import ctypes as ct
import numpy as np
import os
from sharpy.utils.solver_interface import solver, BaseSolver, solver_from_string
import sharpy.utils.settings as settings
import sharpy.utils.solver_interface as solver_interface
import sharpy.utils.cout_utils as cout
import sharpy.structure.utils.xbeamlib as xbeamlib
import sharpy.utils.multibody as mb
import sharpy.structure.utils.lagrangeconstraints as lagrangeconstraints
import sharpy.utils.exceptions as exc
_BaseStructural = solver_from_string('_BaseStructural')
[docs]@solver
class NonLinearDynamicMultibody(_BaseStructural):
"""
Nonlinear dynamic multibody
Nonlinear dynamic step solver for multibody structures.
"""
solver_id = 'NonLinearDynamicMultibody'
solver_classification = 'structural'
settings_types = _BaseStructural.settings_types.copy()
settings_default = _BaseStructural.settings_default.copy()
settings_description = _BaseStructural.settings_description.copy()
settings_options = dict()
settings_types['time_integrator'] = 'str'
settings_default['time_integrator'] = 'NewmarkBeta'
settings_description['time_integrator'] = 'Method to perform time integration'
settings_options['time_integrator'] = ['NewmarkBeta']
settings_types['time_integrator_settings'] = 'dict'
settings_default['time_integrator_settings'] = dict()
settings_description['time_integrator_settings'] = 'Settings for the time integrator'
settings_types['write_lm'] = 'bool'
settings_default['write_lm'] = False
settings_description['write_lm'] = 'Write lagrange multipliers'
settings_types['relax_factor_lm'] = 'float'
settings_default['relax_factor_lm'] = 0.
settings_description['relax_factor_lm'] = 'Relaxation factor for Lagrange Multipliers. 0 no relaxation. 1 full relaxation'
settings_table = settings.SettingsTable()
__doc__ += settings_table.generate(settings_types, settings_default, settings_description)
def __init__(self):
self.data = None
self.settings = None
# Total number of unknowns in the Multybody sistem
self.sys_size = None
# Total number of equations associated to the Lagrange multipliers
self.lc_list = None
self.num_LM_eq = None
self.Lambda = None
self.Lambda_dot = None
self.Lambda_ddot = None
self.gamma = None
self.beta = None
self.prev_Dq = None
def initialise(self, data, custom_settings=None):
self.data = data
if custom_settings is None:
self.settings = data.settings[self.solver_id]
else:
self.settings = custom_settings
settings.to_custom_types(self.settings, self.settings_types, self.settings_default, no_ctype=True)
# load info from dyn dictionary
self.data.structure.add_unsteady_information(
self.data.structure.dyn_dict, self.settings['num_steps'])
# Initialise time integrator
self.time_integrator = solver_interface.initialise_solver(
self.settings['time_integrator'])
self.time_integrator.initialise(
self.data, self.settings['time_integrator_settings'])
# Define the number of equations
self.lc_list = lagrangeconstraints.initialize_constraints(self.data.structure.ini_mb_dict)
self.num_LM_eq = lagrangeconstraints.define_num_LM_eq(self.lc_list)
self.Lambda = np.zeros((self.num_LM_eq,), dtype=ct.c_double, order='F')
self.Lambda_dot = np.zeros((self.num_LM_eq,), dtype=ct.c_double, order='F')
self.Lambda_ddot = np.zeros((self.num_LM_eq,), dtype=ct.c_double, order='F')
if self.settings['write_lm']:
dire = './output/' + self.data.settings['SHARPy']['case'] + '/NonLinearDynamicMultibody/'
if not os.path.isdir(dire):
os.makedirs(dire)
self.fid_lambda = open(dire + 'lambda.dat', "w")
self.fid_lambda_dot = open(dire + 'lambda_dot.dat', "w")
self.fid_lambda_ddot = open(dire + 'lambda_ddot.dat', "w")
self.fid_cond_num = open(dire + 'cond_num.dat', "w")
# Define the number of dofs
self.define_sys_size()
self.prev_Dq = np.zeros((self.sys_size + self.num_LM_eq))
self.settings['time_integrator_settings']['sys_size'] = self.sys_size
self.settings['time_integrator_settings']['num_LM_eq'] = self.num_LM_eq
# Initialise time integrator
self.time_integrator = solver_interface.initialise_solver(
self.settings['time_integrator'])
self.time_integrator.initialise(
self.data, self.settings['time_integrator_settings'])
def add_step(self):
self.data.structure.next_step()
def next_step(self):
pass
[docs] def define_sys_size(self):
"""
This function defines the number of degrees of freedom in a multibody systems
Each body contributes with ``num_dof`` degrees of freedom and 10 more if the
associated local FoR can move or has Lagrange Constraints associated
"""
MBdict = self.data.structure.ini_mb_dict
self.sys_size = self.data.structure.num_dof.value
for ibody in range(self.data.structure.num_bodies):
if (MBdict['body_%02d' % ibody]['FoR_movement'] == 'free'):
self.sys_size += 10
[docs] def assembly_MB_eq_system(self, MB_beam, MB_tstep, ts, dt, Lambda, Lambda_dot, MBdict):
"""
This function generates the matrix and vector associated to the linear system to solve a structural iteration
It usses a Newmark-beta scheme for time integration. Being M, C and K the mass, damping
and stiffness matrices of the system:
.. math::
MB_Asys = MB_K + MB_C \frac{\gamma}{\beta dt} + \frac{1}{\beta dt^2} MB_M
Args:
MB_beam (list(:class:`~sharpy.structure.models.beam.Beam`)): each entry represents a body
MB_tstep (list(:class:`~sharpy.utils.datastructures.StructTimeStepInfo`)): each entry represents a body
ts (int): Time step number
dt(int): time step
Lambda (np.ndarray): Lagrange Multipliers array
Lambda_dot (np.ndarray): Time derivarive of ``Lambda``
MBdict (dict): Dictionary including the multibody information
Returns:
MB_Asys (np.ndarray): Matrix of the systems of equations
MB_Q (np.ndarray): Vector of the systems of equations
"""
self.num_LM_eq = lagrangeconstraints.define_num_LM_eq(self.lc_list)
MB_M = np.zeros((self.sys_size, self.sys_size), dtype=ct.c_double, order='F')
MB_C = np.zeros((self.sys_size, self.sys_size), dtype=ct.c_double, order='F')
MB_K = np.zeros((self.sys_size, self.sys_size), dtype=ct.c_double, order='F')
MB_Q = np.zeros((self.sys_size,), dtype=ct.c_double, order='F')
first_dof = 0
last_dof = 0
# Loop through the different bodies
for ibody in range(len(MB_beam)):
# Initialize matrices
M = None
C = None
K = None
Q = None
# Generate the matrices for each body
if MB_beam[ibody].FoR_movement == 'prescribed':
last_dof = first_dof + MB_beam[ibody].num_dof.value
M, C, K, Q = xbeamlib.cbeam3_asbly_dynamic(MB_beam[ibody], MB_tstep[ibody], self.settings)
elif MB_beam[ibody].FoR_movement == 'free':
last_dof = first_dof + MB_beam[ibody].num_dof.value + 10
M, C, K, Q = xbeamlib.xbeam3_asbly_dynamic(MB_beam[ibody], MB_tstep[ibody], self.settings)
############### Assembly into the global matrices
# Flexible and RBM contribution to Asys
MB_M[first_dof:last_dof, first_dof:last_dof] = M.astype(dtype=ct.c_double, copy=True, order='F')
MB_C[first_dof:last_dof, first_dof:last_dof] = C.astype(dtype=ct.c_double, copy=True, order='F')
MB_K[first_dof:last_dof, first_dof:last_dof] = K.astype(dtype=ct.c_double, copy=True, order='F')
#Q
MB_Q[first_dof:last_dof] = Q
first_dof = last_dof
# Define the number of equations
# Generate matrices associated to Lagrange multipliers
LM_C, LM_K, LM_Q = lagrangeconstraints.generate_lagrange_matrix(
self.lc_list,
MB_beam,
MB_tstep,
ts,
self.num_LM_eq,
self.sys_size,
dt,
Lambda,
Lambda_dot,
"dynamic")
# Include the matrices associated to Lagrange Multipliers
MB_C += LM_C[:self.sys_size, :self.sys_size]
MB_K += LM_K[:self.sys_size, :self.sys_size]
MB_Q += LM_Q[:self.sys_size]
# Only working for non-holonomic constratints
kBnh = LM_C[self.sys_size:, :self.sys_size]
strict_LM_Q = LM_Q[self.sys_size:]
return MB_M, MB_C, MB_K, MB_Q, kBnh, strict_LM_Q
[docs] def integrate_position(self, MB_beam, MB_tstep, dt):
"""
This function integrates the position of each local A FoR after the
structural iteration has been solved.
It uses a Newmark-beta approximation.
Args:
MB_beam (list(:class:`~sharpy.structure.models.beam.Beam`)): each entry represents a body
MB_tstep (list(:class:`~sharpy.utils.datastructures.StructTimeStepInfo`)): each entry represents a body
dt(int): time step
"""
vel = np.zeros((6,),)
acc = np.zeros((6,),)
for ibody in range(0, len(MB_tstep)):
# I think this is the right way to do it, but to make it match the rest I change it temporally
if True:
acc[0:3] = (0.5-self.beta)*np.dot(MB_beam[ibody].timestep_info.cga(),MB_beam[ibody].timestep_info.for_acc[0:3])+self.beta*np.dot(MB_tstep[ibody].cga(),MB_tstep[ibody].for_acc[0:3])
vel[0:3] = np.dot(MB_beam[ibody].timestep_info.cga(),MB_beam[ibody].timestep_info.for_vel[0:3])
MB_tstep[ibody].for_pos[0:3] += dt*(vel[0:3] + dt*acc[0:3])
else:
MB_tstep[ibody].for_pos[0:3] += dt*np.dot(MB_tstep[ibody].cga(),MB_tstep[ibody].for_vel[0:3])
def extract_resultants(self):
# TODO: code
pass
[docs] def compute_forces_constraints(self, MB_beam, MB_tstep, ts, dt, Lambda, Lambda_dot):
"""
This function computes the forces generated at Lagrange Constraints
Args:
MB_beam (list(:class:`~sharpy.structure.models.beam.Beam`)): each entry represents a body
MB_tstep (list(:class:`~sharpy.utils.datastructures.StructTimeStepInfo`)): each entry represents a body
ts (int): Time step number
dt(float): Time step increment
Lambda (np.ndarray): Lagrange Multipliers array
Lambda_dot (np.ndarray): Time derivarive of ``Lambda``
Warning:
This function is underdevelopment and not fully functional
"""
try:
self.lc_list[0]
except IndexError:
return
# TODO the output of this routine is wrong. check at some point.
LM_C, LM_K, LM_Q = lagrangeconstraints.generate_lagrange_matrix(self.lc_list, MB_beam, MB_tstep, ts, self.num_LM_eq, self.sys_size, dt, Lambda, Lambda_dot, "dynamic")
F = -np.dot(LM_C[:, -self.num_LM_eq:], Lambda_dot) - np.dot(LM_K[:, -self.num_LM_eq:], Lambda)
first_dof = 0
for ibody in range(len(MB_beam)):
# Forces associated to nodes
body_numdof = MB_beam[ibody].num_dof.value
body_freenodes = np.sum(MB_beam[ibody].vdof > -1)
last_dof = first_dof + body_numdof
MB_tstep[ibody].forces_constraints_nodes[(MB_beam[ibody].vdof > -1), :] = F[first_dof:last_dof].reshape(body_freenodes, 6, order='C')
# Forces associated to the frame of reference
if MB_beam[ibody].FoR_movement == 'free':
# TODO: How are the forces in the quaternion equation interpreted?
MB_tstep[ibody].forces_constraints_FoR[ibody, :] = F[last_dof:last_dof+10]
last_dof += 10
first_dof = last_dof
# TODO: right now, these forces are only used as an output, they are not read when the multibody is splitted
def write_lm_cond_num(self, iteration, Lambda, Lambda_dot, Lambda_ddot, cond_num, cond_num_lm):
self.fid_lambda.write("%d %d " % (self.data.ts, iteration))
self.fid_lambda_dot.write("%d %d " % (self.data.ts, iteration))
self.fid_lambda_ddot.write("%d %d " % (self.data.ts, iteration))
self.fid_cond_num.write("%d %d " % (self.data.ts, iteration))
for ilm in range(self.num_LM_eq):
self.fid_lambda.write("%f " % Lambda[ilm])
self.fid_lambda_dot.write("%f " % Lambda_dot[ilm])
self.fid_lambda_ddot.write("%f " % Lambda_ddot[ilm])
self.fid_lambda.write("\n")
self.fid_lambda_dot.write("\n")
self.fid_lambda_ddot.write("\n")
self.fid_cond_num.write("%e %e\n" % (cond_num, cond_num_lm))
def run(self, structural_step=None, dt=None):
if structural_step is None:
structural_step = self.data.structure.timestep_info[-1]
if structural_step.mb_dict is not None:
MBdict = structural_step.mb_dict
else:
MBdict = self.data.structure.ini_mb_dict
if dt is None:
dt = self.settings['dt']
else:
self.settings['dt'] = dt
if self.data.structure.ini_info.in_global_AFoR:
self.data.structure.ini_info.whole_structure_to_local_AFoR(self.data.structure)
if structural_step.in_global_AFoR:
structural_step.whole_structure_to_local_AFoR(self.data.structure)
self.num_LM_eq = lagrangeconstraints.define_num_LM_eq(self.lc_list)
MB_beam, MB_tstep = mb.split_multibody(
self.data.structure,
structural_step,
MBdict,
self.data.ts)
# Lagrange multipliers parameters
num_LM_eq = self.num_LM_eq
# Initialize
q = np.zeros((self.sys_size + num_LM_eq,), dtype=ct.c_double, order='F')
dqdt = np.zeros((self.sys_size + num_LM_eq,), dtype=ct.c_double, order='F')
dqddt = np.zeros((self.sys_size + num_LM_eq,), dtype=ct.c_double, order='F')
if not num_LM_eq == 0:
Lambda = self.Lambda.astype(dtype=ct.c_double, copy=True, order='F')
Lambda_dot = self.Lambda_dot.astype(dtype=ct.c_double, copy=True, order='F')
Lambda_ddot = self.Lambda_ddot.astype(dtype=ct.c_double, copy=True, order='F')
else:
Lambda = 0
Lambda_dot = 0
# Predictor step
q, dqdt, dqddt = mb.disp_and_accel2state(MB_beam, MB_tstep, Lambda, Lambda_dot, self.sys_size, num_LM_eq)
self.time_integrator.predictor(q, dqdt, dqddt)
# Reference residuals
old_Dq = 1.0
LM_old_Dq = 1.0
converged = False
for iteration in range(self.settings['max_iterations']):
# Check if the maximum of iterations has been reached
if iteration == self.settings['max_iterations'] - 1:
error = ('Solver did not converge in %d iterations.\n res = %e \n LM_res = %e' %
(iteration, res, LM_res))
raise exc.NotConvergedSolver(error)
# Update positions and velocities
Lambda, Lambda_dot = mb.state2disp_and_accel(q, dqdt, dqddt, MB_beam, MB_tstep, num_LM_eq)
if self.settings['write_lm'] and iteration:
self.write_lm_cond_num(iteration, Lambda, Lambda_dot, Lambda_ddot, cond_num, cond_num_lm)
MB_M, MB_C, MB_K, MB_Q, kBnh, LM_Q = self.assembly_MB_eq_system(MB_beam,
MB_tstep,
self.data.ts,
dt,
Lambda,
Lambda_dot,
MBdict)
Asys, Q = self.time_integrator.build_matrix(MB_M, MB_C, MB_K, MB_Q,
kBnh, LM_Q)
if self.settings['write_lm']:
cond_num = np.linalg.cond(Asys[:self.sys_size, :self.sys_size])
cond_num_lm = np.linalg.cond(Asys)
Dq = np.linalg.solve(Asys, -Q)
# Evaluate convergence
if iteration:
res = np.max(np.abs(Dq[0:self.sys_size]))/old_Dq
if np.isnan(res):
raise exc.NotConvergedSolver('Multibody res = NaN')
if num_LM_eq:
LM_res = np.max(np.abs(Dq[self.sys_size:self.sys_size+num_LM_eq]))/LM_old_Dq
else:
LM_res = 0.0
if (res < self.settings['min_delta']) and (LM_res < self.settings['min_delta']):
converged = True
# Relaxation
relax_Dq = np.zeros_like(Dq)
relax_Dq[:self.sys_size] = Dq[:self.sys_size].copy()
relax_Dq[self.sys_size:] = ((1. - self.settings['relax_factor_lm'])*Dq[self.sys_size:] +
self.settings['relax_factor_lm']*self.prev_Dq[self.sys_size:])
self.prev_Dq = Dq.copy()
# Corrector step
self.time_integrator.corrector(q, dqdt, dqddt, relax_Dq)
if converged:
break
if not iteration:
old_Dq = np.max(np.abs(Dq[0:self.sys_size]))
if num_LM_eq:
LM_old_Dq = np.max(np.abs(Dq[self.sys_size:self.sys_size+num_LM_eq]))
Lambda, Lambda_dot = mb.state2disp_and_accel(q, dqdt, dqddt, MB_beam, MB_tstep, num_LM_eq)
if self.settings['write_lm']:
self.write_lm_cond_num(iteration, Lambda, Lambda_dot, Lambda_ddot, cond_num, cond_num_lm)
# end: comment time stepping
# End of Newmark-beta iterations
# self.integrate_position(MB_beam, MB_tstep, dt)
lagrangeconstraints.postprocess(self.lc_list, MB_beam, MB_tstep, "dynamic")
self.compute_forces_constraints(MB_beam, MB_tstep, self.data.ts, dt, Lambda, Lambda_dot)
if self.settings['gravity_on']:
for ibody in range(len(MB_beam)):
xbeamlib.cbeam3_correct_gravity_forces(MB_beam[ibody], MB_tstep[ibody], self.settings)
mb.merge_multibody(MB_tstep, MB_beam, self.data.structure, structural_step, MBdict, dt)
if not structural_step.in_global_AFoR:
structural_step.whole_structure_to_global_AFoR(self.data.structure)
self.Lambda = Lambda.astype(dtype=ct.c_double, copy=True, order='F')
self.Lambda_dot = Lambda_dot.astype(dtype=ct.c_double, copy=True, order='F')
self.Lambda_ddot = Lambda_ddot.astype(dtype=ct.c_double, copy=True, order='F')
return self.data