def test_generalized_alpha_nonlinear_dynamics_solver(self):
self.system.apply_neumann_boundaries(key=3,
val=2.5e8,
direct=(0, -1),
time_func=lambda t: 1)
self.solver = amfe.GeneralizedAlphaNonlinearDynamicsSolver(
mechanical_system=self.system, **self.options)
self.solver.solve()
x = np.array([
self.system.T_output[:],
[displacement[2] for displacement in self.system.u_output]
])
y = np.array([
self.system.T_output[:],
[displacement[3] for displacement in self.system.u_output]
])
fnx = amfe.amfe_dir(
'tests/kratos/Kratos_beam10x1Quad8_nonlinear_dynamics_x_wbzalpha_rhoinf095_dt1e-6.grf'
)
fny = amfe.amfe_dir(
'tests/kratos/Kratos_beam10x1Quad8_nonlinear_dynamics_y_wbzalpha_rhoinf095_dt1e-6.grf'
)
reference_x = read_grf(fnx)
reference_y = read_grf(fny)
assert_allclose(x[1, 1:],
reference_x[1, 499::500],
rtol=1e-12,
atol=0.06)
assert_allclose(y[1, 1:],
reference_y[1, 499::500],
rtol=1e-12,
atol=0.06)
solver.solve()
q_static = system.constrain_vec(system.u_output[-1][:])
system.clear_timesteps()
if not statics: # dynamics
system.apply_neumann_boundaries(key=3, val=-2.5e8, direct=(0, -1), time_func=lambda t: t) # delete static NBCs
system.apply_neumann_boundaries(key=3, val=2.5e8, direct=(0, -1), time_func=lambda t: 1) # reset dynamic NBCs
# > convert system to state-space form
state_space_system = amfe.mechanical_system.convert_mechanical_system_to_state_space(
system, regular_matrix=system.K(q_static), overwrite=False)
# solve system
if not statics:
if not linear: # non-linear dynamics
if scheme is 'GeneralizedAlpha':
solver = amfe.GeneralizedAlphaNonlinearDynamicsSolver(mechanical_system=system, **options)
elif scheme is 'WBZAlpha':
solver = amfe.GeneralizedAlphaNonlinearDynamicsSolver(mechanical_system=system, **options)
solver.set_wbz_alpha_parameters(rho_inf=rho_inf)
elif scheme is 'HHTAlpha':
solver = amfe.GeneralizedAlphaNonlinearDynamicsSolver(mechanical_system=system, **options)
solver.set_hht_alpha_parameters(rho_inf=rho_inf)
elif scheme is 'NewmarkBeta':
solver = amfe.GeneralizedAlphaNonlinearDynamicsSolver(mechanical_system=system, **options)
solver.set_newmark_beta_parameters(beta=0.25*(1 + alpha)**2, gamma=0.5 + alpha)
elif scheme is 'JWHAlpha':
solver = amfe.JWHAlphaNonlinearDynamicsSolver(mechanical_system=system, **options)
elif scheme is 'JWHAlphaStateSpace':
system = state_space_system
solver = amfe.JWHAlphaNonlinearDynamicsSolverStateSpace(mechanical_system=system, **options)
else:
#
# Distributed under BSD-3-Clause License. See LICENSE-File for more information
#
"""
Rubber boot example
"""
import amfe
input_file = amfe.amfe_dir('meshes/gmsh/rubber_boot.msh')
output_file = amfe.amfe_dir('results/rubber_boot/boot')
# PE-LD; better material would be Mooney-Rivlin
my_material = amfe.KirchhoffMaterial(E=200E6, nu=0.3, rho=1E3)
my_system = amfe.MechanicalSystem(stress_recovery=False)
my_system.load_mesh_from_gmsh(input_file, 977, my_material, scale_factor=1E-3)
my_system.apply_dirichlet_boundaries(978, 'xyz')
my_system.apply_neumann_boundaries(979, 1E7, (0, 1, 0), lambda t: 1)
#%%
solver = amfe.GeneralizedAlphaNonlinearDynamicsSolver(my_system)
solver.solve()
my_system.export_paraview(output_file + '_full_ti')
#amfe.vibration_modes(my_system, save=True)
#my_system.export_paraview(output_file + '_modes')
#%%
###############################################################################
## time integration
###############################################################################
ndof = my_system.dirichlet_class.no_of_constrained_dofs
q0 = np.zeros(ndof)
dq0 = np.zeros(ndof)
initial_conditions = {'q0': q0, 'dq0': dq0}
dt = 5e-4
t_end = 2
#%%
solver = amfe.GeneralizedAlphaNonlinearDynamicsSolver(my_system,dt=dt, t_end=t_end, initial_conditions=initial_conditions)
solver.solve()
my_system.export_paraview(paraview_output_file + '_full_model')
my_system.clear_timesteps()
solver = amfe.GeneralizedAlphaLinearDynamicsSolver(my_system, dt=dt, t_end=t_end, initial_conditions=initial_conditions)
solver.solve()
my_system.export_paraview(paraview_output_file + '_linear_model')
my_system.clear_timesteps()
omega, V = amfe.vibration_modes(my_system, 7, save=True)
my_system.export_paraview(paraview_output_file + '_modes')
Theta, Theta_tilde = amfe.shifted_modal_derivatives(V, my_system.K, my_system.M(), omega)
my_system.clear_timesteps()
V_temp = amfe.augment_with_derivatives(None, Theta, deflate=False)
def harmonic_excitation(t):
return np.sin(2.4 * 2 * np.pi * t) + np.sin(3.0 * 2 * np.pi * t)
my_system.apply_neumann_boundaries(85, 1E5, (1, 1, 0), harmonic_excitation)
#%%
omega, V = amfe.vibration_modes(my_system)
#%%
dt = 0.001
T = 10
ndof = my_system.K().shape[0]
q0 = np.zeros(ndof)
dq0 = np.zeros(ndof)
#amfe.integrate_nonlinear_system(my_system, q0, dq0, T, dt, alpha=0.1,
# track_niter=True)
dynsolver = amfe.GeneralizedAlphaNonlinearDynamicsSolver(my_system,
initial_conditions={
'q0': q0,
'dq0': dq0
},
t_end=T,
dt=dt,
track_iterations=True)
dynsolver.solve()
my_system.export_paraview(output_file + '_3')