def console_output(self, xopt, image_file):
self.topology_factory.update_topology(xopt)
tup = (2*self.topology_factory.a, 2*self.topology_factory.b)
print('The element dimensions are (um): %gx%g' % tup)
params = self.topology_factory.get_params()
cantilever = microfem.Cantilever(*params)
microfem.plot_topology(cantilever, image_file)
if self.topology_factory.is_connected is True:
fem = microfem.PlateFEM(self.material, cantilever)
coords = (cantilever.xtip, cantilever.ytip)
opr = microfem.PlateDisplacement(fem, coords).get_operator()
mode_ident = microfem.ModeIdentification(fem, cantilever, 'plate')
w, _, vall = fem.modal_analysis(self.n_modes)
freq = np.sqrt(w) / (2*np.pi)
kuu = fem.get_stiffness_matrix(free=False)
phis = [vall[:, [i]] for i in range(self.n_modes)]
wtips = [opr @ p for p in phis]
kfunc = lambda p, w: np.asscalar(p.T @ kuu @ p / w ** 2)
ks = [kfunc(p, w) for p, w in zip(phis, wtips)]
types = [mode_ident.is_mode_flexural(p) for p in phis]
tup = ('Disp', 'Freq (Hz)', 'Stiffness', 'Flexural')
print('\n %-15s %-15s %-15s %-10s' % tup)
for i in range(self.n_modes):
tup = (i, wtips[i], freq[i], ks[i], str(types[i]))
print('%-2d: %-15g %-15g %-15g %-10s' % tup)
for i in range(self.n_modes):
microfem.plot_mode(fem, vall[:, i])
def console_output(self, xopt, image_file):
self.topology_factory.update_topology(xopt)
topology = self.topology_factory.topology
cantilever = microfem.Cantilever(topology, self.a, self.b)
microfem.plot_topology(cantilever, image_file)
if self.topology_factory.is_connected is True:
fem = microfem.PlateFEM(self.material, cantilever)
coords = (cantilever.xtip, cantilever.ytip)
opr = PlateDisplacement(fem, coords).get_operator()
mode_ident = ModeIdentification(fem, cantilever)
w, _, vall = fem.modal_analysis(self.n_modes)
freq = np.sqrt(w) / (2*np.pi)
kuu = fem.get_stiffness_matrix(free=False)
phis = [vall[:, [i]] for i in range(self.n_modes)]
wtips = [opr @ p for p in phis]
ks = [np.asscalar(p.T @ kuu @ p / w ** 2) for p, w in zip(phis, wtips)]
costs = [k / ks[0] for k in ks]
types = [mode_ident.is_mode_flexural(p) for p in phis]
tup = ('Disp', 'Freq (Hz)', 'Stiffness', 'Ratio', 'Flexural')
print('\n %-15s %-15s %-15s %-15s %-10s' % tup)
for i in range(self.n_modes):
tup = (i, wtips[i], freq[i], ks[i], costs[i], str(types[i]))
print('%-2d: %-15g %-15g %-15g %-15g %-10s' % tup)
for i in range(self.n_modes):
microfem.plot_mode(fem, vall[:, i])
def console_output(self, xopt, image_file):
self.topology_factory.update_topology(xopt)
params = self.topology_factory.get_params()
cantilever = microfem.Cantilever(*params)
microfem.plot_topology(cantilever, image_file)
if self.topology_factory.is_connected is True:
fem = microfem.PlateFEM(self.material, cantilever)
w, _, vall = fem.modal_analysis(1)
f = np.asscalar(np.sqrt(w) / (2 * np.pi))
print('The first modal frequency is (Hz): %g' % f)
microfem.plot_mode(fem, vall[:, 0])
def to_console_final(self, xopt):
print()
print('--- Solution Characteristics ---')
if self.exe_time != 0:
print('Time (s): %g' % (self.exe_time))
self.topology_factory.update_topology(xopt)
topology = self.topology_factory.topology
cantilever = microfem.Cantilever(topology, self.a, self.b)
fn = ''.join((self.dir, '/', self.tag, '-image.png'))
microfem.plot_topology(cantilever, fn)
if self.topology_factory.is_connected is True:
self.fem.update_mesh(cantilever)
coords = (cantilever.xtip, cantilever.ytip)
opr = PlateDisplacement(self.fem, coords).get_operator()
mode_ident = ModeIdentification(self.fem, cantilever)
w, _, vall = self.fem.modal_analysis(self.n_modes)
freq = np.sqrt(w) / (2 * np.pi)
kuu = self.fem.get_stiffness_matrix(free=False)
phis = [vall[:, [i]] for i in range(self.n_modes)]
wtips = [opr @ p for p in phis]
ks = [
np.asscalar(p.T @ kuu @ p / w**2) for p, w in zip(phis, wtips)
]
costs = [k / ks[0] for k in ks]
types = [mode_ident.is_mode_flexural(p) for p in phis]
tup = ('Disp', 'Freq (Hz)', 'Stiffness', 'Ratio', 'Flexural')
print('\n %-15s %-15s %-15s %-15s %-10s' % tup)
for i in range(self.n_modes):
tup = (i, wtips[i], freq[i], ks[i], costs[i], str(types[i]))
print('%-2d: %-15g %-15g %-15g %-15g %-10s' % tup)
for i in range(self.n_modes):
microfem.plot_mode(self.fem, vall[:, i])
# With the FEM model buitl, modal analysis can be performed. This returns the
# resonance frequencies and mode shapes of the cantilever. These can then be
# plotted.
n_modes = 3
ws, _, vall = fem.modal_analysis(n_modes=n_modes)
# Using the results of the modal analysis, the frequency, stiffness,
# tip displacement, and mode type (flexural, torsional), can be determined.
coords = (cantilever.xtip, cantilever.ytip)
opr = microfem.LaminateDisplacement(fem, coords).get_operator()
mode_ident = microfem.ModeIdentification(fem, cantilever, type_='laminate')
freq = np.sqrt(ws) / (2 * np.pi)
kuu = fem.get_stiffness_matrix(free=False)
kuv = fem.get_piezoelectric_matrix(free=False)
phis = [vall[:, [i]] for i in range(n_modes)]
wtips = [opr @ p for p in phis]
kfunc = lambda p, w: np.asscalar(p.T @ kuu @ p / w**2)
ks = [kfunc(p, w) for p, w in zip(phis, wtips)]
charges = [kuv.T @ p / w for p, w in zip(phis, wtips)]
types = [mode_ident.is_mode_flexural(p) for p in phis]
tup = ('Disp', 'Freq (Hz)', 'Stiffness (N/m)', 'Flexural', 'Charge (C/m)')
print('\n %-15s %-15s %-15s %-10s %-15s' % tup)
for i in range(n_modes):
tup = (i + 1, wtips[i], freq[i], ks[i], str(types[i]), charges[i])
print('%-2d: %-15g %-15g %-15g %-10s %-15g' % tup)
microfem.plot_mode(fem, vall[:, 0])
microfem.plot_mode(fem, vall[:, 1])
microfem.plot_mode(fem, vall[:, 2])