def objective_function(self, xs): self.topology_factory.update_topology(xs) if self.topology_factory.is_connected is True: params = self.topology_factory.get_params() cantilever = microfem.Cantilever(*params) 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') try: w, _, vall = fem.modal_analysis(1) except RuntimeError: print('singular') kuu = fem.get_stiffness_matrix(free=False) f1 = np.asscalar(np.sqrt(w) / (2 * np.pi)) phi1 = vall[:, [0]] wtip1 = np.asscalar(opr @ phi1) kfunc = lambda p, w: np.asscalar(p.T @ kuu @ p / w**2) k1 = kfunc(phi1, wtip1) type1 = mode_ident.is_mode_flexural(phi1) if type1 is False: cost = 1e8 else: cost = -f1 * 1e-6 if k1 < self.k1 else k1 return (cost, ) return (self.topology_factory.connectivity_penalty, )
def objective_function(self, xs): self.topology_factory.update_topology(xs) if self.topology_factory.is_connected is True: params = self.topology_factory.get_params() cantilever = microfem.Cantilever(*params) 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) kuu = fem.get_stiffness_matrix(free=False) fs = np.sqrt(w) / (2*np.pi) 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] if types[0] is False: cost = 1e8 elif types[1] is True: cost = self.evaluation(fs[0], fs[1], ks[0], ks[1]) elif types[2] is True: cost = self.evaluation(fs[0], fs[2], ks[0], ks[2]) else: cost = 2e7 return (cost,) return (self.topology_factory.connectivity_penalty,)
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])
microfem.plot_topology(cantilever) material = microfem.PiezoMumpsMaterial() fem = microfem.LaminateFEM(material, cantilever) # 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])