def solve_linear_static(system, formulation, component):
"""
Solves a linear, static MechanicalSystem.
Parameters
----------
system : MechanicalSystem
MechanicalSystem object describing the equilibrium forces
formulation : ConstraintFormulation
A ConstraintFormulation object that can recover the nodal unconstrained displacements of the component
from the constrained states of the system
component : StructuralComponent
Structural Component belonging to the system
Returns
-------
solution : AmfeSolution
Simple Container for solutions of AMfe simulations
"""
solfac = SolverFactory()
solfac.set_system(system)
solfac.set_analysis_type('static')
solfac.set_linear_solver('scipy-sparse')
solver, solver_options = solfac.create_solver()
solution_writer = AmfeSolution()
no_of_dofs = system.dimension
q0 = np.zeros(no_of_dofs)
dq0 = q0
ddq0 = dq0
q = solver.solve(system.K(q0, dq0, 0), system.f_ext(q0, dq0, 0))
u, du, ddu = formulation.recover(q, dq0, ddq0, 0)
solution_writer.write_timestep(0, u, None, None)
logger = logging.getLogger(__name__)
logger.info(
'Strains and stresses are currently not supported for linear models. Only nonlinear kinematics are '
'currently used during their calculation.')
print('Solution finished')
return solution_writer
def solve_nonlinear_dynamic(component, t0, t_end):
system, formulation = create_mechanical_system(
component,
constant_mass=True,
constant_damping=True,
constraint_formulation='boolean')
solfac = SolverFactory()
solfac.set_system(system)
solfac.set_analysis_type('transient')
solfac.set_integrator('genalpha')
solfac.set_large_deflection(True)
solfac.set_nonlinear_solver('newton')
solfac.set_linear_solver('scipy-sparse')
solfac.set_acceleration_intializer('zero')
solfac.set_newton_maxiter(30)
solfac.set_newton_atol(1e-6)
solfac.set_newton_rtol(1e-8)
solfac.set_dt_initial(0.001)
solver = solfac.create_solver()
solution_writer = AmfeSolution()
def write_callback(t, x, dx, ddx):
u, du, ddu = formulation.recover(x, dx, ddx, t)
solution_writer.write_timestep(t, u, None, None)
no_of_dofs = system.dimension
q0 = np.zeros(no_of_dofs)
dq0 = q0
solver.solve(write_callback, t0, q0, dq0, t_end)
return solution_writer
set_dirichlet_by_group(my_component, 83, ('ux', 'uy', 'uz'))
set_neumann_by_group(my_component,
85,
np.array([0.0, 1.0, 0.0]),
F=lambda t: 1E6 * t)
#%%
system, formulation = create_constrained_mechanical_system_from_component(
my_component,
constant_mass=True,
constant_damping=True,
constraint_formulation='boolean')
solfac = SolverFactory()
solfac.set_system(system)
solfac.set_analysis_type('static')
solfac.set_dt_initial(0.05)
solfac.set_analysis_type('zero')
solfac.set_linear_solver('pardiso')
solfac.set_newton_verbose(True)
solfac.set_nonlinear_solver('newton')
solfac.set_newton_atol(1e-5)
solfac.set_newton_rtol(1e-7)
solver = solfac.create_solver()
solution = AmfeSolution()
for dof in supportdofs_x.reshape(-1):
my_component.assign_constraint('Leftfixation', dirichlet, np.array([dof], dtype=int), np.array([], dtype=int))
for dof in supportdofs_y.reshape(-1):
my_component.assign_constraint('Leftmotion', dirichlet2, np.array([dof], dtype=int), np.array([], dtype=int))
# END Variant B
# ----------------------------------------- NONLINEAR DYNAMIC ANALYSIS ------------------------------------------------
system, formulation = create_constrained_mechanical_system_from_component(my_component, constant_mass=True,
constant_damping=True,
constraint_formulation='lagrange',
scaling=10.0, penalty=3.0)
solfac = SolverFactory()
solfac.set_system(system)
solfac.set_analysis_type('transient')
solfac.set_integrator('genalpha')
solfac.set_nonlinear_solver('newton')
solfac.set_linear_solver('scipy-sparse')
solfac.set_acceleration_intializer('zero')
solfac.set_newton_maxiter(20)
solfac.set_newton_atol(1e-8)
solfac.set_newton_rtol(1e-9)
solfac.set_dt_initial(0.00001)
solfac._alpha_f = 0.25
solfac._alpha_m = 0.25
solfac._gamma = 0.75
solfac._beta = 0.390625
my_component.assign_constraint('Leftmotion', dirichlet2,
np.array([dof], dtype=int),
np.array([], dtype=int))
# END Variant B
# ----------------------------------------- NONLINEAR DYNAMIC ANALYSIS ------------------------------------------------
system, formulation = create_constrained_mechanical_system_from_component(
my_component,
constant_mass=True,
constant_damping=True,
constraint_formulation='lagrange',
scaling=10.0,
penalty=3.0)
solfac = SolverFactory()
solfac.set_system(system)
solfac.set_analysis_type('transient')
solfac.set_integrator('genalpha')
solfac.set_large_deflection(True)
solfac.set_nonlinear_solver('newton')
solfac.set_linear_solver('scipy-sparse')
solfac.set_acceleration_intializer('zero')
solfac.set_newton_maxiter(30)
solfac.set_newton_atol(1e-6)
solfac.set_newton_rtol(1e-8)
solfac.set_dt_initial(0.001)
residuals = list()
mysolver = solfac.create_solver()
def solve_nonlinear_dynamic(system,
formulation,
component,
t0,
t_end,
dt,
write_each=1):
"""
Solves a system
Parameters
----------
system : MechanicalSystem
Created MechanicalSystem object describing the Structural Component
formulation : ConstraintFormulation
A ConstraintFormulation object that can recover the nodal unconstrained displacements of the component
from the constrained states of the system
component : StructuralComponent
StructuralComponent belonging to the system
t0 : float
initial time
t_end : float
final time
dt : float
increment between time steps
write_each : int
Specifies that the solver writes every n'th solution (eg. type 2 to write every second timestep)
Returns
-------
solution : amfe.solution.AmfeSolution
Simple Container for solutions of AMfe simulations
"""
solfac = SolverFactory()
solfac.set_system(system)
solfac.set_analysis_type('transient')
solfac.set_integrator('genalpha')
solfac.set_nonlinear_solver('newton')
solfac.set_linear_solver('scipy-sparse')
solfac.set_acceleration_intializer('zero')
solfac.set_newton_maxiter(10)
solfac.set_newton_atol(1e-8)
solfac.set_newton_rtol(2e-11)
solfac.set_dt_initial(dt)
solver = solfac.create_solver()
solution_writer = AmfeSolution()
def write_callback(t, x, dx, ddx):
cur_ts = int((t - t0) // dt)
if abs(cur_ts % write_each) <= 1e-7:
u, du, ddu = formulation.recover(x, dx, ddx, t)
strains, stresses = component.strains_and_stresses(u, du, t)
solution_writer.write_timestep(t, u, du, ddu, strains, stresses)
no_of_dofs = system.dimension
q0 = np.zeros(no_of_dofs)
dq0 = q0
solver.solve(write_callback, t0, q0, dq0, t_end)
print('Solution finished')
return solution_writer
def solve_nonlinear_static(system, formulation, component, load_steps):
"""
Solves a MechanicalSystem using a nonlinear static method using newton for the nonlinear solver.
The deformation is divided into an amount of intermediate steps which are defined in the number of load_steps.
Parameters
----------
system : MechanicalSystem
Created MechanicalSystem object describing the Structural Component
formulation : ConstraintFormulation
A ConstraintFormulation object that can recover the nodal unconstrained displacements of the component
from the constrained states of the system
component : StructuralComponent
StructuralComponent belonging to the system
load_steps : int
Number of load steps used for the solution
Returns
-------
solution : amfe.solution.AmfeSolution
Simple Container for solutions of AMfe simulations
"""
solfac = SolverFactory()
solfac.set_system(system)
solfac.set_analysis_type('static')
solfac.set_nonlinear_solver('newton')
solfac.set_linear_solver('scipy-sparse')
solfac.set_acceleration_intializer('zero')
solfac.set_newton_maxiter(10)
solfac.set_newton_atol(1e-8)
solfac.set_newton_rtol(2e-9)
solfac.set_dt_initial(1.0 / load_steps)
solver = solfac.create_solver()
solution_writer = AmfeSolution()
no_of_dofs = system.dimension
q0 = np.zeros(no_of_dofs)
dq0 = q0
t0 = 0.0
t_end = 1.0
def write_callback(t, x, dx, ddx):
if isclose(t, t_end):
u, du, ddu = formulation.recover(x, dx, ddx, t)
strains, stresses = component.strains_and_stresses(u, du, t)
solution_writer.write_timestep(t, u, None, None, strains, stresses)
solver.solve(write_callback, t0, q0, dq0, t_end)
print('Solution finished')
return solution_writer
def solve_linear_dynamic(system,
formulation,
component,
t0,
t_end,
dt,
write_each=1):
"""
Solves a linear, dynamic MechanicalSystem from t0 to t_end with dt as intermediate steps.
Parameters
----------
system : MechanicalSystem
MechanicalSystem object describing the equations of motion
formulation : ConstraintFormulation
A ConstraintFormulation object that can recover the nodal unconstrained displacements of the component
from the constrained states of the system
component : StructuralComponent
StructuralComponent belonging to the system
t0 : float
initial time
t_end : float
final time
dt : float
increment between time steps
write_each : int
Specifies that the solver writes every n'th solution (eg. type 2 to write every second timestep)
Returns
-------
solution : amfe.solution.AmfeSolution
AmfeSolution container that contains the solution
"""
solfac = SolverFactory()
solfac.set_system(system)
solfac.set_analysis_type('transient')
solfac.set_linear_solver('scipy-sparse')
solfac.set_integrator('newmarkbeta')
solfac.set_acceleration_intializer('zero')
solfac.set_dt_initial(dt)
solver = solfac.create_solver()
no_of_dofs = system.dimension
q0 = np.zeros(no_of_dofs)
dq0 = q0
solution_writer = AmfeSolution()
def write_callback(t, x, dx, ddx):
cur_ts = int((t - t0) // dt)
if abs(cur_ts % write_each) <= 1e-7:
u, du, ddu = formulation.recover(x, dx, ddx, t)
solution_writer.write_timestep(t, u, du, ddu)
solver.solve(write_callback, t0, q0, dq0, t_end)
logger = logging.getLogger(__name__)
logger.info(
'Strains and stresses are currently not supported for linear models. Only nonlinear kinematics are '
'currently used during their calculation.')
print('Solution finished')
return solution_writer