.invert_xaxis()
if title != '':
ax.set_title(str(title))
elif add_title:
if self.analysis.last_analysis == 'static':
ax.set_title('$m, n={0}, {1}$'.format(self.m, self.n))
elif self.analysis.last_analysis == 'lb':
ax.set_title(
r'$m, n={0}, {1}$, $\lambda_{{CR}}={4:1.3e}$'.format(
self.m, self.n, self.eigvals[0]))
fig.tight_layout()
ax.set_aspect(aspect)
ax.grid(False)
ax.set_frame_on(False)
if clean:
ax.xaxis.set_ticks_position('none')
ax.yaxis.set_ticks_position('none')
ax.xaxis.set_ticklabels([])
ax.yaxis.set_ticklabels([])
else:
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
for kwargs in texts:
ax.text(transform=ax.transAxes, **kwargs)
if save:
if not filename:
filename = 'test.png'
fig.savefig(filename, transparent=True,
bbox_inches='tight', pad_inches=0.05, dpi=dpi)
plt.close()
if ubkp is not None:
self.u = ubkp
if vbkp is not None:
self.v = vbkp
if wbkp is not None:
self.w = wbkp
if phixbkp is not None:
self.phix = phixbkp
if phiybkp is not None:
self.phiy = phiybkp
msg('finished!')
return ax
def inv_weighted(data, mesh, num_sub, col, ncp=5, power_parameter=2):
r"""Interpolates the values taken at one group of points into
another using an inverse-weighted algorithm
In the inverse-weighted algorithm a number of `n_{CP}` measured points
of the input parameter ``data`` that are closest to a given node in
the input parameter ``mesh`` are found and the imperfection value of
this node (represented by the normal displacement `{w_0}_{node}`) is
calculated as follows:
.. math::
{w_0}_{node} = \frac{\sum_{i}^{n_{CP}}{{w_0}_i\frac{1}{w_i}}}
{\sum_{i}^{n_{CP}}{\frac{1}{w_i}}}
where `w_i` is the imperfection at each measured point, calculated as:
.. math::
w_i = \left[(x_{node}-x_i)^2+(y_{node}-y_i)^2+(z_{node}-y_i)^2
\right]^p
with `p` being a power parameter that when increased will increase the
relative influence of a closest point.
Parameters
----------
data : numpy.ndarray, shape (N, ndim+1)
The data or an array containing the imperfection file. The values
to be interpolated must be in the last column.
mesh : numpy.ndarray, shape (M, ndim)
The new coordinates where the values will be interpolated to.
num_sub : int
The number of sub-sets used during the interpolation. The points
are divided in sub-sets to increase the algorithm's efficiency.
col : int
The index of the column to be used in order to divide the data
in sub-sets. Note that the first column index is ``0``.
ncp : int, optional
Number of closest points used in the inverse-weighted interpolation.
power_parameter : float, optional
Power of inverse weighted interpolation function.
Returns
-------
ans : numpy.ndarray
A 1-D array with the interpolated values. The size of this array
is ``mesh.shape[0]``.
"""
if mesh.shape[1] != data.shape[1] - 1:
raise ValueError('Invalid input: mesh.shape[1] != data.shape[1]')
msg('Interpolating... ')
num_sub = int(num_sub)
mesh_size = mesh.shape[0]
# memory control
mem_limit = 1024 * 1024 * 1024 * 8 * 2 # 2 GB
mem_entries = int(mem_limit / 64) # if float64 is used
sec_size = int(mesh_size / num_sub)
while sec_size**2 * 10 > mem_entries:
num_sub += 1
sec_size = int(mesh_size / num_sub)
if sec_size**2 * 10 <= mem_entries:
warn('New num_sub: {0}'.format(int(mesh_size / float(sec_size))))
break
mesh_seq = np.arange(mesh.shape[0])
mesh_argsort = np.argsort(mesh[:, col])
mesh_seq = mesh_seq[mesh_argsort]
back_argsort = np.argsort(mesh_seq)
mesh = np.asarray(mesh[mesh_argsort], order='F')
length = mesh[:, col].max() - mesh[:, col].min()
data = np.asarray(data[np.argsort(data[:, col])], order='F')
ans = np.zeros(mesh.shape[0], dtype=mesh.dtype)
# max_num_limits defines how many times the log will print
# "processed ... out of ... entries"
max_num_limits = 10
for den in range(max_num_limits, 0, -1):
if num_sub % den == 0:
limit = int(num_sub / den)
break
for i in range(num_sub + 1):
i_inf = sec_size * i
i_sup = sec_size * (i + 1)
if i % limit == 0:
msg('\t processed {0:7d} out of {1:7d} entries'.format(
min(i_sup, mesh_size), mesh_size))
sub_mesh = mesh[i_inf:i_sup]
if not np.any(sub_mesh):
continue
inf = sub_mesh[:, col].min()
sup = sub_mesh[:, col].max()
tol = 0.03
if i == 0 or i == num_sub:
tol = 0.06
while True:
cond1 = data[:, col] >= inf - tol * length
cond2 = data[:, col] <= sup + tol * length
cond = np.all(np.array((cond1, cond2)), axis=0)
sub_data = data[cond]
if not np.any(sub_data):
tol += 0.01
else:
break
dist = np.subtract.outer(sub_mesh[:, 0], sub_data[:, 0])**2
for j in range(1, sub_mesh.shape[1]):
dist += np.subtract.outer(sub_mesh[:, j], sub_data[:, j])**2
asort = np.argsort(dist, axis=1)
lenn = sub_mesh.shape[0]
lenp = sub_data.shape[0]
asort_mesh = asort + np.meshgrid(
np.arange(lenn) * lenp, np.arange(lenp))[0].transpose()
# getting the distance of the closest points
dist_cp = np.take(dist, asort_mesh[:, :ncp])
# avoiding division by zero
dist_cp[(dist_cp == 0)] == 1.e-12
# fetching the imperfection of the sub-data
imp = sub_data[:, -1]
# taking only the imperfection of the closest points
imp_cp = np.take(imp, asort[:, :ncp])
# weight calculation
total_weight = np.sum(1. / (dist_cp**power_parameter), axis=1)
weight = 1. / (dist_cp**power_parameter)
# computing the new imp
imp_new = np.sum(imp_cp * weight, axis=1) / total_weight
# updating the answer array
ans[i_inf:i_sup] = imp_new
ans = ans[back_argsort]
msg('Interpolation completed!')
return ans
def lb(K, KG, tol=0, sparse_solver=True, silent=False,
num_eigvalues=25, num_eigvalues_print=5):
"""Linear Buckling Analysis
It can also be used for more general eigenvalue analyzes if `K` is the
tangent stiffness matrix of a given load state.
Parameters
----------
K : sparse_matrix
Stiffness matrix. Should include all constant terms of the initial
stress stiffness matrix, aerodynamic matrix and so forth when
applicable.
KG : sparse_matrix
Initial stress stiffness matrix that multiplies the load multiplcator
`\lambda` of the eigenvalue problem.
tol : float, optional
A float tolerance passsed to the eigenvalue solver.
sparse_solver : bool, optional
Tells if solver :func:`scipy.linalg.eigh` or
:func:`scipy.sparse.linalg.eigsh` should be used.
silent : bool, optional
A boolean to tell whether the log messages should be printed.
num_eigvalues : int, optional
Number of calculated eigenvalues.
num_eigvalues_print : int, optional
Number of eigenvalues to print.
Notes
-----
The extracted eigenvalues are stored in the ``eigvals`` parameter
of the ``Panel`` object and the `i^{th}` eigenvector in the
``eigvecs[:, i-1]`` parameter.
"""
msg('Running linear buckling analysis...', silent=silent)
msg('Eigenvalue solver... ', level=2, silent=silent)
k = min(num_eigvalues, KG.shape[0]-2)
if sparse_solver:
mode = 'cayley'
try:
msg('eigsh() solver...', level=3, silent=silent)
eigvals, eigvecs = eigsh(A=KG, k=k,
which='SM', M=K, tol=tol, sigma=1., mode=mode)
msg('finished!', level=3, silent=silent)
except Exception as e:
warn(str(e), level=4, silent=silent)
msg('aborted!', level=3, silent=silent)
sizebkp = KG.shape[0]
K, KG, used_cols = remove_null_cols(K, KG, silent=silent)
msg('eigsh() solver...', level=3, silent=silent)
eigvals, peigvecs = eigsh(A=KG, k=k,
which='SM', M=K, tol=tol, sigma=1., mode=mode)
msg('finished!', level=3, silent=silent)
eigvecs = np.zeros((sizebkp, num_eigvalues),
dtype=peigvecs.dtype)
eigvecs[used_cols, :] = peigvecs
else:
size = KG.shape[0]
K, KG, used_cols = remove_null_cols(K, KG, silent=silent)
K = K.toarray()
KG = KG.toarray()
msg('eigh() solver...', level=3, silent=silent)
eigvals, peigvecs = eigh(a=KG, b=K)
msg('finished!', level=3, silent=silent)
eigvecs = np.zeros((size, num_eigvalues), dtype=peigvecs.dtype)
eigvecs[used_cols, :] = peigvecs[:, :num_eigvalues]
eigvals = -1./eigvals
eigvals = eigvals
eigvecs = eigvecs
msg('finished!', level=2, silent=silent)
msg('first {0} eigenvalues:'.format(num_eigvalues_print), level=1,
silent=silent)
for eig in eigvals[:num_eigvalues_print]:
msg('{0}'.format(eig), level=2, silent=silent)
return eigvals, eigvecs
