def calculate_forces(self):
for self.ts in range(self.ts_max):
rot = algebra.quat2rotation(
self.data.structure.timestep_info[self.ts].quat)
force = self.data.aero.timestep_info[self.ts].forces
unsteady_force = self.data.aero.timestep_info[
self.ts].dynamic_forces
n_surf = len(force)
for i_surf in range(n_surf):
total_steady_force = np.zeros((3, ))
total_unsteady_force = np.zeros((3, ))
_, n_rows, n_cols = force[i_surf].shape
for i_m in range(n_rows):
for i_n in range(n_cols):
total_steady_force += force[i_surf][0:3, i_m, i_n]
total_unsteady_force += unsteady_force[i_surf][0:3,
i_m,
i_n]
self.data.aero.timestep_info[self.ts].inertial_steady_forces[
i_surf, 0:3] = total_steady_force
self.data.aero.timestep_info[self.ts].inertial_unsteady_forces[
i_surf, 0:3] = total_unsteady_force
self.data.aero.timestep_info[self.ts].body_steady_forces[
i_surf, 0:3] = np.dot(rot.T, total_steady_force)
self.data.aero.timestep_info[self.ts].body_unsteady_forces[
i_surf, 0:3] = np.dot(rot.T, total_unsteady_force)
def wing_tip_deflection(self,
frame='a',
alpha=0,
reference_line=np.array([0, 0, 0], dtype=float)):
param_array = []
deflection = []
if frame == 'g':
try:
import sharpy.utils.algebra as algebra
except ModuleNotFoundError:
raise (ModuleNotFoundError('Please load sharpy'))
else:
cga = algebra.quat2rotation(
algebra.euler2quat(np.array([0, alpha * np.pi / 180, 0])))
for case in self.cases['aeroelastic']:
param_array.append(case.parameter_value)
if frame == 'a':
deflection.append(
case.get_deflection_at_line(reference_line)[-1, -3:])
elif frame == 'g':
deflection.append(
cga.dot(
case.get_deflection_at_line(reference_line)[-1, -3:]))
param_array = np.array(param_array)
order = np.argsort(param_array)
param_array = param_array[order]
deflection = np.array([deflection[ith] for ith in order])
return param_array, deflection
def test_rotation_G_to_A(self):
"""
Tests the rotation of a vector in G frame to a vector in A frame by a roll, pitch and yaw considering that
SHARPy employs an SEU frame.
In the inertial frame, the ``x_g`` axis is aligned with the longitudinal axis of the aircraft pointing backwards,
``z_g`` points upwards and ``y_g`` completes the set
Returns:
"""
aircraft_nose = np.array([-1, 0, 0])
z_A = np.array([0, 0, 1])
euler = np.array([90, 90, 90]) * np.pi / 180
quat = algebra.euler2quat(euler)
aircraft_nose_rotated = np.array([0, 0,
1]) # in G frame pointing upwards
z_A_rotated_g = np.array([1, 0, 0])
Cga = algebra.euler2rot(euler)
Cga_quat = algebra.quat2rotation(quat)
np.testing.assert_array_almost_equal(
Cga.dot(aircraft_nose),
aircraft_nose_rotated,
err_msg='Rotation using Euler angles not performed properly')
np.testing.assert_array_almost_equal(
Cga_quat.dot(aircraft_nose),
aircraft_nose_rotated,
err_msg='Rotation using quaternions not performed properly')
np.testing.assert_array_almost_equal(
Cga.dot(z_A),
z_A_rotated_g,
err_msg='Rotation using Euler angles not performed properly')
np.testing.assert_array_almost_equal(
Cga_quat.dot(z_A),
z_A_rotated_g,
err_msg='Rotation using quaternions not performed properly')
# Check projections
Pag = Cga.T
Pag_quat = Cga_quat.T
np.testing.assert_array_almost_equal(
Pag.dot(z_A_rotated_g),
z_A,
err_msg='Error in projection from A to G using Euler angles')
np.testing.assert_array_almost_equal(
Pag.dot(aircraft_nose_rotated),
aircraft_nose,
err_msg='Error in projection from A to G using Euler angles')
np.testing.assert_array_almost_equal(
Pag_quat.dot(z_A_rotated_g),
z_A,
err_msg='Error in projection from A to G using quaternions')
np.testing.assert_array_almost_equal(
Pag_quat.dot(aircraft_nose_rotated),
aircraft_nose,
err_msg='Error in projection from A to G using quaternions')
def update_mb_dB_before_merge(tstep, MB_tstep):
"""
update_mb_db_before_merge
Updates the FoR information database before merge the bodies
Longer description
Args:
tstep (StructTimeStepInfo): timestep information of the multibody system
MB_tstep (list of StructTimeStepInfo): each entry represents a body
Returns:
Examples:
Notes:
"""
for ibody in range(len(MB_tstep)):
CAslaveG = algebra.quat2rotation(MB_tstep[ibody].quat).T
tstep.mb_FoR_pos[ibody, :] = MB_tstep[ibody].for_pos
tstep.mb_FoR_vel[ibody, 0:3] = np.dot(np.transpose(CAslaveG),
MB_tstep[ibody].for_vel[0:3])
tstep.mb_FoR_vel[ibody, 3:6] = np.dot(np.transpose(CAslaveG),
MB_tstep[ibody].for_vel[3:6])
tstep.mb_FoR_acc[ibody, 0:3] = np.dot(np.transpose(CAslaveG),
MB_tstep[ibody].for_acc[0:3])
tstep.mb_FoR_acc[ibody, 3:6] = np.dot(np.transpose(CAslaveG),
MB_tstep[ibody].for_acc[3:6])
tstep.mb_quat[ibody, :] = MB_tstep[ibody].quat.astype(
dtype=ct.c_double, order='F', copy=True)
tstep.mb_dqddt_quat[ibody, :] = MB_tstep[ibody].dqddt[-4:].astype(
dtype=ct.c_double, order='F', copy=True)
# TODO: Is it convenient to do this?
for ibody in range(len(MB_tstep)):
MB_tstep[ibody].mb_FoR_pos = tstep.mb_FoR_pos.astype(dtype=ct.c_double,
order='F',
copy=True)
MB_tstep[ibody].mb_FoR_vel = tstep.mb_FoR_vel.astype(dtype=ct.c_double,
order='F',
copy=True)
MB_tstep[ibody].mb_FoR_acc = tstep.mb_FoR_acc.astype(dtype=ct.c_double,
order='F',
copy=True)
MB_tstep[ibody].mb_quat = tstep.mb_quat.astype(dtype=ct.c_double,
order='F',
copy=True)
MB_tstep[ibody].mb_dqddt_quat = tstep.mb_dqddt_quat.astype(
dtype=ct.c_double, order='F', copy=True)
def update_mb_db_before_split(tstep, beam, mb_data_dict, ts):
"""
update_mb_db_before_split
Updates the FoR information database before splitting system
Args:
tstep (:class:`~sharpy.utils.datastructures.StructTimeStepInfo`): timestep information of the multibody system
beam (:class:`~sharpy.structure.models.beam.Beam`): structural information of the multibody system
mb_data_dict (dict): Dictionary including the multibody information
ts (int): time step number
Notes:
At this point, this function does nothing, but we might need it at some point
"""
return
raise NotImplementedError("This function is useless right now")
# TODO: Right now, the Amaster FoR is not expected to move
# when it does, the rest of FoR positions should be updated accordingly
# right now, this function should be useless (I check it below)
# if mb_data_dict['body_%02d' % 0]['FoR_movement']:
# CGAmaster = algebra.quat2rotation(tstep.quat)
# tstep.mb_FoR_vel[0, 0:3] = np.dot(CGAmaster, tstep.for_vel[0:3])
# tstep.mb_FoR_vel[0, 3:6] = np.dot(CGAmaster, tstep.for_vel[3:6])
# tstep.mb_FoR_acc[0, 0:3] = np.dot(CGAmaster, tstep.for_acc[0:3])
# tstep.mb_FoR_acc[0, 3:6] = np.dot(CGAmaster, tstep.for_acc[3:6])
if ((mb_data_dict['body_00']['FoR_movement'] == 'prescribed')
and (ts > 0)):
tstep.for_vel[:] = beam.dynamic_input[ts - 1]['for_vel'].astype(
dtype=ct.c_double, order='F', copy=True)
tstep.for_acc[:] = beam.dynamic_input[ts - 1]['for_acc'].astype(
dtype=ct.c_double, order='F', copy=True)
if True:
CGAmaster = algebra.quat2rotation(tstep.quat)
tstep.mb_FoR_pos[0, :] = tstep.for_pos.astype(dtype=ct.c_double,
order='F',
copy=True)
tstep.mb_FoR_vel[0, 0:3] = np.dot(CGAmaster, tstep.for_vel[0:3])
tstep.mb_FoR_vel[0, 3:6] = np.dot(CGAmaster, tstep.for_vel[3:6])
tstep.mb_FoR_acc[0, 0:3] = np.dot(CGAmaster, tstep.for_acc[0:3])
tstep.mb_FoR_acc[0, 3:6] = np.dot(CGAmaster, tstep.for_acc[3:6])
tstep.mb_quat[0, :] = tstep.quat.astype(dtype=ct.c_double,
order='F',
copy=True)
else:
pass
def update_mb_db_before_split(tstep, beam, mb_data_dict, ts):
"""
update_mb_db_before_split
Updates the FoR information database before split the system
Longer description
Args:
tstep (StructTimeStepInfo): timestep information of the multibody system
Returns:
Examples:
Notes:
At this point, this function does nothing, but we might need it at some point
"""
# TODO: Right now, the Amaster FoR is not expected to move
# when it does, the rest of FoR positions should be updated accordingly
# right now, this function should be useless (I check it below)
# if mb_data_dict['body_%02d' % 0]['FoR_movement']:
# CGAmaster = algebra.quat2rotation(tstep.quat)
# tstep.mb_FoR_vel[0, 0:3] = np.dot(CGAmaster, tstep.for_vel[0:3])
# tstep.mb_FoR_vel[0, 3:6] = np.dot(CGAmaster, tstep.for_vel[3:6])
# tstep.mb_FoR_acc[0, 0:3] = np.dot(CGAmaster, tstep.for_acc[0:3])
# tstep.mb_FoR_acc[0, 3:6] = np.dot(CGAmaster, tstep.for_acc[3:6])
if ((mb_data_dict['body_00']['FoR_movement'] == 'prescribed')
and (ts > 0)):
tstep.for_vel[:] = beam.dynamic_input[ts - 1]['for_vel'].astype(
dtype=ct.c_double, order='F', copy=True)
tstep.for_acc[:] = beam.dynamic_input[ts - 1]['for_acc'].astype(
dtype=ct.c_double, order='F', copy=True)
if True:
CGAmaster = algebra.quat2rotation(tstep.quat)
tstep.mb_FoR_pos[0, :] = tstep.for_pos.astype(dtype=ct.c_double,
order='F',
copy=True)
tstep.mb_FoR_vel[0, 0:3] = np.dot(CGAmaster, tstep.for_vel[0:3])
tstep.mb_FoR_vel[0, 3:6] = np.dot(CGAmaster, tstep.for_vel[3:6])
tstep.mb_FoR_acc[0, 0:3] = np.dot(CGAmaster, tstep.for_acc[0:3])
tstep.mb_FoR_acc[0, 3:6] = np.dot(CGAmaster, tstep.for_acc[3:6])
tstep.mb_quat[0, :] = tstep.quat.astype(dtype=ct.c_double,
order='F',
copy=True)
else:
pass
def rigid_aero_forces(self):
# Debug adding rigid forces from tornado
derivatives_alpha = np.zeros((6, 5))
derivatives_alpha[0, :] = np.array([0.0511, 0, 0, 0.08758,
0]) # drag derivatives
derivatives_alpha[1, :] = np.array([0, 0, -0.05569, 0,
0]) # Y derivatives
derivatives_alpha[2, :] = np.array([5.53, 0, 0, 11.35,
0]) # lift derivatives
derivatives_alpha[3, :] = np.array([0, 0, -0.609, 0,
0]) # roll derivatives
derivatives_alpha[4, :] = np.array([-9.9988, 0, 0, -37.61,
0]) # pitch derivatives
derivatives_alpha[5, :] = np.array([0, 0, -0.047, 0,
0]) # yaw derivatives
Cx0 = -0.0324
Cz0 = 0.436
Cm0 = -0.78966
quat = self.tsstruct0.quat
Cga = algebra.quat2rotation(quat)
data0 = sharpy.sharpy_main.main(
['...', route_main + case_main + '.solver.txt'])
tsaero0 = data0.aero.timestep_info[0]
tsaero0.rho = ws.config['LinearUvlm']['density']
### ----- retrieve transformation matrices
# this is necessary so as to project input motion and output forces in the
# rolled frame of reference R
tsstr0 = data0.structure.timestep_info[0]
### check all CRV are the same
crv_ref = tsstr0.psi[0][0]
for ee in range(data0.structure.num_elem):
for nn_node in range(3):
assert np.linalg.norm(crv_ref - tsstr0.psi[ee, nn_node, :]) < 1e-13, \
'CRV distribution along beam nodes not uniform!'
Cga = algebra.quat2rotation(tsstr0.quat)
Cab = algebra.crv2rotation(tsstr0.psi[0][0])
Cgb = np.dot(Cga, Cab)
### rolled FoR:
# note that, if RollNodes is False, this is equivalent to the FoR A. While
# this transformation is redundant for RollNodes=False, we keep it for debug
Roll0Rad = np.pi / 180. * Roll0Deg
crv_roll = Roll0Rad * np.array([1., 0., 0.])
Cgr = algebra.crv2rotation(crv_roll)
Crg = Cgr.T
Crb = np.dot(Crg, Cgb)
Cra = np.dot(Crg, Cga)
### ----- linearisation
Sol = lin_aeroelastic.LinAeroEla(data0)
def initialise(self, data, custom_settings=None):
r"""
Initialises the Linear UVLM aerodynamic solver and the chosen velocity generator.
Settings are parsed into the standard SHARPy settings format for solvers. It then checks whether there is
any previous information about the linearised system (in order for a solution to be restarted without
overwriting the linearisation).
If a linearised system does not exist, a linear UVLM system is created linearising about the current time step.
The reference values for the input and output are transformed into column vectors :math:`\mathbf{u}`
and :math:`\mathbf{y}`, respectively.
The information pertaining to the linear system is stored in a dictionary ``self.data.aero.linear`` within
the main ``data`` variable.
Args:
data (PreSharpy): class containing the problem information
custom_settings (dict): custom settings dictionary
"""
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)
settings.to_custom_types(self.settings['ScalingDict'],
self.scaling_settings_types,
self.scaling_settings_default,
no_ctype=True)
# Check whether linear UVLM has been initialised
try:
self.data.aero.linear
except AttributeError:
self.data.aero.linear = dict()
aero_tstep = self.data.aero.timestep_info[-1]
### Record body orientation/velocities at time 0
# This option allows to rotate the linearised UVLM with the A frame
# or a specific body (multi-body solution)
if self.settings['track_body']:
self.num_body_track = self.settings['track_body_number']
# track A frame
if self.num_body_track == -1:
self.quat0 = self.data.structure.timestep_info[
-1].quat.copy()
self.for_vel0 = self.data.structure.timestep_info[
-1].for_vel.copy()
else: # track a specific body
self.quat0 = \
self.data.structure.timestep_info[-1].mb_quat[self.num_body_track,:].copy()
self.for_vel0 = \
self.data.structure.timestep_info[-1].mb_FoR_vel[self.num_body_track ,:].copy()
# convert to G frame
self.Cga0 = algebra.quat2rotation(self.quat0)
self.Cga = self.Cga0.copy()
self.for_vel0[:3] = self.Cga0.dot(self.for_vel0[:3])
self.for_vel0[3:] = self.Cga0.dot(self.for_vel0[3:])
else: # check/record initial rotation speed
self.num_body_track = None
self.quat0 = None
self.Cag0 = None
self.Cga = None
self.for_vel0 = np.zeros((6, ))
# TODO: verify of a better way to implement rho
aero_tstep.rho = self.settings['density']
# Generate instance of linuvlm.Dynamic()
lin_uvlm_system = linuvlm.DynamicBlock(
aero_tstep,
dynamic_settings=self.settings,
# dt=self.settings['dt'].value,
# integr_order=self.settings['integr_order'].value,
# ScalingDict=self.settings['ScalingDict'],
# RemovePredictor=self.settings['remove_predictor'].value,
# UseSparse=self.settings['use_sparse'].value,
for_vel=self.for_vel0)
# add rotational speed
for ii in range(lin_uvlm_system.MS.n_surf):
lin_uvlm_system.MS.Surfs[ii].omega = self.for_vel0[3:]
# Save reference values
# System Inputs
u_0 = self.pack_input_vector()
# Linearised state
dt = self.settings['dt']
x_0 = self.pack_state_vector(aero_tstep, None, dt,
self.settings['integr_order'])
# Reference forces
f_0 = np.concatenate([
aero_tstep.forces[ss][0:3].reshape(-1, order='C')
for ss in range(aero_tstep.n_surf)
])
# Assemble the state space system
lin_uvlm_system.assemble_ss()
self.data.aero.linear['System'] = lin_uvlm_system
self.data.aero.linear['SS'] = lin_uvlm_system.SS
self.data.aero.linear['x_0'] = x_0
self.data.aero.linear['u_0'] = u_0
self.data.aero.linear['y_0'] = f_0
# self.data.aero.linear['gamma_0'] = gamma
# self.data.aero.linear['gamma_star_0'] = gamma_star
# self.data.aero.linear['gamma_dot_0'] = gamma_dot
# TODO: Implement in AeroTimeStepInfo a way to store the state vectors
# aero_tstep.linear.x = x_0
# aero_tstep.linear.u = u_0
# aero_tstep.linear.y = f_0
# Initialise velocity generator
velocity_generator_type = gen_interface.generator_from_string(
self.settings['velocity_field_generator'])
self.velocity_generator = velocity_generator_type()
self.velocity_generator.initialise(
self.settings['velocity_field_input'])
def get_body(self, beam, num_dof_ibody, ibody):
"""
get_body
Extract the body number 'ibody' from a multibody system
Given 'self' as a StructTimeStepInfo class of a multibody system, this
function returns another StructTimeStepInfo class (ibody_StructTimeStepInfo)
that only includes the body number 'ibody' of the original system
Args:
self(StructTimeStepInfo): timestep information of the multibody system
beam(Beam): beam information of the multibody system
ibody(int): body number to be extracted
Returns:
ibody_StructTimeStepInfo(StructTimeStepInfo): timestep information of the isolated body
Examples:
Notes:
"""
# Define the nodes and elements belonging to the body
ibody_elems, ibody_nodes = mb.get_elems_nodes_list(beam, ibody)
ibody_num_node = len(ibody_nodes)
ibody_num_elem = len(ibody_elems)
ibody_first_dof = 0
for index_body in range(ibody - 1):
aux_elems, aux_nodes = mb.get_elems_nodes_list(beam, index_body)
ibody_first_dof += np.sum(beam.vdof[aux_nodes] > -1) * 6
# Initialize the new StructTimeStepInfo
ibody_StructTimeStepInfo = StructTimeStepInfo(
ibody_num_node,
ibody_num_elem,
self.num_node_elem,
num_dof=num_dof_ibody,
num_bodies=beam.num_bodies)
# Assign all the variables
# ibody_StructTimeStepInfo.quat = self.quat.astype(dtype=ct.c_double, order='F', copy=True)
# ibody_StructTimeStepInfo.for_pos = self.for_pos.astype(dtype=ct.c_double, order='F', copy=True)
# ibody_StructTimeStepInfo.for_vel = self.for_vel.astype(dtype=ct.c_double, order='F', copy=True)
# ibody_StructTimeStepInfo.for_acc = self.for_acc.astype(dtype=ct.c_double, order='F', copy=True)
CAslaveG = algebra.quat2rotation(self.mb_quat[ibody, :]).T
ibody_StructTimeStepInfo.quat = self.mb_quat[ibody, :].astype(
dtype=ct.c_double, order='F', copy=True)
ibody_StructTimeStepInfo.for_pos = self.mb_FoR_pos[ibody, :].astype(
dtype=ct.c_double, order='F', copy=True)
ibody_StructTimeStepInfo.for_vel[0:3] = np.dot(
CAslaveG, self.mb_FoR_vel[ibody, 0:3])
ibody_StructTimeStepInfo.for_vel[3:6] = np.dot(
CAslaveG, self.mb_FoR_vel[ibody, 3:6])
ibody_StructTimeStepInfo.for_acc[0:3] = np.dot(
CAslaveG, self.mb_FoR_acc[ibody, 0:3])
ibody_StructTimeStepInfo.for_acc[3:6] = np.dot(
CAslaveG, self.mb_FoR_acc[ibody, 3:6])
ibody_StructTimeStepInfo.pos = self.pos[ibody_nodes, :].astype(
dtype=ct.c_double, order='F', copy=True)
ibody_StructTimeStepInfo.pos_dot = self.pos_dot[ibody_nodes, :].astype(
dtype=ct.c_double, order='F', copy=True)
ibody_StructTimeStepInfo.psi = self.psi[ibody_elems, :, :].astype(
dtype=ct.c_double, order='F', copy=True)
ibody_StructTimeStepInfo.psi_dot = self.psi_dot[
ibody_elems, :, :].astype(dtype=ct.c_double, order='F', copy=True)
ibody_StructTimeStepInfo.gravity_vector_inertial = self.gravity_vector_inertial.astype(
dtype=ct.c_double, order='F', copy=True)
ibody_StructTimeStepInfo.gravity_vector_body = self.gravity_vector_body.astype(
dtype=ct.c_double, order='F', copy=True)
ibody_StructTimeStepInfo.steady_applied_forces = self.steady_applied_forces[
ibody_nodes, :].astype(dtype=ct.c_double, order='F', copy=True)
ibody_StructTimeStepInfo.unsteady_applied_forces = self.unsteady_applied_forces[
ibody_nodes, :].astype(dtype=ct.c_double, order='F', copy=True)
ibody_StructTimeStepInfo.gravity_forces = self.gravity_forces[
ibody_nodes, :].astype(dtype=ct.c_double, order='F', copy=True)
ibody_StructTimeStepInfo.total_gravity_forces = self.total_gravity_forces.astype(
dtype=ct.c_double, order='F', copy=True)
ibody_StructTimeStepInfo.q[0:num_dof_ibody.value] = self.q[
ibody_first_dof:ibody_first_dof + num_dof_ibody.value].astype(
dtype=ct.c_double, order='F', copy=True)
ibody_StructTimeStepInfo.dqdt[0:num_dof_ibody.value] = self.dqdt[
ibody_first_dof:ibody_first_dof + num_dof_ibody.value].astype(
dtype=ct.c_double, order='F', copy=True)
ibody_StructTimeStepInfo.dqddt[0:num_dof_ibody.value] = self.dqddt[
ibody_first_dof:ibody_first_dof + num_dof_ibody.value].astype(
dtype=ct.c_double, order='F', copy=True)
# ibody_StructTimeStepInfo.q[-10:] = self.q[-10:].astype(dtype=ct.c_double, order='F', copy=True)
# ibody_StructTimeStepInfo.dqdt[-10:] = self.dqdt[-10:].astype(dtype=ct.c_double, order='F', copy=True)
ibody_StructTimeStepInfo.dqdt[
-4:] = ibody_StructTimeStepInfo.quat.astype(dtype=ct.c_double,
order='F',
copy=True)
# ibody_StructTimeStepInfo.dqddt[-10:] = self.dqddt[-10:].astype(dtype=ct.c_double, order='F', copy=True)
ibody_StructTimeStepInfo.mb_quat = self.mb_quat.astype(
dtype=ct.c_double, order='F', copy=True)
ibody_StructTimeStepInfo.mb_FoR_pos = self.mb_FoR_pos.astype(
dtype=ct.c_double, order='F', copy=True)
ibody_StructTimeStepInfo.mb_FoR_vel = self.mb_FoR_vel.astype(
dtype=ct.c_double, order='F', copy=True)
ibody_StructTimeStepInfo.mb_FoR_acc = self.mb_FoR_acc.astype(
dtype=ct.c_double, order='F', copy=True)
ibody_StructTimeStepInfo.mb_dqddt_quat = self.mb_dqddt_quat.astype(
dtype=ct.c_double, order='F', copy=True)
return ibody_StructTimeStepInfo
def change_to_global_AFoR(self, global_ibody):
"""
change_to_global_AFoR
Reference a StructTimeStepInfo to the global A frame of reference
Given 'self' as a StructTimeStepInfo class, this function references
it to the global A frame of reference
Args:
self(StructTimeStepInfo): timestep information
global_ibody(int): body number (as defined in the mutibody system) to be modified
Returns:
Examples:
Notes:
"""
# Define the rotation matrices between the different FoR
CAslaveG = algebra.quat2rotation(self.mb_quat[global_ibody, :]).T
CGAmaster = algebra.quat2rotation(self.mb_quat[0, :])
Csm = np.dot(CAslaveG, CGAmaster)
delta_pos_ms = self.mb_FoR_pos[global_ibody, :] - self.mb_FoR_pos[0, :]
delta_vel_ms = self.mb_FoR_vel[global_ibody, :] - self.mb_FoR_vel[0, :]
for inode in range(self.pos.shape[0]):
pos_previous = self.pos[inode, :] + np.zeros((3, ), )
self.pos[inode, :] = (
np.dot(np.transpose(Csm), self.pos[inode, :]) +
np.dot(np.transpose(CGAmaster), delta_pos_ms[0:3]))
self.pos_dot[inode, :] = (
np.dot(np.transpose(Csm), self.pos_dot[inode, :]) +
np.dot(np.transpose(CGAmaster), delta_vel_ms[0:3]) + np.dot(
Csm.T,
np.dot(
algebra.skew(
np.dot(CAslaveG, self.mb_FoR_vel[global_ibody,
3:6])),
pos_previous)) -
np.dot(
algebra.skew(np.dot(CGAmaster.T, self.mb_FoR_vel[0, 3:6])),
self.pos[inode, :]))
self.gravity_forces[inode,
0:3] = np.dot(Csm.T, self.gravity_forces[inode,
0:3])
self.gravity_forces[inode,
3:6] = np.dot(Csm.T, self.gravity_forces[inode,
3:6])
# np.cross(np.dot(CGAmaster.T, delta_vel_ms[3:6]), pos_previous))
for ielem in range(self.psi.shape[0]):
for inode in range(3):
psi_previous = self.psi[ielem, inode, :] + np.zeros((3, ), )
self.psi[ielem, inode, :] = algebra.rotation2crv(
np.dot(Csm.T,
algebra.crv2rotation(self.psi[ielem, inode, :])))
self.psi_dot[ielem, inode, :] = np.dot(
algebra.crv2tan(self.psi[ielem, inode, :]), (np.dot(
Csm.T,
np.dot(
algebra.crv2tan(psi_previous).T,
self.psi_dot[ielem, inode, :])) + np.dot(
algebra.quat2rotation(self.mb_quat[0, :]).T,
delta_vel_ms[3:6])))
# Set the output FoR variables
self.for_pos = self.mb_FoR_pos[0, :].astype(dtype=ct.c_double,
order='F',
copy=True)
self.for_vel[0:3] = np.dot(np.transpose(CGAmaster),
self.mb_FoR_vel[0, 0:3])
self.for_vel[3:6] = np.dot(np.transpose(CGAmaster),
self.mb_FoR_vel[0, 3:6])
self.for_acc[0:3] = np.dot(np.transpose(CGAmaster),
self.mb_FoR_acc[0, 0:3])
self.for_acc[3:6] = np.dot(np.transpose(CGAmaster),
self.mb_FoR_acc[0, 3:6])
self.quat = self.mb_quat[0, :].astype(dtype=ct.c_double,
order='F',
copy=True)
def polars(data, aero_kstep, structural_kstep, struct_forces, **kwargs):
r"""
This function corrects the aerodynamic forces from UVLM based on the airfoil polars provided by the user in the aero.h5 file
These are the steps needed to correct the forces:
* The force coming from UVLM is divided into induced drag (parallel to the incoming flow velocity) and lift (the remaining force).
* The angle of attack is computed based on that lift force and the angle of zero lift computed form the airfoil polar and assuming a slope of :math:`2 \pi`
* The drag force is computed based on the angle of attack and the polars provided by the user
Args:
data (:class:`sharpy.PreSharpy`): SHARPy data
aero_kstep (:class:`sharpy.utils.datastructures.AeroTimeStepInfo`): Current aerodynamic substep
structural_kstep (:class:`sharpy.utils.datastructures.StructTimeStepInfo`): Current structural substep
struct_forces (np.array): Array with the aerodynamic forces mapped on the structure in the B frame of reference
Keyword Arguments:
rho (float): air density
correct_lift (bool): correct also lift coefficient according to the polars
cd_from_cl (bool): interpolate drag from lift instead of computing the AoA first
Returns:
np.ndarray: corresponding aerodynamic force at the structural node from the force and moment at a grid vertex
"""
aerogrid = data.aero
beam = data.structure
rho = kwargs.get('rho', 1.225)
correct_lift = kwargs.get('correct_lift', False)
cd_from_cl = kwargs.get('cd_from_cl', False)
aero_dict = aerogrid.aero_dict
if aerogrid.polars is None:
return struct_forces
new_struct_forces = np.zeros_like(struct_forces)
nnode = struct_forces.shape[0]
for inode in range(nnode):
new_struct_forces[inode, :] = struct_forces[inode, :].copy()
if aero_dict['aero_node'][inode]:
ielem, inode_in_elem = beam.node_master_elem[inode]
iairfoil = aero_dict['airfoil_distribution'][ielem, inode_in_elem]
isurf = aerogrid.struct2aero_mapping[inode][0]['i_surf']
i_n = aerogrid.struct2aero_mapping[inode][0]['i_n']
N = aerogrid.aero_dimensions[isurf, 1]
polar = aerogrid.polars[iairfoil]
cab = algebra.crv2rotation(structural_kstep.psi[ielem, inode_in_elem, :])
cga = algebra.quat2rotation(structural_kstep.quat)
cgb = np.dot(cga, cab)
# Deal with the extremes
if i_n == 0:
node1 = 0
node2 = 1
elif i_n == N:
node1 = nnode - 1
node2 = nnode - 2
else:
node1 = inode + 1
node2 = inode - 1
# Define the span and the span direction
dir_span = 0.5*np.dot(cga,
structural_kstep.pos[node1, :] - structural_kstep.pos[node2, :])
span = np.linalg.norm(dir_span)
dir_span = algebra.unit_vector(dir_span)
# Define the chord and the chord direction
dir_chord = aero_kstep.zeta[isurf][:, -1, i_n] - aero_kstep.zeta[isurf][:, 0, i_n]
chord = np.linalg.norm(dir_chord)
dir_chord = algebra.unit_vector(dir_chord)
# Define the relative velocity and its direction
urel = (structural_kstep.pos_dot[inode, :] +
structural_kstep.for_vel[0:3] +
np.cross(structural_kstep.for_vel[3:6],
structural_kstep.pos[inode, :]))
urel = -np.dot(cga, urel)
urel += np.average(aero_kstep.u_ext[isurf][:, :, i_n], axis=1)
# uind = uvlmlib.uvlm_calculate_total_induced_velocity_at_points(aero_kstep,
# np.array([structural_kstep.pos[inode, :] - np.array([0, 0, 1])]),
# structural_kstep.for_pos,
# ct.c_uint(8))[0]
# print(inode, urel, uind)
# urel -= uind
dir_urel = algebra.unit_vector(urel)
# Force in the G frame of reference
force = np.dot(cgb,
struct_forces[inode, 0:3])
dir_force = algebra.unit_vector(force)
# Coefficient to change from aerodynamic coefficients to forces (and viceversa)
coef = 0.5*rho*np.linalg.norm(urel)**2*chord*span
# Divide the force in drag and lift
drag_force = np.dot(force, dir_urel)*dir_urel
lift_force = force - drag_force
# Compute the associated lift
cl = np.linalg.norm(lift_force)/coef
cd_sharpy = np.linalg.norm(drag_force)/coef
if cd_from_cl:
# Compute the drag from the lift
cd, cm = polar.get_cdcm_from_cl(cl)
else:
# Compute the angle of attack assuming that UVLM gives a 2pi polar
aoa_deg_2pi = polar.get_aoa_deg_from_cl_2pi(cl)
# Compute the coefficients assocaited to that angle of attack
cl_new, cd, cm = polar.get_coefs(aoa_deg_2pi)
# print(cl, cl_new)
if correct_lift:
cl = cl_new
# Recompute the forces based on the coefficients
lift_force = cl*algebra.unit_vector(lift_force)*coef
drag_force += cd*dir_urel*coef
force = lift_force + drag_force
new_struct_forces[inode, 0:3] = np.dot(cgb.T,
force)
return new_struct_forces
def cga(self):
return algebra.quat2rotation(self.quat)
def get_gebm2uvlm_gains(self, data):
r"""
Provides:
- the gain matrices required to connect the linearised GEBM and UVLM
inputs/outputs
- the stiffening and damping factors to be added to the linearised
GEBM equations in order to account for non-zero aerodynamic loads at
the linearisation point.
The function produces the gain matrices:
- ``Kdisp``: gains from GEBM to UVLM grid displacements
- ``Kvel_disp``: influence of GEBM dofs displacements to UVLM grid
velocities.
- ``Kvel_vel``: influence of GEBM dofs displacements to UVLM grid
displacements.
- ``Kforces`` (UVLM->GEBM) dimensions are the transpose than the
Kdisp and Kvel* matrices. Hence, when allocation this term, ``ii``
and ``jj`` indices will unintuitively refer to columns and rows,
respectively.
And the stiffening/damping terms accounting for non-zero aerodynamic
forces at the linearisation point:
- ``Kss``: stiffness factor (flexible dof -> flexible dof) accounting
for non-zero forces at the linearisation point.
- ``Csr``: damping factor (rigid dof -> flexible dof)
- ``Crs``: damping factor (flexible dof -> rigid dof)
- ``Crr``: damping factor (rigid dof -> rigid dof)
Stiffening and damping related terms due to the non-zero aerodynamic forces at the linearisation point:
.. math::
\mathbf{F}_{A,n} = C^{AG}(\mathbf{\chi})\sum_j \mathbf{f}_{G,j} \rightarrow
\delta\mathbf{F}_{A,n} = C^{AG}_0 \sum_j \delta\mathbf{f}_{G,j} + \frac{\partial}{\partial\chi}(C^{AG}\sum_j
\mathbf{f}_{G,j}^0)\delta\chi
The term multiplied by the variation in the quaternion, :math:`\delta\chi`, couples the forces with the rigid
body equations and becomes part of :math:`\mathbf{C}_{sr}`.
Similarly, the linearisation of the moments results in expression that contribute to the stiffness and
damping matrices.
.. math::
\mathbf{M}_{B,n} = \sum_j \tilde{X}_B C^{BA}(\Psi)C^{AG}(\chi)\mathbf{f}_{G,j}
.. math::
\delta\mathbf{M}_{B,n} = \sum_j \tilde{X}_B\left(C_0^{BG}\delta\mathbf{f}_{G,j}
+ \frac{\partial}{\partial\Psi}(C^{BA}\delta\mathbf{f}^0_{A,j})\delta\Psi
+ \frac{\partial}{\partial\chi}(C^{BA}_0 C^{AG} \mathbf{f}_{G,j})\delta\chi\right)
The linearised equations of motion for the geometrically exact beam model take the input term :math:`\delta
\mathbf{Q}_n = \{\delta\mathbf{F}_{A,n},\, T_0^T\delta\mathbf{M}_{B,n}\}`, which means that the moments
should be provided as :math:`T^T(\Psi)\mathbf{M}_B` instead of :math:`\mathbf{M}_A = C^{AB}\mathbf{M}_B`,
where :math:`T(\Psi)` is the tangential operator.
.. math::
\delta(T^T\mathbf{M}_B) = T^T_0\delta\mathbf{M}_B
+ \frac{\partial}{\partial\Psi}(T^T\delta\mathbf{M}_B^0)\delta\Psi
is the linearised expression for the moments, where the first term would correspond to the input terms to the
beam equations and the second arises due to the non-zero aerodynamic moment at the linearisation point and
must be subtracted (since it comes from the forces) to form part of :math:`\mathbf{K}_{ss}`. In addition, the
:math:`\delta\mathbf{M}_B` term depends on both :math:`\delta\Psi` and :math:`\delta\chi`, therefore those
terms would also contribute to :math:`\mathbf{K}_{ss}` and :math:`\mathbf{C}_{sr}`, respectively.
The contribution from the total forces and moments will be accounted for in :math:`\mathbf{C}_{rr}` and
:math:`\mathbf{C}_{rs}`.
.. math::
\delta\mathbf{F}_{tot,A} = \sum_n\left(C^{GA}_0 \sum_j \delta\mathbf{f}_{G,j}
+ \frac{\partial}{\partial\chi}(C^{AG}\sum_j
\mathbf{f}_{G,j}^0)\delta\chi\right)
Therefore, after running this method, the beam matrices will be updated as:
>>> K_beam[:flex_dof, :flex_dof] += Kss
>>> C_beam[:flex_dof, -rigid_dof:] += Csr
>>> C_beam[-rigid_dof:, :flex_dof] += Crs
>>> C_beam[-rigid_dof:, -rigid_dof:] += Crr
Track body option
The ``track_body`` setting restricts the UVLM grid to linear translation motions and therefore should be used to
ensure that the forces are computed using the reference linearisation frame.
The UVLM and beam are linearised about a reference equilibrium condition. The UVLM is defined in the inertial
reference frame while the beam employs the body attached frame and therefore a projection from one frame onto
another is required during the coupling process.
However, the inputs to the UVLM (i.e. the lattice grid coordinates) are obtained from the beam deformation which
is expressed in A frame and therefore the grid coordinates need to be projected onto the inertial frame ``G``.
As the beam rotates, the projection onto the ``G`` frame of the lattice grid coordinates will result in a grid
that is not coincident with that at the linearisation reference and therefore the grid coordinates must be
projected onto the original frame, which will be referred to as ``U``. The transformation between the inertial
frame ``G`` and the ``U`` frame is a function of the rotation of the ``A`` frame and the original position:
.. math:: C^{UG}(\chi) = C^{GA}(\chi_0)C^{AG}(\chi)
Therefore, the grid coordinates obtained in ``A`` frame and projected onto the ``G`` frame can be transformed
to the ``U`` frame using
.. math:: \zeta_U = C^{UG}(\chi) \zeta_G
which allows the grid lattice coordinates to be projected onto the original linearisation frame.
In a similar fashion, the output lattice vertex forces of the UVLM are defined in the original linearisation
frame ``U`` and need to be transformed onto the inertial frame ``G`` prior to projecting them onto the ``A``
frame to use them as the input forces to the beam system.
.. math:: \boldsymbol{f}_G = C^{GU}(\chi)\boldsymbol{f}_U
The linearisation of the above relations lead to the following expressions that have to be added to the
coupling matrices:
* ``Kdisp_vel`` terms:
.. math::
\delta\boldsymbol{\zeta}_U= C^{GA}_0 \frac{\partial}{\partial \boldsymbol{\chi}}
\left(C^{AG}\boldsymbol{\zeta}_{G,0}\right)\delta\boldsymbol{\chi} + \delta\boldsymbol{\zeta}_G
* ``Kvel_vel`` terms:
.. math::
\delta\dot{\boldsymbol{\zeta}}_U= C^{GA}_0 \frac{\partial}{\partial \boldsymbol{\chi}}
\left(C^{AG}\dot{\boldsymbol{\zeta}}_{G,0}\right)\delta\boldsymbol{\chi}
+ \delta\dot{\boldsymbol{\zeta}}_G
The transformation of the forces and moments introduces terms that are functions of the orientation and
are included as stiffening and damping terms in the beam's matrices:
* ``Csr`` damping terms relating to translation forces:
.. math::
C_{sr}^{tra} -= \frac{\partial}{\partial\boldsymbol{\chi}}
\left(C^{GA} C^{AG}_0 \boldsymbol{f}_{G,0}\right)\delta\boldsymbol{\chi}
* ``Csr`` damping terms related to moments:
.. math::
C_{sr}^{rot} -= T^\top\widetilde{\mathbf{X}}_B C^{BG}
\frac{\partial}{\partial\boldsymbol{\chi}}
\left(C^{GA} C^{AG}_0 \boldsymbol{f}_{G,0}\right)\delta\boldsymbol{\chi}
The ``track_body`` setting.
When ``track_body`` is enabled, the UVLM grid is no longer coincident with the inertial reference frame
throughout the simulation but rather it is able to rotate as the ``A`` frame rotates. This is to simulate a free
flying vehicle, where, for instance, the orientation does not affect the aerodynamics. The UVLM defined in this
frame of reference, named ``U``, satisfies the following convention:
* The ``U`` frame is coincident with the ``G`` frame at the time of linearisation.
* The ``U`` frame rotates as the ``A`` frame rotates.
Transformations related to the ``U`` frame of reference:
* The angle between the ``U`` frame and the ``A`` frame is always constant and equal
to :math:`\boldsymbol{\Theta}_0`.
* The angle between the ``A`` frame and the ``G`` frame is :math:`\boldsymbol{\Theta}=\boldsymbol{\Theta}_0
+ \delta\boldsymbol{\Theta}`
* The projection of a vector expressed in the ``G`` frame onto the ``U`` frame is expressed by:
.. math:: \boldsymbol{v}^U = C^{GA}_0 C^{AG} \boldsymbol{v}^G
* The reverse, a projection of a vector expressed in the ``U`` frame onto the ``G`` frame, is expressed by
.. math:: \boldsymbol{v}^U = C^{GA} C^{AG}_0 \boldsymbol{v}^U
The effect this has on the aeroelastic coupling between the UVLM and the structural dynamics is that the
orientation and change of orientation of the vehicle has no effect on the aerodynamics. The aerodynamics are
solely affected by the contribution of the 6-rigid body velocities (as well as the flexible DOFs velocities).
"""
aero = data.aero
structure = data.structure
tsaero = self.uvlm.tsaero0
tsstr = self.beam.tsstruct0
Kzeta = self.uvlm.sys.Kzeta
num_dof_str = self.beam.sys.num_dof_str
num_dof_rig = self.beam.sys.num_dof_rig
num_dof_flex = self.beam.sys.num_dof_flex
use_euler = self.beam.sys.use_euler
# allocate output
Kdisp = np.zeros((3 * Kzeta, num_dof_str))
Kdisp_vel = np.zeros(
(3 * Kzeta, num_dof_str)) # Orientation is in velocity DOFs
Kvel_disp = np.zeros((3 * Kzeta, num_dof_str))
Kvel_vel = np.zeros((3 * Kzeta, num_dof_str))
Kforces = np.zeros((num_dof_str, 3 * Kzeta))
Kss = np.zeros((num_dof_flex, num_dof_flex))
Csr = np.zeros((num_dof_flex, num_dof_rig))
Crs = np.zeros((num_dof_rig, num_dof_flex))
Crr = np.zeros((num_dof_rig, num_dof_rig))
Krs = np.zeros((num_dof_rig, num_dof_flex))
# get projection matrix A->G
# (and other quantities indep. from nodal position)
Cga = algebra.quat2rotation(tsstr.quat) # NG 6-8-19 removing .T
Cag = Cga.T
# for_pos=tsstr.for_pos
for_vel = tsstr.for_vel[:3]
for_rot = tsstr.for_vel[3:]
skew_for_rot = algebra.skew(for_rot)
Der_vel_Ra = np.dot(Cga, skew_for_rot)
Faero = np.zeros(3)
FaeroA = np.zeros(3)
# GEBM degrees of freedom
jj_for_tra = range(num_dof_str - num_dof_rig,
num_dof_str - num_dof_rig + 3)
jj_for_rot = range(num_dof_str - num_dof_rig + 3,
num_dof_str - num_dof_rig + 6)
if use_euler:
jj_euler = range(num_dof_str - 3, num_dof_str)
euler = algebra.quat2euler(tsstr.quat)
tsstr.euler = euler
else:
jj_quat = range(num_dof_str - 4, num_dof_str)
jj = 0 # nodal dof index
for node_glob in range(structure.num_node):
### detect bc at node (and no. of dofs)
bc_here = structure.boundary_conditions[node_glob]
if bc_here == 1: # clamp (only rigid-body)
dofs_here = 0
jj_tra, jj_rot = [], []
# continue
elif bc_here == -1 or bc_here == 0: # (rigid+flex body)
dofs_here = 6
jj_tra = 6 * structure.vdof[node_glob] + np.array([0, 1, 2],
dtype=int)
jj_rot = 6 * structure.vdof[node_glob] + np.array([3, 4, 5],
dtype=int)
else:
raise NameError('Invalid boundary condition (%d) at node %d!' \
% (bc_here, node_glob))
jj += dofs_here
# retrieve element and local index
ee, node_loc = structure.node_master_elem[node_glob, :]
# get position, crv and rotation matrix
Ra = tsstr.pos[node_glob, :] # in A FoR, w.r.t. origin A-G
Rg = np.dot(Cag.T, Ra) # in G FoR, w.r.t. origin A-G
psi = tsstr.psi[ee, node_loc, :]
psi_dot = tsstr.psi_dot[ee, node_loc, :]
Cab = algebra.crv2rotation(psi)
Cba = Cab.T
Cbg = np.dot(Cab.T, Cag)
Tan = algebra.crv2tan(psi)
track_body = self.settings['track_body']
### str -> aero mapping
# some nodes may be linked to multiple surfaces...
for str2aero_here in aero.struct2aero_mapping[node_glob]:
# detect surface/span-wise coordinate (ss,nn)
nn, ss = str2aero_here['i_n'], str2aero_here['i_surf']
# print('%.2d,%.2d'%(nn,ss))
# surface panelling
M = aero.aero_dimensions[ss][0]
N = aero.aero_dimensions[ss][1]
Kzeta_start = 3 * sum(self.uvlm.sys.MS.KKzeta[:ss])
shape_zeta = (3, M + 1, N + 1)
for mm in range(M + 1):
# get bound vertex index
ii_vert = [
Kzeta_start + np.ravel_multi_index(
(cc, mm, nn), shape_zeta) for cc in range(3)
]
# get position vectors
zetag = tsaero.zeta[ss][:, mm,
nn] # in G FoR, w.r.t. origin A-G
zetaa = np.dot(Cag, zetag) # in A FoR, w.r.t. origin A-G
Xg = zetag - Rg # in G FoR, w.r.t. origin B
Xb = np.dot(Cbg, Xg) # in B FoR, w.r.t. origin B
# get rotation terms
Xbskew = algebra.skew(Xb)
XbskewTan = np.dot(Xbskew, Tan)
# get velocity terms
zetag_dot = tsaero.zeta_dot[ss][:, mm, nn] - Cga.dot(
for_vel) # in G FoR, w.r.t. origin A-G
zetaa_dot = np.dot(
Cag, zetag_dot) # in A FoR, w.r.t. origin A-G
# get aero force
faero = tsaero.forces[ss][:3, mm, nn]
Faero += faero
faero_a = np.dot(Cag, faero)
FaeroA += faero_a
maero_g = np.cross(Xg, faero)
maero_b = np.dot(Cbg, maero_g)
### ---------------------------------------- allocate Kdisp
if bc_here != 1:
# wrt pos - Eq 25 second term
Kdisp[np.ix_(ii_vert, jj_tra)] += Cga
# wrt psi - Eq 26
Kdisp[np.ix_(ii_vert,
jj_rot)] -= np.dot(Cbg.T, XbskewTan)
# w.r.t. position of FoR A (w.r.t. origin G)
# null as A and G have always same origin in SHARPy
# # ### w.r.t. quaternion (attitude changes)
if use_euler:
Kdisp_vel[np.ix_(ii_vert, jj_euler)] += \
algebra.der_Ceuler_by_v(tsstr.euler, zetaa)
# Track body - project inputs as for A not moving
if track_body:
Kdisp_vel[np.ix_(ii_vert, jj_euler)] += \
Cga.dot(algebra.der_Peuler_by_v(tsstr.euler, zetag))
else:
# Equation 25
# Kdisp[np.ix_(ii_vert, jj_quat)] += \
# algebra.der_Cquat_by_v(tsstr.quat, zetaa)
Kdisp_vel[np.ix_(ii_vert, jj_quat)] += \
algebra.der_Cquat_by_v(tsstr.quat, zetaa)
# Track body - project inputs as for A not moving
if track_body:
Kdisp_vel[np.ix_(ii_vert, jj_quat)] += \
Cga.dot(algebra.der_CquatT_by_v(tsstr.quat, zetag))
### ------------------------------------ allocate Kvel_disp
if bc_here != 1:
# # wrt pos
Kvel_disp[np.ix_(ii_vert, jj_tra)] += Der_vel_Ra
# wrt psi (at zero psi_dot)
Kvel_disp[np.ix_(ii_vert, jj_rot)] -= \
np.dot(Cga,
np.dot(skew_for_rot,
np.dot(Cab, XbskewTan)))
# # wrt psi (psi_dot contributions - verified)
Kvel_disp[np.ix_(ii_vert, jj_rot)] += np.dot(
Cbg.T,
np.dot(algebra.skew(np.dot(XbskewTan, psi_dot)),
Tan))
if np.linalg.norm(psi) >= 1e-6:
Kvel_disp[np.ix_(ii_vert, jj_rot)] -= \
np.dot(Cbg.T,
np.dot(Xbskew,
algebra.der_Tan_by_xv(psi, psi_dot)))
# # w.r.t. position of FoR A (w.r.t. origin G)
# # null as A and G have always same origin in SHARPy
# # ### w.r.t. quaternion (attitude changes) - Eq 30
if use_euler:
Kvel_vel[np.ix_(ii_vert, jj_euler)] += \
algebra.der_Ceuler_by_v(tsstr.euler, zetaa_dot)
# Track body if ForA is rotating
if track_body:
Kvel_vel[np.ix_(ii_vert, jj_euler)] += \
Cga.dot(algebra.der_Peuler_by_v(tsstr.euler, zetag_dot))
else:
Kvel_vel[np.ix_(ii_vert, jj_quat)] += \
algebra.der_Cquat_by_v(tsstr.quat, zetaa_dot)
# Track body if ForA is rotating
if track_body:
Kvel_vel[np.ix_(ii_vert, jj_quat)] += \
Cga.dot(algebra.der_CquatT_by_v(tsstr.quat, zetag_dot))
### ------------------------------------- allocate Kvel_vel
if bc_here != 1:
# wrt pos_dot
Kvel_vel[np.ix_(ii_vert, jj_tra)] += Cga
# # wrt crv_dot
Kvel_vel[np.ix_(ii_vert,
jj_rot)] -= np.dot(Cbg.T, XbskewTan)
# # wrt velocity of FoR A
Kvel_vel[np.ix_(ii_vert, jj_for_tra)] += Cga
Kvel_vel[np.ix_(ii_vert, jj_for_rot)] -= \
np.dot(Cga, algebra.skew(zetaa))
# wrt rate of change of quaternion: not implemented!
### -------------------------------------- allocate Kforces
if bc_here != 1:
# nodal forces
Kforces[np.ix_(jj_tra, ii_vert)] += Cag
# nodal moments
Kforces[np.ix_(jj_rot, ii_vert)] += \
np.dot(Tan.T, np.dot(Cbg, algebra.skew(Xg)))
# or, equivalently, np.dot( algebra.skew(Xb),Cbg)
# total forces
Kforces[np.ix_(jj_for_tra, ii_vert)] += Cag
# total moments
Kforces[np.ix_(jj_for_rot, ii_vert)] += \
np.dot(Cag, algebra.skew(zetag))
# quaternion equation
# null, as not dep. on external forces
### --------------------------------------- allocate Kstiff
### flexible dof equations (Kss and Csr)
if bc_here != 1:
# nodal forces
if use_euler:
if not track_body:
Csr[jj_tra, -3:] -= algebra.der_Peuler_by_v(
tsstr.euler, faero)
# Csr[jj_tra, -3:] -= algebra.der_Ceuler_by_v(tsstr.euler, Cga.T.dot(faero))
else:
if not track_body:
Csr[jj_tra, -4:] -= algebra.der_CquatT_by_v(
tsstr.quat, faero)
# Track body
# if track_body:
# Csr[jj_tra, -4:] -= algebra.der_Cquat_by_v(tsstr.quat, Cga.T.dot(faero))
### moments
TanTXbskew = np.dot(Tan.T, Xbskew)
# contrib. of TanT (dpsi) - Eq 37 - Integration of UVLM and GEBM
Kss[np.ix_(jj_rot, jj_rot)] -= algebra.der_TanT_by_xv(
psi, maero_b)
# contrib of delta aero moment (dpsi) - Eq 36
Kss[np.ix_(jj_rot, jj_rot)] -= \
np.dot(TanTXbskew, algebra.der_CcrvT_by_v(psi, np.dot(Cag, faero)))
# contribution of delta aero moment (dquat)
if use_euler:
if not track_body:
Csr[jj_rot, -3:] -= \
np.dot(TanTXbskew,
np.dot(Cba,
algebra.der_Peuler_by_v(tsstr.euler, faero)))
# if track_body:
# Csr[jj_rot, -3:] -= \
# np.dot(TanTXbskew,
# np.dot(Cbg,
# algebra.der_Peuler_by_v(tsstr.euler, Cga.T.dot(faero))))
else:
if not track_body:
Csr[jj_rot, -4:] -= \
np.dot(TanTXbskew,
np.dot(Cba,
algebra.der_CquatT_by_v(tsstr.quat, faero)))
# Track body
# if track_body:
# Csr[jj_rot, -4:] -= \
# np.dot(TanTXbskew,
# np.dot(Cbg,
# algebra.der_CquatT_by_v(tsstr.quat, Cga.T.dot(faero))))
### rigid body eqs (Crs and Crr)
if bc_here != 1:
# Changed Crs to Krs - NG 14/5/19
# moments contribution due to delta_Ra (+ sign intentional)
Krs[3:6, jj_tra] += algebra.skew(faero_a)
# moment contribution due to delta_psi (+ sign intentional)
Krs[3:6,
jj_rot] += np.dot(algebra.skew(faero_a),
algebra.der_Ccrv_by_v(psi, Xb))
if use_euler:
if not track_body:
# total force
Crr[:3, -3:] -= algebra.der_Peuler_by_v(
tsstr.euler, faero)
# total moment contribution due to change in euler angles
Crr[3:6, -3:] -= algebra.der_Peuler_by_v(
tsstr.euler, np.cross(zetag, faero))
Crr[3:6, -3:] += np.dot(
np.dot(Cag, algebra.skew(faero)),
algebra.der_Peuler_by_v(
tsstr.euler, np.dot(Cab, Xb)))
else:
if not track_body:
# total force
Crr[:3, -4:] -= algebra.der_CquatT_by_v(
tsstr.quat, faero)
# total moment contribution due to quaternion
Crr[3:6, -4:] -= algebra.der_CquatT_by_v(
tsstr.quat, np.cross(zetag, faero))
Crr[3:6, -4:] += np.dot(
np.dot(Cag, algebra.skew(faero)),
algebra.der_CquatT_by_v(
tsstr.quat, np.dot(Cab, Xb)))
# # Track body
# if track_body:
# # NG 20/8/19 - is the Cag needed here? Verify
# Crr[:3, -4:] -= Cag.dot(algebra.der_Cquat_by_v(tsstr.quat, Cga.T.dot(faero)))
#
# Crr[3:6, -4:] -= Cag.dot(algebra.skew(zetag).dot(algebra.der_Cquat_by_v(tsstr.quat, Cga.T.dot(faero))))
# Crr[3:6, -4:] += Cag.dot(algebra.skew(faero)).dot(algebra.der_Cquat_by_v(tsstr.quat, Cga.T.dot(zetag)))
# transfer
self.Kdisp = Kdisp
self.Kvel_disp = Kvel_disp
self.Kdisp_vel = Kdisp_vel
self.Kvel_vel = Kvel_vel
self.Kforces = Kforces
# stiffening factors
self.Kss = Kss
self.Krs = Krs
self.Csr = Csr
self.Crs = Crs
self.Crr = Crr
def test_quat_wrt_rot(self):
"""
We define:
- G: initial frame
- A: frame obtained upon rotation, Cga, defined by the quaternion q0
- B: frame obtained upon further rotation, Cab, of A defined by
the "infinitesimal" Cartesian rotation vector dcrv
The test verifies that:
1. the total rotation matrix Cgb(q0+dq) is equal to
Cgb = Cga(q0) Cab(dcrv)
where
dq = algebra.der_quat_wrt_crv(q0)
2. the difference between analytically computed delta quaternion, dq,
and the numerical delta
dq_num = algebra.crv2quat(algebra.rotation2crv(Cgb_ref))-q0
is comparable to the step used to compute the delta dcrv
3. The equality:
d(Cga(q0)*v)*dq = Cga(q0) * d(Cab*dv)*dcrv
where d(Cga(q0)*v) and d(Cab*dv) are the derivatives computed through
algebra.der_Cquat_by_v and algebra.der_Ccrv_by_v
for a random vector v.
Warning:
- The relation dcrv->dquat is not uniquely defined. However, the
resulting rotation matrix is, namely:
Cga(q0+dq)=Cga(q0)*Cab(dcrv)
"""
### case 1: simple rotation about the same axis
# linearisation point
a0 = 30. * np.pi / 180
n0 = np.array([0, 0, 1])
n0 = n0 / np.linalg.norm(n0)
q0 = algebra.crv2quat(a0 * n0)
Cga = algebra.quat2rotation(q0)
# direction of perturbation
n2 = n0
A = np.array([1e-2, 1e-3, 1e-4, 1e-5, 1e-6])
for a in A:
drot = a * n2
# build rotation manually
atot = a0 + a
Cgb_exp = algebra.crv2rotation(atot * n0) # ok
# build combined rotation
Cab = algebra.crv2rotation(drot)
Cgb_ref = np.dot(Cga, Cab)
# verify expected vs combined rotation matrices
assert np.linalg.norm(Cgb_exp - Cgb_ref) / a < 1e-8, \
'Verify test case - these matrices need to be identical'
# verify analytical rotation matrix
dq_an = np.dot(algebra.der_quat_wrt_crv(q0), drot)
Cgb_an = algebra.quat2rotation(q0 + dq_an)
erel_rot = np.linalg.norm(Cgb_an - Cgb_ref) / a
assert erel_rot < 3e-3, \
'Relative error of rotation matrix (%.2e) too large!' % erel_rot
# verify delta quaternion
erel_dq = np.linalg.norm(Cgb_an - Cgb_ref)
dq_num = algebra.crv2quat(algebra.rotation2crv(Cgb_ref)) - q0
erel_dq = np.linalg.norm(dq_num -
dq_an) / np.linalg.norm(dq_an) / a
assert erel_dq < .3, \
'Relative error delta quaternion (%.2e) too large!' % erel_dq
# verify algebraic relation
v = np.ones((3, ))
D1 = algebra.der_Cquat_by_v(q0, v)
D2 = algebra.der_Ccrv_by_v(np.zeros((3, )), v)
res = np.dot(D1, dq_num) - np.dot(np.dot(Cga, D2), drot)
erel_res = np.linalg.norm(res) / a
assert erel_res < 5e-1 * a, \
'Relative error of residual (%.2e) too large!' % erel_res
### case 2: random rotation
# linearisation point
a0 = 30. * np.pi / 180
n0 = np.array([-2, -1, 1])
n0 = n0 / np.linalg.norm(n0)
q0 = algebra.crv2quat(a0 * n0)
Cga = algebra.quat2rotation(q0)
# direction of perturbation
n2 = np.array([0.5, 1., -2.])
n2 = n2 / np.linalg.norm(n2)
A = np.array([1e-2, 1e-3, 1e-4, 1e-5, 1e-6])
for a in A:
drot = a * n2
# build combined rotation
Cab = algebra.crv2rotation(drot)
Cgb_ref = np.dot(Cga, Cab)
# verify analytical rotation matrix
dq_an = np.dot(algebra.der_quat_wrt_crv(q0), drot)
Cgb_an = algebra.quat2rotation(q0 + dq_an)
erel_rot = np.linalg.norm(Cgb_an - Cgb_ref) / a
assert erel_rot < 3e-3, \
'Relative error of rotation matrix (%.2e) too large!' % erel_rot
# verify delta quaternion
erel_dq = np.linalg.norm(Cgb_an - Cgb_ref)
dq_num = algebra.crv2quat(algebra.rotation2crv(Cgb_ref)) - q0
erel_dq = np.linalg.norm(dq_num -
dq_an) / np.linalg.norm(dq_an) / a
assert erel_dq < .3, \
'Relative error delta quaternion (%.2e) too large!' % erel_dq
# verify algebraic relation
v = np.ones((3, ))
D1 = algebra.der_Cquat_by_v(q0, v)
D2 = algebra.der_Ccrv_by_v(np.zeros((3, )), v)
res = np.dot(D1, dq_num) - np.dot(np.dot(Cga, D2), drot)
erel_res = np.linalg.norm(res) / a
assert erel_res < 5e-1 * a, \
'Relative error of residual (%.2e) too large!' % erel_res
def run(self,
aero_tstep,
structure_tstep,
convect_wake=False,
dt=None,
t=None,
unsteady_contribution=False):
r"""
Solve the linear aerodynamic UVLM model at the current time step ``n``. The step increment is solved as:
.. math::
\mathbf{x}^n &= \mathbf{A\,x}^{n-1} + \mathbf{B\,u}^n \\
\mathbf{y}^n &= \mathbf{C\,x}^n + \mathbf{D\,u}^n
A change of state is possible in order to solve the system without the predictor term. In which case the system
is solved by:
.. math::
\mathbf{h}^n &= \mathbf{A\,h}^{n-1} + \mathbf{B\,u}^{n-1} \\
\mathbf{y}^n &= \mathbf{C\,h}^n + \mathbf{D\,u}^n
Variations are taken with respect to initial reference state. The state and input vectors for the linear
UVLM system are of the form:
If ``integr_order==1``:
.. math:: \mathbf{x}_n = [\delta\mathbf{\Gamma}^T_n,\,
\delta\mathbf{\Gamma_w}_n^T,\,
\Delta t \,\delta\mathbf{\dot{\Gamma}}_n^T]^T
Else, if ``integr_order==2``:
.. math:: \mathbf{x}_n = [\delta\mathbf{\Gamma}_n^T,\,
\delta\mathbf{\Gamma_w}_n^T,\,
\Delta t \,\delta\mathbf{\dot{\Gamma}}_n^T,\,
\delta\mathbf{\Gamma}_{n-1}^T]^T
And the input vector:
.. math:: \mathbf{u}_n = [\delta\mathbf{\zeta}_n^T,\,
\delta\dot{\mathbf{\zeta}}_n^T,\,\delta\mathbf{u_{ext}}^T_n]^T
where the subscript ``n`` refers to the time step.
The linear UVLM system is then solved as detailed in :func:`sharpy.linear.src.linuvlm.Dynamic.solve_step`.
The output is a column vector containing the aerodynamic forces at the panel vertices.
To Do: option for impulsive start?
Args:
aero_tstep (AeroTimeStepInfo): object containing the aerodynamic data at the current time step
structure_tstep (StructTimeStepInfo): object containing the structural data at the current time step
convect_wake (bool): for backward compatibility only. The linear UVLM assumes a frozen wake geometry
dt (float): time increment
t (float): current time
unsteady_contribution (bool): (backward compatibily). Unsteady aerodynamic effects are always included
Returns:
PreSharpy: updated ``self.data`` class with the new forces and circulation terms of the system
"""
if aero_tstep is None:
aero_tstep = self.data.aero.timestep_info[-1]
if structure_tstep is None:
structure_tstep = self.data.structure.timestep_info[-1]
if dt is None:
dt = self.settings['dt']
if t is None:
t = self.data.ts * dt
integr_order = self.settings['integr_order']
### Define Input
# Generate external velocity field u_ext
self.velocity_generator.generate(
{
'zeta': aero_tstep.zeta,
'override': True,
't': t,
'ts': self.data.ts,
'dt': dt,
'for_pos': structure_tstep.for_pos
}, aero_tstep.u_ext)
### Proj from FoR G to linearisation frame
# - proj happens in self.pack_input_vector and unpack_ss_vectors
if self.settings['track_body']:
# track A frame
if self.num_body_track == -1:
self.Cga = algebra.quat2rotation(structure_tstep.quat)
else: # track a specific body
self.Cga = algebra.quat2rotation(
structure_tstep.mb_quat[self.num_body_track, :])
# Column vector that will be the input to the linearised UVLM system
# Input is at time step n, since it is updated in the aeroelastic solver prior to aerodynamic solver
u_n = self.pack_input_vector()
du_n = u_n - self.data.aero.linear['u_0']
if self.settings['remove_predictor']:
u_m1 = self.pack_input_vector()
du_m1 = u_m1 - self.data.aero.linear['u_0']
else:
du_m1 = None
# Retrieve State vector at time n-1
if len(self.data.aero.timestep_info) < 2:
x_m1 = self.pack_state_vector(aero_tstep, None, dt, integr_order)
else:
x_m1 = self.pack_state_vector(aero_tstep,
self.data.aero.timestep_info[-2], dt,
integr_order)
# dx is at timestep n-1
dx_m1 = x_m1 - self.data.aero.linear['x_0']
### Solve system - output is the variation in force
dx_n, dy_n = self.data.aero.linear['System'].solve_step(
dx_m1, du_m1, du_n, transform_state=True)
x_n = self.data.aero.linear['x_0'] + dx_n
y_n = self.data.aero.linear['y_0'] + dy_n
# if self.settings['physical_model']:
forces, gamma, gamma_dot, gamma_star = self.unpack_ss_vectors(
y_n, x_n, u_n, aero_tstep)
aero_tstep.forces = forces
aero_tstep.gamma = gamma
aero_tstep.gamma_dot = gamma_dot
aero_tstep.gamma_star = gamma_star
return self.data
def __init__(self,
data,
custom_settings_linear=None,
uvlm_block=False,
chosen_ts=None):
self.data = data
if custom_settings_linear is None:
settings_here = data.settings['LinearUvlm']
else:
settings_here = custom_settings_linear
sharpy.utils.settings.to_custom_types(settings_here,
linuvlm.settings_types_dynamic,
linuvlm.settings_default_dynamic)
if chosen_ts is None:
self.chosen_ts = self.data.ts
else:
self.chosen_ts = chosen_ts
## TEMPORARY - NEED TO INCLUDE PROPER INTEGRATION OF SETTINGS
try:
self.rigid_body_motions = settings_here['rigid_body_motion']
except KeyError:
self.rigid_body_motions = False
try:
self.use_euler = settings_here['use_euler']
except KeyError:
self.use_euler = False
if self.rigid_body_motions and settings_here['track_body']:
self.track_body = True
else:
self.track_body = False
## -------
### extract aeroelastic info
self.dt = settings_here['dt'].value
### reference to timestep_info
# aero
aero = data.aero
self.tsaero = aero.timestep_info[self.chosen_ts]
# structure
structure = data.structure
self.tsstr = structure.timestep_info[self.chosen_ts]
# --- backward compatibility
try:
rho = settings_here['density'].value
except KeyError:
warnings.warn(
"Key 'density' not found in 'LinearUvlm' solver settings. '\
'Trying to read it from 'StaticCoupled'."
)
rho = data.settings['StaticCoupled']['aero_solver_settings']['rho']
if type(rho) == str:
rho = np.float(rho)
if hasattr(rho, 'value'):
rho = rho.value
self.tsaero.rho = rho
# --- backward compatibility
### gebm
if self.use_euler:
self.num_dof_rig = 9
else:
self.num_dof_rig = 10
self.num_dof_flex = np.sum(self.data.structure.vdof >= 0) * 6
self.num_dof_str = self.num_dof_flex + self.num_dof_rig
self.reshape_struct_input()
try:
beam_settings = settings_here['beam_settings']
except KeyError:
beam_settings = dict()
self.lingebm_str = lingebm.FlexDynamic(self.tsstr, structure,
beam_settings)
cga = algebra.quat2rotation(self.tsstr.quat)
### uvlm
if uvlm_block:
self.linuvlm = linuvlm.DynamicBlock(
self.tsaero,
dt=settings_here['dt'].value,
dynamic_settings=settings_here,
RemovePredictor=settings_here['remove_predictor'].value,
UseSparse=settings_here['use_sparse'].value,
integr_order=settings_here['integr_order'].value,
ScalingDict=settings_here['ScalingDict'],
for_vel=np.hstack((cga.dot(self.tsstr.for_vel[:3]),
cga.dot(self.tsstr.for_vel[3:]))))
else:
self.linuvlm = linuvlm.Dynamic(
self.tsaero,
dt=settings_here['dt'].value,
dynamic_settings=settings_here,
RemovePredictor=settings_here['remove_predictor'].value,
UseSparse=settings_here['use_sparse'].value,
integr_order=settings_here['integr_order'].value,
ScalingDict=settings_here['ScalingDict'],
for_vel=np.hstack((cga.dot(self.tsstr.for_vel[:3]),
cga.dot(self.tsstr.for_vel[3:]))))
def derivatives(self, Y_freq):
Cng = np.array([[-1, 0, 0], [0, 1, 0],
[0, 0,
-1]]) # Project SEU on NED - TODO implementation
u_inf = self.settings['u_inf'].value
s_ref = self.settings['S_ref'].value
b_ref = self.settings['b_ref'].value
c_ref = self.settings['c_ref'].value
rho = self.data.linear.tsaero0.rho
# Inertial frame
try:
euler = self.data.linear.tsstruct0.euler
Pga = algebra.euler2rot(euler)
rig_dof = 9
except AttributeError:
quat = self.data.linear.tsstruct0.quat
Pga = algebra.quat2rotation(quat)
rig_dof = 10
derivatives_g = np.zeros((6, Y_freq.shape[1] + 2))
coefficients = {
'force':
0.5 * rho * u_inf**2 * s_ref,
'moment_lon':
0.5 * rho * u_inf**2 * s_ref * c_ref,
'moment_lat':
0.5 * rho * u_inf**2 * s_ref * b_ref,
'force_angular_vel':
0.5 * rho * u_inf**2 * s_ref * c_ref / u_inf,
'moment_lon_angular_vel':
0.5 * rho * u_inf**2 * s_ref * c_ref * c_ref / u_inf
} # missing rates
for in_channel in range(Y_freq.shape[1]):
derivatives_g[:3, in_channel] = Pga.dot(Y_freq[:3, in_channel])
derivatives_g[3:, in_channel] = Pga.dot(Y_freq[3:, in_channel])
derivatives_g[:3, :3] /= coefficients['force']
derivatives_g[:3, 3:6] /= coefficients['force_angular_vel']
derivatives_g[4, :3] /= coefficients['moment_lon']
derivatives_g[4, 3:6] /= coefficients['moment_lon_angular_vel']
derivatives_g[[3, 5], :] /= coefficients['moment_lat']
derivatives_g[:, -2] = derivatives_g[:, 2] * u_inf # ders wrt alpha
derivatives_g[:, -1] = derivatives_g[:, 1] * u_inf # ders wrt beta
der_matrix = np.zeros((6, self.inputs - (rig_dof - 6)))
der_col = 0
for i in list(range(6)) + list(range(rig_dof, self.inputs)):
der_matrix[:3, der_col] = Y_freq[:3, i]
der_matrix[3:6, der_col] = Y_freq[3:6, i]
der_col += 1
labels_force = {0: 'X', 1: 'Y', 2: 'Z', 3: 'L', 4: 'M', 5: 'N'}
labels_velocity = {
0: 'u',
1: 'v',
2: 'w',
3: 'p',
4: 'q',
5: 'r',
6: 'flap1',
7: 'flap2',
8: 'flap3'
}
table = cout.TablePrinter(
n_fields=7,
field_length=12,
field_types=['s', 'f', 'f', 'f', 'f', 'f', 'f'])
table.print_header(['der'] + list(labels_force.values()))
for i in range(der_matrix.shape[1]):
table.print_line([labels_velocity[i]] + list(der_matrix[:, i]))
table_coeff = cout.TablePrinter(n_fields=7,
field_length=12,
field_types=['s'] + 6 * ['f'])
labels_out = {
0: 'C_D',
1: 'C_Y',
2: 'C_L',
3: 'C_l',
4: 'C_m',
5: 'C_n'
}
labels_der = {
0: 'u',
1: 'v',
2: 'w',
3: 'p',
4: 'q',
5: 'r',
6: 'alpha',
7: 'beta'
}
table_coeff.print_header(['der'] + list(labels_out.values()))
for i in range(6):
table_coeff.print_line([labels_der[i]] + list(derivatives_g[:, i]))
table_coeff.print_line([labels_der[6]] + list(derivatives_g[:, -2]))
table_coeff.print_line([labels_der[7]] + list(derivatives_g[:, -1]))
return der_matrix, derivatives_g
def merge_multibody(MB_tstep, MB_beam, beam, tstep, mb_data_dict, dt):
"""
merge_multibody
This functions merges a series of bodies into a multibody system at a certain time step
Longer description
Args:
MB_beam (list of beam): each entry represents a body
MB_tstep (list of StructTimeStepInfo): each entry represents a body
beam (beam): structural information of the multibody system
tstep (StructTimeStepInfo): timestep information of the multibody system
mb_data_dict (): Dictionary including the multibody information
dt(int): time step
Returns:
beam (beam): structural information of the multibody system
tstep (StructTimeStepInfo): timestep information of the multibody system
Examples:
Notes:
"""
update_mb_dB_before_merge(tstep, MB_tstep)
first_dof = 0
for ibody in range(beam.num_bodies):
# Renaming for clarity
ibody_elems = MB_beam[ibody].global_elems_num
ibody_nodes = MB_beam[ibody].global_nodes_num
# Merge tstep
MB_tstep[ibody].change_to_global_AFoR(ibody)
tstep.pos[ibody_nodes, :] = MB_tstep[ibody].pos.astype(
dtype=ct.c_double, order='F', copy=True)
tstep.pos_dot[ibody_nodes, :] = MB_tstep[ibody].pos_dot.astype(
dtype=ct.c_double, order='F', copy=True)
tstep.psi[ibody_elems, :, :] = MB_tstep[ibody].psi.astype(
dtype=ct.c_double, order='F', copy=True)
tstep.psi_dot[ibody_elems, :, :] = MB_tstep[ibody].psi_dot.astype(
dtype=ct.c_double, order='F', copy=True)
tstep.gravity_forces[
ibody_nodes, :] = MB_tstep[ibody].gravity_forces.astype(
dtype=ct.c_double, order='F', copy=True)
# TODO: Do I need a change in FoR for the following variables? Maybe for the FoR ones.
tstep.forces_constraints_nodes[
ibody_nodes, :] = MB_tstep[ibody].forces_constraints_nodes.astype(
dtype=ct.c_double, order='F', copy=True)
tstep.forces_constraints_FoR[ibody, :] = MB_tstep[
ibody].forces_constraints_FoR[ibody, :].astype(dtype=ct.c_double,
order='F',
copy=True)
# Merge states
ibody_num_dof = MB_beam[ibody].num_dof.value
tstep.q[first_dof:first_dof +
ibody_num_dof] = MB_tstep[ibody].q[:-10].astype(
dtype=ct.c_double, order='F', copy=True)
tstep.dqdt[first_dof:first_dof +
ibody_num_dof] = MB_tstep[ibody].dqdt[:-10].astype(
dtype=ct.c_double, order='F', copy=True)
tstep.dqddt[first_dof:first_dof +
ibody_num_dof] = MB_tstep[ibody].dqddt[:-10].astype(
dtype=ct.c_double, order='F', copy=True)
first_dof += ibody_num_dof
tstep.q[-10:] = MB_tstep[0].q[-10:].astype(dtype=ct.c_double,
order='F',
copy=True)
tstep.dqdt[-10:] = MB_tstep[0].dqdt[-10:].astype(dtype=ct.c_double,
order='F',
copy=True)
tstep.dqddt[-10:] = MB_tstep[0].dqddt[-10:].astype(dtype=ct.c_double,
order='F',
copy=True)
# Define the new FoR information
CAG = algebra.quat2rotation(tstep.quat).T
tstep.for_pos = tstep.mb_FoR_pos[0, :].astype(dtype=ct.c_double,
order='F',
copy=True)
tstep.for_vel[0:3] = np.dot(CAG, tstep.mb_FoR_vel[0, 0:3])
tstep.for_vel[3:6] = np.dot(CAG, tstep.mb_FoR_vel[0, 3:6])
tstep.for_acc[0:3] = np.dot(CAG, tstep.mb_FoR_acc[0, 0:3])
tstep.for_acc[3:6] = np.dot(CAG, tstep.mb_FoR_acc[0, 3:6])
tstep.quat = tstep.mb_quat[0, :].astype(dtype=ct.c_double,
order='F',
copy=True)
def state2disp(q, dqdt, dqddt, MB_beam, MB_tstep):
"""
state2disp
Recovers the displacements from the states
Longer description
Args:
MB_beam (list of beam): each entry represents a body
MB_tstep (list of StructTimeStepInfo): each entry represents a body
q(numpy array): Vector of states
dqdt(numpy array): Time derivatives of states
dqddt(numpy array): Second time derivatives of states
Returns:
Examples:
Notes:
"""
first_dof = 0
for ibody in range(len(MB_beam)):
ibody_num_dof = MB_beam[ibody].num_dof.value
if (MB_beam[ibody].FoR_movement == 'prescribed'):
MB_tstep[ibody].q[:-10] = q[first_dof:first_dof +
ibody_num_dof].astype(
dtype=ct.c_double,
order='F',
copy=True)
MB_tstep[ibody].dqdt[:-10] = dqdt[first_dof:first_dof +
ibody_num_dof].astype(
dtype=ct.c_double,
order='F',
copy=True)
MB_tstep[ibody].dqddt[:-10] = dqddt[first_dof:first_dof +
ibody_num_dof].astype(
dtype=ct.c_double,
order='F',
copy=True)
xbeamlib.cbeam3_solv_state2disp(MB_beam[ibody], MB_tstep[ibody])
first_dof += ibody_num_dof
elif (MB_beam[ibody].FoR_movement == 'free'):
MB_tstep[ibody].q = q[first_dof:first_dof + ibody_num_dof +
10].astype(dtype=ct.c_double,
order='F',
copy=True)
# dqdt[first_dof+ibody_num_dof+6:first_dof+ibody_num_dof+10] = algebra.unit_quat(dqdt[first_dof+ibody_num_dof+6:first_dof+ibody_num_dof+10])
MB_tstep[ibody].dqdt = dqdt[first_dof:first_dof + ibody_num_dof +
10].astype(dtype=ct.c_double,
order='F',
copy=True)
MB_tstep[ibody].dqddt = dqddt[first_dof:first_dof + ibody_num_dof +
10].astype(dtype=ct.c_double,
order='F',
copy=True)
xbeamlib.xbeam_solv_state2disp(MB_beam[ibody], MB_tstep[ibody])
# if onlyFlex:
# xbeamlib.cbeam3_solv_state2disp(MB_beam[ibody], MB_tstep[ibody])
# else:
# xbeamlib.xbeam_solv_state2disp(MB_beam[ibody], MB_tstep[ibody])
first_dof += ibody_num_dof + 10
for ibody in range(len(MB_beam)):
CAslaveG = algebra.quat2rotation(MB_tstep[ibody].quat).T
# MB_tstep[0].mb_FoR_pos[ibody,:] = MB_tstep[ibody].for_pos.astype(dtype=ct.c_double, order='F', copy=True)
MB_tstep[0].mb_FoR_vel[ibody,
0:3] = np.dot(CAslaveG.T,
MB_tstep[ibody].for_vel[0:3])
MB_tstep[0].mb_FoR_vel[ibody,
3:6] = np.dot(CAslaveG.T,
MB_tstep[ibody].for_vel[3:6])
MB_tstep[0].mb_FoR_acc[ibody,
0:3] = np.dot(CAslaveG.T,
MB_tstep[ibody].for_acc[0:3])
MB_tstep[0].mb_FoR_acc[ibody,
3:6] = np.dot(CAslaveG.T,
MB_tstep[ibody].for_acc[3:6])
MB_tstep[0].mb_quat[ibody, :] = MB_tstep[ibody].quat.astype(
dtype=ct.c_double, order='F', copy=True)
for ibody in range(len(MB_beam)):
# MB_tstep[ibody].mb_FoR_pos = MB_tstep[0].mb_FoR_pos.astype(dtype=ct.c_double, order='F', copy=True)
MB_tstep[ibody].mb_FoR_vel = MB_tstep[0].mb_FoR_vel.astype(
dtype=ct.c_double, order='F', copy=True)
MB_tstep[ibody].mb_FoR_acc = MB_tstep[0].mb_FoR_acc.astype(
dtype=ct.c_double, order='F', copy=True)
MB_tstep[ibody].mb_quat = MB_tstep[0].mb_quat.astype(dtype=ct.c_double,
order='F',
copy=True)
def test_rotation_matrices(self):
"""
Checks routines and consistency of functions to generate rotation
matrices.
Note: test only includes triad <-> CRV <-> quaternions conversions
"""
### Verify that function build rotation matrix (not projection matrix)
# set an easy rotation (x axis)
a = np.pi / 6.
nv = np.array([1, 0, 0])
sa, ca = np.sin(a), np.cos(a)
Cab_exp = np.array([
[1, 0, 0],
[0, ca, -sa],
[0, sa, ca],
])
### rot from triad
Cab_num = algebra.triad2rotation(Cab_exp[:, 0], Cab_exp[:, 1],
Cab_exp[:, 2])
assert np.linalg.norm(Cab_num - Cab_exp) < 1e-15, \
'crv2rotation not producing the right result'
### rot from crv
fv = a * nv
Cab_num = algebra.crv2rotation(fv)
assert np.linalg.norm(Cab_num - Cab_exp) < 1e-15, \
'crv2rotation not producing the right result'
### rot from quat
quat = algebra.crv2quat(fv)
Cab_num = algebra.quat2rotation(quat)
assert np.linalg.norm(Cab_num - Cab_exp) < 1e-15, \
'quat2rotation not producing the right result'
### inverse relations
# check crv2rotation and rotation2crv are biunivolcal in [-pi,pi]
# check quat2rotation and rotation2quat are biunivocal in [-pi,pi]
N = 100
for nn in range(N):
# def random rotation in [-pi,pi]
a = np.pi * (2. * np.random.rand() - 1)
nv = 2. * np.random.rand(3) - 1
nv = nv / np.linalg.norm(nv)
# inverse crv
fv0 = a * nv
Cab = algebra.crv2rotation(fv0)
fv = algebra.rotation2crv(Cab)
assert np.linalg.norm(fv - fv0) < 1e-12, \
'rotation2crv not producing the right result'
# triad2crv
xa, ya, za = Cab[:, 0], Cab[:, 1], Cab[:, 2]
assert np.linalg.norm(
algebra.triad2crv(xa, ya, za) - fv0) < 1e-12, \
'triad2crv not producing the right result'
# inverse quat
quat0 = np.zeros((4, ))
quat0[0] = np.cos(.5 * a)
quat0[1:] = np.sin(.5 * a) * nv
quat = algebra.rotation2quat(algebra.quat2rotation(quat0))
assert np.linalg.norm(quat - quat0) < 1e-12, \
'rotation2quat not producing the right result'
### combined rotation
# assume 3 FoR, G, A and B where:
# - G is the initial FoR
# - A derives from a 90 deg rotation about zG
# - B derives from a 90 deg rotation about yA
crv_G_to_A = .5 * np.pi * np.array([0, 0, 1])
crv_A_to_B = .5 * np.pi * np.array([0, 1, 0])
Cga = algebra.crv2rotation(crv_G_to_A)
Cab = algebra.crv2rotation(crv_A_to_B)
# rotation G to B (i.e. projection B onto G)
Cgb = np.dot(Cga, Cab)
Cgb_exp = np.array([[0, -1, 0], [0, 0, 1], [-1, 0, 0]])
assert np.linalg.norm(Cgb - Cgb_exp) < 1e-15, \
'combined rotation not as expected!'
def get_gebm2uvlm_gains(self):
"""
Gain matrix to transfer GEBM dofs to UVLM lattice vertices and stiffening
term due to non-zero forces at the linearisation point.
The function produces the matrices:
- ``Kdisp``: from GEBM to UVLM grid displacements
- ``Kvel_disp``: influence of GEBM dofs displacements to UVLM grid
velocities.
- ``Kvel_vel``: influence of GEBM dofs displacements to UVLM grid
displacements.
- ``Kforces`` (UVLM->GEBM) dimensions are the transpose than the Kdisp and
Kvel* matrices. Hence, when allocation this term, ``ii`` and ``jj`` indices
will unintuitively refer to columns and rows, respectively.
- ``Kss``: stiffness factor accounting for non-zero forces at the
linearisation point. (flexible dof -> flexible dof)
- ``Ksr``: stiffness factor accounting for non-zero forces at the
linearisation point. (rigid dof -> flexible dof)
Notes:
- The following terms have been verified against SHARPy (to ensure same sign conventions and accuracy):
- :math:`\\mathbf{C}^{AB}`
- accuracy of :math:`X^B=\\mathbf{C}^{AB}*X^A`
- accuracy of :math:`X^G` and :math:`X^A`
"""
data = self.data
aero = self.data.aero
structure = self.data.structure # data.aero.beam
tsaero = self.tsaero
tsstr = self.tsstr
# allocate output
Kdisp = np.zeros((3 * self.linuvlm.Kzeta, self.num_dof_str))
Kvel_disp = np.zeros((3 * self.linuvlm.Kzeta, self.num_dof_str))
Kvel_vel = np.zeros((3 * self.linuvlm.Kzeta, self.num_dof_str))
Kforces = np.zeros((self.num_dof_str, 3 * self.linuvlm.Kzeta))
Kss = np.zeros((self.num_dof_flex, self.num_dof_flex))
Ksr = np.zeros((self.num_dof_flex, self.num_dof_rig))
# get projection matrix A->G
# (and other quantities indep. from nodal position)
Cga = algebra.quat2rotation(tsstr.quat)
Cag = Cga.T
# for_pos=tsstr.for_pos
for_tra = tsstr.for_vel[:3]
for_rot = tsstr.for_vel[3:]
skew_for_rot = algebra.skew(for_rot)
Der_vel_Ra = np.dot(Cga, skew_for_rot)
# GEBM degrees of freedom
jj_for_tra = range(self.num_dof_str - 10, self.num_dof_str - 7)
jj_for_rot = range(self.num_dof_str - 7, self.num_dof_str - 4)
jj_quat = range(self.num_dof_str - 4, self.num_dof_str)
jj = 0 # nodal dof index
for node_glob in range(structure.num_node):
### detect bc at node (and no. of dofs)
bc_here = structure.boundary_conditions[node_glob]
if bc_here == 1: # clamp (only rigid-body)
dofs_here = 0
jj_tra, jj_rot = [], []
# continue
elif bc_here == -1 or bc_here == 0: # (rigid+flex body)
dofs_here = 6
jj_tra = 6 * structure.vdof[node_glob] + np.array([0, 1, 2],
dtype=int)
jj_rot = 6 * structure.vdof[node_glob] + np.array([3, 4, 5],
dtype=int)
# jj_tra=[jj ,jj+1,jj+2]
# jj_rot=[jj+3,jj+4,jj+5]
else:
raise NameError('Invalid boundary condition (%d) at node %d!' \
% (bc_here, node_glob))
jj += dofs_here
# retrieve element and local index
ee, node_loc = structure.node_master_elem[node_glob, :]
# get position, crv and rotation matrix
Ra = tsstr.pos[node_glob, :] # in A FoR, w.r.t. origin A-G
Rg = np.dot(Cag.T, Ra) # in G FoR, w.r.t. origin A-G
psi = tsstr.psi[ee, node_loc, :]
psi_dot = tsstr.psi_dot[ee, node_loc, :]
Cab = algebra.crv2rotation(psi)
Cba = Cab.T
Cbg = np.dot(Cab.T, Cag)
### str -> aero mapping
# some nodes may be linked to multiple surfaces...
for str2aero_here in aero.struct2aero_mapping[node_glob]:
# detect surface/span-wise coordinate (ss,nn)
nn, ss = str2aero_here['i_n'], str2aero_here['i_surf']
# print('%.2d,%.2d'%(nn,ss))
# surface panelling
M = aero.aero_dimensions[ss][0]
N = aero.aero_dimensions[ss][1]
Kzeta_start = 3 * sum(self.linuvlm.MS.KKzeta[:ss])
shape_zeta = (3, M + 1, N + 1)
for mm in range(M + 1):
# get bound vertex index
ii_vert = [
Kzeta_start + np.ravel_multi_index(
(cc, mm, nn), shape_zeta) for cc in range(3)
]
# get aero force
faero = tsaero.forces[ss][:3, mm, nn]
# get position vectors
zetag = tsaero.zeta[ss][:, mm,
nn] # in G FoR, w.r.t. origin A-G
zetaa = np.dot(Cag, zetag) # in A FoR, w.r.t. origin A-G
Xg = zetag - Rg # in G FoR, w.r.t. origin B
Xb = np.dot(Cbg, Xg) # in B FoR, w.r.t. origin B
# get rotation terms
Xbskew = algebra.skew(Xb)
Tan = algebra.crv2tan(psi)
XbskewTan = np.dot(Xbskew, Tan)
# get velocity terms
zetag_dot = tsaero.zeta_dot[
ss][:, mm, nn] # in G FoR, w.r.t. origin A-G
zetaa_dot = np.dot(
Cag, zetag_dot) # in A FoR, w.r.t. origin A-G
### ---------------------------------------- allocate Kdisp
if bc_here != 1:
# wrt pos
Kdisp[np.ix_(ii_vert, jj_tra)] += Cga
# wrt psi
Kdisp[np.ix_(ii_vert,
jj_rot)] -= np.dot(Cbg.T, XbskewTan)
# w.r.t. position of FoR A (w.r.t. origin G)
# null as A and G have always same origin in SHARPy
# # ### w.r.t. quaternion (attitude changes)
Kdisp[np.ix_(ii_vert, jj_quat)] = \
algebra.der_Cquat_by_v(tsstr.quat, zetaa)
### ------------------------------------ allocate Kvel_disp
if bc_here != 1:
# # wrt pos
Kvel_disp[np.ix_(ii_vert, jj_tra)] += Der_vel_Ra
# wrt psi (at zero psi_dot)
Kvel_disp[np.ix_(ii_vert, jj_rot)] -= \
np.dot(Cga,
np.dot(skew_for_rot,
np.dot(Cab, XbskewTan)))
# # wrt psi (psi_dot contributions - verified)
Kvel_disp[np.ix_(ii_vert, jj_rot)] += np.dot(
Cbg.T,
np.dot(algebra.skew(np.dot(XbskewTan, psi_dot)),
Tan))
Kvel_disp[np.ix_(ii_vert, jj_rot)] -= \
np.dot(Cbg.T,
np.dot(Xbskew,
algebra.der_Tan_by_xv(psi, psi_dot)))
# # w.r.t. position of FoR A (w.r.t. origin G)
# # null as A and G have always same origin in SHARPy
# # ### w.r.t. quaternion (attitude changes)
Kvel_disp[np.ix_(ii_vert, jj_quat)] = \
algebra.der_Cquat_by_v(tsstr.quat, zetaa_dot)
### ------------------------------------- allocate Kvel_vel
if bc_here != 1:
# wrt pos_dot
Kvel_vel[np.ix_(ii_vert, jj_tra)] += Cga
# # wrt crv_dot
Kvel_vel[np.ix_(ii_vert,
jj_rot)] -= np.dot(Cbg.T, XbskewTan)
# # wrt velocity of FoR A
Kvel_vel[np.ix_(ii_vert, jj_for_tra)] += Cga
Kvel_vel[np.ix_(ii_vert, jj_for_rot)] -= \
np.dot(Cga, algebra.skew(zetaa))
# wrt rate of change of quaternion: not implemented!
### -------------------------------------- allocate Kforces
if bc_here != 1:
# nodal forces
Kforces[np.ix_(jj_tra, ii_vert)] += Cbg
# nodal moments
Kforces[np.ix_(jj_rot, ii_vert)] += \
np.dot(Cbg, algebra.skew(Xg))
# or, equivalently, np.dot( algebra.skew(Xb),Cbg)
# total forces
Kforces[np.ix_(jj_for_tra, ii_vert)] += Cag
# total moments
Kforces[np.ix_(jj_for_rot, ii_vert)] += \
np.dot(Cag, algebra.skew(zetag))
# quaternion equation
# null, as not dep. on external forces
### --------------------------------------- allocate Kstiff
if bc_here != 1:
# forces
Dfdcrv = algebra.der_CcrvT_by_v(
psi, np.dot(Cag, faero))
Dfdquat = np.dot(
Cba, algebra.der_CquatT_by_v(tsstr.quat, faero))
Kss[np.ix_(jj_tra, jj_rot)] -= Dfdcrv
Ksr[jj_tra, -4:] -= Dfdquat
# moments
Kss[np.ix_(jj_rot, jj_rot)] -= np.dot(Xbskew, Dfdcrv)
Ksr[jj_rot, -4:] -= np.dot(Xbskew, Dfdquat)
# embed()
# transfer
self.Kdisp = Kdisp
self.Kvel_disp = Kvel_disp
self.Kvel_vel = Kvel_vel
self.Kforces = Kforces
# stiffening factors
self.Kss = Kss
self.Ksr = Ksr
def get_mode_zeta(data, eigvect):
"""
Retrieves the UVLM grid nodal displacements associated to the eigenvector ``eigvect``
"""
### initialise
aero = data.aero
struct = data.structure
tsaero = data.aero.timestep_info[data.ts]
tsstr = data.structure.timestep_info[data.ts]
try:
num_dof = struct.num_dof.value
except AttributeError:
num_dof = struct.num_dof
eigvect = eigvect[:num_dof]
zeta_mode = []
for ss in range(aero.n_surf):
zeta_mode.append(tsaero.zeta[ss].copy())
jj = 0 # structural dofs index
Cga0 = algebra.quat2rotation(tsstr.quat)
Cag0 = Cga0.T
for node_glob in range(struct.num_node):
### detect bc at node (and no. of dofs)
bc_here = struct.boundary_conditions[node_glob]
if bc_here == 1: # clamp
dofs_here = 0
continue
elif bc_here == -1 or bc_here == 0:
dofs_here = 6
jj_tra = [jj, jj + 1, jj + 2]
jj_rot = [jj + 3, jj + 4, jj + 5]
jj += dofs_here
# retrieve element and local index
ee, node_loc = struct.node_master_elem[node_glob, :]
# get original position and crv
Ra0 = tsstr.pos[node_glob, :]
psi0 = tsstr.psi[ee, node_loc, :]
Rg0 = np.dot(Cga0, Ra0)
Cab0 = algebra.crv2rotation(psi0)
Cbg0 = np.dot(Cab0.T, Cag0)
# update position and crv of mode
Ra = tsstr.pos[node_glob, :] + eigvect[jj_tra]
psi = tsstr.psi[ee, node_loc, :] + eigvect[jj_rot]
Rg = np.dot(Cga0, Ra)
Cab = algebra.crv2rotation(psi)
Cbg = np.dot(Cab.T, Cag0)
### str -> aero mapping
# some nodes may be linked to multiple surfaces...
for str2aero_here in aero.struct2aero_mapping[node_glob]:
# detect surface/span-wise coordinate (ss,nn)
nn, ss = str2aero_here['i_n'], str2aero_here['i_surf']
# print('%.2d,%.2d'%(nn,ss))
# surface panelling
M = aero.aero_dimensions[ss][0]
N = aero.aero_dimensions[ss][1]
for mm in range(M + 1):
# get position of vertex in B FoR
zetag0 = tsaero.zeta[ss][:, mm,
nn] # in G FoR, w.r.t. origin A-G
Xb = np.dot(Cbg0, zetag0 - Rg0) # in B FoR, w.r.t. origin B
# update vertex position
zeta_mode[ss][:, mm, nn] = Rg + np.dot(np.dot(Cga0, Cab), Xb)
return zeta_mode
def generate(self, linuvlm=None, tsaero0=None, tsstruct0=None, aero=None, structure=None):
"""
Generates a matrix mapping a linear control surface deflection onto the aerodynamic grid.
The parsing of arguments is temporary since this state space element will include a full actuator model.
The parsing of arguments is optional if the class has been previously initialised.
Args:
linuvlm:
tsaero0:
tsstruct0:
aero:
structure:
Returns:
"""
if self.aero is not None:
aero = self.aero
structure = self.structure
linuvlm = self.linuvlm
tsaero0 = self.tsaero0
tsstruct0 = self.tsstruct0
# Find the vertices corresponding to a control surface from beam coordinates to aerogrid
aero_dict = aero.aero_dict
n_surf = aero.timestep_info[0].n_surf
n_control_surfaces = self.n_control_surfaces
if self.under_development:
import matplotlib.pyplot as plt # Part of the testing process
Kdisp = np.zeros((3 * linuvlm.Kzeta, n_control_surfaces))
Kvel = np.zeros((3 * linuvlm.Kzeta, n_control_surfaces))
Kmom = np.zeros((3 * linuvlm.Kzeta, n_control_surfaces))
zeta0 = np.concatenate([tsaero0.zeta[i_surf].reshape(-1, order='C') for i_surf in range(n_surf)])
Cga = algebra.quat2rotation(tsstruct0.quat).T
Cag = Cga.T
# Initialise these parameters
hinge_axis = None # Will be set once per control surface to the hinge axis
with_control_surface = False # Will be set to true if the spanwise node contains a control surface
for global_node in range(structure.num_node):
# Retrieve elements and local nodes to which a single node is attached
for i_elem in range(structure.num_elem):
if global_node in structure.connectivities[i_elem, :]:
i_local_node = np.where(structure.connectivities[i_elem, :] == global_node)[0][0]
for_delta = structure.frame_of_reference_delta[i_elem, :, 0]
# CRV to transform from G to B frame
psi = tsstruct0.psi[i_elem, i_local_node]
Cab = algebra.crv2rotation(psi)
Cba = Cab.T
Cbg = np.dot(Cab.T, Cag)
Cgb = Cbg.T
# print(global_node)
if self.under_development:
print('Node -- ' + str(global_node))
# Map onto aerodynamic coordinates. Some nodes may be part of two aerodynamic surfaces. This will happen
# at the surface boundary
for structure2aero_node in aero.struct2aero_mapping[global_node]:
# Retrieve surface and span-wise coordinate
i_surf, i_node_span = structure2aero_node['i_surf'], structure2aero_node['i_n']
# Surface panelling
M = aero.aero_dimensions[i_surf][0]
N = aero.aero_dimensions[i_surf][1]
K_zeta_start = 3 * sum(linuvlm.MS.KKzeta[:i_surf])
shape_zeta = (3, M + 1, N + 1)
i_control_surface = aero_dict['control_surface'][i_elem, i_local_node]
if i_control_surface >= 0:
if not with_control_surface:
i_start_of_cs = i_node_span.copy()
with_control_surface = True
control_surface_chord = aero_dict['control_surface_chord'][i_control_surface]
i_node_hinge = M - control_surface_chord
i_vertex_hinge = [K_zeta_start +
np.ravel_multi_index((i_axis, i_node_hinge, i_node_span), shape_zeta)
for i_axis in range(3)]
i_vertex_next_hinge = [K_zeta_start +
np.ravel_multi_index((i_axis, i_node_hinge, i_start_of_cs + 1),
shape_zeta) for i_axis in range(3)]
zeta_hinge = zeta0[i_vertex_hinge]
zeta_next_hinge = zeta0[i_vertex_next_hinge]
if hinge_axis is None:
# Hinge axis not yet set for current control surface
# Hinge axis is in G frame
hinge_axis = zeta_next_hinge - zeta_hinge
hinge_axis = hinge_axis / np.linalg.norm(hinge_axis)
for i_node_chord in range(M + 1):
i_vertex = [K_zeta_start +
np.ravel_multi_index((i_axis, i_node_chord, i_node_span), shape_zeta)
for i_axis in range(3)]
if i_node_chord > i_node_hinge:
# Zeta in G frame
zeta_node = zeta0[i_vertex] # Gframe
zeta_nodeA = Cag.dot(zeta_node)
zeta_hingeA = Cag.dot(zeta_hinge)
zeta_hingeB = Cbg.dot(zeta_hinge)
zeta_nodeB = Cbg.dot(zeta_node)
chord_vec = (zeta_node - zeta_hinge)
if self.under_development:
print('G Frame')
print('Hinge axis = ' + str(hinge_axis))
print('\tHinge = ' + str(zeta_hinge))
print('\tNode = ' + str(zeta_node))
print('A Frame')
print('\tHinge = ' + str(zeta_hingeA))
print('\tNode = ' + str(zeta_nodeA))
print('B Frame')
print('\tHinge axis = ' + str(Cbg.dot(hinge_axis)))
print('\tHinge = ' + str(zeta_hingeB))
print('\tNode = ' + str(zeta_nodeB))
print('Chordwise Vector')
print('GVec = ' + str(chord_vec/np.linalg.norm(chord_vec)))
print('BVec = ' + str(Cbg.dot(chord_vec/np.linalg.norm(chord_vec))))
# pass
# Removing the += because cs where being added twice
Kdisp[i_vertex, i_control_surface] = \
Cgb.dot(der_R_arbitrary_axis_times_v(Cbg.dot(hinge_axis),
0,
-for_delta * Cbg.dot(chord_vec)))
# Kdisp[i_vertex, i_control_surface] = \
# der_R_arbitrary_axis_times_v(hinge_axis, 0, chord_vec)
# Flap velocity
Kvel[i_vertex, i_control_surface] = -algebra.skew(chord_vec).dot(
hinge_axis)
# Flap hinge moment - future work
# Kmom[i_vertex, i_control_surface] += algebra.skew(chord_vec)
# Testing progress
if self.under_development:
plt.scatter(zeta_hingeB[1], zeta_hingeB[2], color='k')
plt.scatter(zeta_nodeB[1], zeta_nodeB[2], color='b')
# plt.scatter(zeta_hinge[1], zeta_hinge[2], color='k')
# plt.scatter(zeta_node[1], zeta_node[2], color='b')
# Testing out
delta = 5*np.pi/180
# zeta_newB = Cbg.dot(Kdisp[i_vertex, 1].dot(delta)) + zeta_nodeB
zeta_newB = Cbg.dot(Kdisp[i_vertex, -1].dot(delta)) + zeta_nodeB
plt.scatter(zeta_newB[1], zeta_newB[2], color='r')
old_vector = zeta_nodeB - zeta_hingeB
new_vector = zeta_newB - zeta_hingeB
angle = np.arccos(new_vector.dot(old_vector) /
(np.linalg.norm(new_vector) * np.linalg.norm(old_vector)))
print(angle)
if self.under_development:
plt.axis('equal')
plt.show()
else:
with_control_surface = False
hinge_axis = None # Reset for next control surface
self.Kzeta_delta = Kdisp
self.Kdzeta_ddelta = Kvel
# self.Kmom = Kmom
return Kdisp, Kvel
def generate(self):
"""
Generates a matrix mapping a linear control surface deflection onto the aerodynamic grid.
This generates two matrices:
* `Kzeta_delta` maps the deflection angle onto displacements. It has as many columns as independent control
surfaces.
* `Kdzeta_ddelta` maps the deflection rate onto grid velocities. Again, it has as many columns as
independent control surfaces.
Returns:
tuple: Tuple containing `Kzeta_delta` and `Kdzeta_ddelta`.
"""
# For future development
# In hindsight, building this matrix iterating through structural node was a big mistake that
# has led to very messy code. Would rework by element and in B frame
aero = self.aero
structure = self.structure
linuvlm = self.linuvlm
tsaero0 = self.tsaero0
tsstruct0 = self.tsstruct0
# Find the vertices corresponding to a control surface from beam coordinates to aerogrid
aero_dict = aero.aero_dict
n_surf = tsaero0.n_surf
n_control_surfaces = self.n_control_surfaces
Kdisp = np.zeros((3 * linuvlm.Kzeta, n_control_surfaces))
Kvel = np.zeros((3 * linuvlm.Kzeta, n_control_surfaces))
zeta0 = np.concatenate([tsaero0.zeta[i_surf].reshape(-1, order='C') for i_surf in range(n_surf)])
Cga = algebra.quat2rotation(tsstruct0.quat).T
Cag = Cga.T
# Initialise these parameters
hinge_axis = None # Will be set once per control surface to the hinge axis
with_control_surface = False # Will be set to true if the spanwise node contains a control surface
for global_node in range(structure.num_node):
# Retrieve elements and local nodes to which a single node is attached
for i_elem in range(structure.num_elem):
if global_node in structure.connectivities[i_elem, :]:
i_local_node = np.where(structure.connectivities[i_elem, :] == global_node)[0][0]
for_delta = structure.frame_of_reference_delta[i_elem, :, 0]
# CRV to transform from G to B frame
psi = tsstruct0.psi[i_elem, i_local_node]
Cab = algebra.crv2rotation(psi)
Cba = Cab.T
Cbg = np.dot(Cab.T, Cag)
Cgb = Cbg.T
# Map onto aerodynamic coordinates. Some nodes may be part of two aerodynamic surfaces.
for structure2aero_node in aero.struct2aero_mapping[global_node]:
# Retrieve surface and span-wise coordinate
i_surf, i_node_span = structure2aero_node['i_surf'], structure2aero_node['i_n']
# Although a node may be part of 2 aerodynamic surfaces, we need to ensure that the current
# element for the given node is indeed part of that surface.
elems_in_surf = np.where(aero_dict['surface_distribution'] == i_surf)[0]
if i_elem not in elems_in_surf:
continue
# Surface panelling
M = aero.aero_dimensions[i_surf][0]
N = aero.aero_dimensions[i_surf][1]
K_zeta_start = 3 * sum(linuvlm.MS.KKzeta[:i_surf])
shape_zeta = (3, M + 1, N + 1)
i_control_surface = aero_dict['control_surface'][i_elem, i_local_node]
if i_control_surface >= 0:
if not with_control_surface:
i_start_of_cs = i_node_span.copy()
with_control_surface = True
control_surface_chord = aero_dict['control_surface_chord'][i_control_surface]
try:
control_surface_hinge_coord = \
aero_dict['control_surface_hinge_coord'][i_control_surface] * \
aero_dict['chord'][i_elem, i_local_node]
except KeyError:
control_surface_hinge_coord = None
i_node_hinge = M - control_surface_chord
i_vertex_hinge = [K_zeta_start +
np.ravel_multi_index((i_axis, i_node_hinge, i_node_span), shape_zeta)
for i_axis in range(3)]
i_vertex_next_hinge = [K_zeta_start +
np.ravel_multi_index((i_axis, i_node_hinge, i_start_of_cs + 1),
shape_zeta) for i_axis in range(3)]
if control_surface_hinge_coord is not None and M == control_surface_chord: # fully articulated control surface
zeta_hinge = Cgb.dot(Cba.dot(tsstruct0.pos[global_node]) + for_delta * np.array([0, control_surface_hinge_coord, 0]))
zeta_next_hinge = Cgb.dot(Cbg.dot(zeta_hinge) + np.array([1, 0, 0])) # parallel to the x_b vector
else:
zeta_hinge = zeta0[i_vertex_hinge]
zeta_next_hinge = zeta0[i_vertex_next_hinge]
if hinge_axis is None:
# Hinge axis not yet set for current control surface
# Hinge axis is in G frame
hinge_axis = zeta_next_hinge - zeta_hinge
hinge_axis = hinge_axis / np.linalg.norm(hinge_axis)
for i_node_chord in range(M + 1):
i_vertex = [K_zeta_start +
np.ravel_multi_index((i_axis, i_node_chord, i_node_span), shape_zeta)
for i_axis in range(3)]
if i_node_chord >= i_node_hinge:
# Zeta in G frame
zeta_node = zeta0[i_vertex] # Gframe
chord_vec = (zeta_node - zeta_hinge)
Kdisp[i_vertex, i_control_surface] = \
Cgb.dot(der_R_arbitrary_axis_times_v(Cbg.dot(hinge_axis),
0,
-for_delta * Cbg.dot(chord_vec))) * for_delta * -1
# Flap velocity
Kvel[i_vertex, i_control_surface] = -algebra.skew(-for_delta * chord_vec).dot(
hinge_axis) * for_delta * -1
else:
with_control_surface = False
hinge_axis = None # Reset for next control surface
# >>>> Merge control surfaces 0 and 1
# Kdisp[:, 0] -= Kdisp[:, 1]
# Kvel[:, 0] -= Kvel[:, 1]
self.Kzeta_delta = Kdisp
self.Kdzeta_ddelta = Kvel
return Kdisp, Kvel
int(np.round(100*RollVecDeg[ii])) )
case_here=case_main+'_ainf%.4da%.4ds%.4dr%.4d'%tplparams
route_here=route_main
os.system('mkdir -p %s'%(route_here,))
### ------------------------------------------------------ Build wing model
ws=flying_wings.Goland( M=M,N=N,Mstar_fact=Mstar_fact,n_surfaces=Nsurf,
u_inf=u_inf,
alpha=AlphaVecDeg[ii],
beta=-SideVecDeg[ii],
route=route_here,
case_name=case_here)
# updte wind direction
quat_wind=algebra.euler2quat(-np.pi/180.*np.array([0.,AlphaInfVecDeg[ii],0.]))
u_inf_dir=np.dot( algebra.quat2rotation(quat_wind),np.array([1.,0.,0.]))
ws.main_ea-=.25/M
ws.main_cg-=.25/M
ws.root_airfoil_P = 4
ws.root_airfoil_M = 2
ws.tip_airfoil_P = 4
ws.tip_airfoil_M = 2
ws.clean_test_files()
ws.update_derived_params()
ws.generate_fem_file()
ws.generate_aero_file()
### solution flow
def update_orientation(self, quat, ts=-1):
rot = algebra.quat2rotation(quat)
self.timestep_info[ts].update_orientation(rot.T)
def test_rotation_matrices_derivatives(self):
"""
Checks derivatives of rotation matrix derivatives with respect to
quaternions and Cartesian rotation vectors
Note: test only includes CRV <-> quaternions conversions
"""
### linearisation point
# fi0=np.pi/6
# nv0=np.array([1,3,1])
fi0 = 2.0 * np.pi * random.random() - np.pi
nv0 = np.array([random.random(), random.random(), random.random()])
nv0 = nv0 / np.linalg.norm(nv0)
fv0 = fi0 * nv0
qv0 = algebra.crv2quat(fv0)
ev0 = algebra.quat2euler(qv0)
# direction of perturbation
# fi1=np.pi/3
# nv1=np.array([-2,4,1])
fi1 = 2.0 * np.pi * random.random() - np.pi
nv1 = np.array([random.random(), random.random(), random.random()])
nv1 = nv1 / np.linalg.norm(nv1)
fv1 = fi1 * nv1
qv1 = algebra.crv2quat(fv1)
ev1 = algebra.quat2euler(qv1)
# linearsation point
Cga0 = algebra.quat2rotation(qv0)
Cag0 = Cga0.T
Cab0 = algebra.crv2rotation(fv0)
Cba0 = Cab0.T
Cga0_euler = algebra.euler2rot(ev0)
Cag0_euler = Cga0_euler.T
# derivatives
# xv=np.ones((3,)) # dummy vector
xv = np.array([random.random(),
random.random(),
random.random()]) # dummy vector
derCga = algebra.der_Cquat_by_v(qv0, xv)
derCag = algebra.der_CquatT_by_v(qv0, xv)
derCab = algebra.der_Ccrv_by_v(fv0, xv)
derCba = algebra.der_CcrvT_by_v(fv0, xv)
derCga_euler = algebra.der_Ceuler_by_v(ev0, xv)
derCag_euler = algebra.der_Peuler_by_v(ev0, xv)
A = np.array([1e-1, 1e-2, 1e-3, 1e-4, 1e-5, 1e-6])
er_ag = 10.
er_ga = 10.
er_ab = 10.
er_ba = 10.
er_ag_euler = 10.
er_ga_euler = 10.
for a in A:
# perturbed
qv = a * qv1 + (1. - a) * qv0
fv = a * fv1 + (1. - a) * fv0
ev = a * ev1 + (1. - a) * ev0
dqv = qv - qv0
dfv = fv - fv0
dev = ev - ev0
Cga = algebra.quat2rotation(qv)
Cag = Cga.T
Cab = algebra.crv2rotation(fv)
Cba = Cab.T
Cga_euler = algebra.euler2rot(ev)
Cag_euler = Cga_euler.T
dCag_num = np.dot(Cag - Cag0, xv)
dCga_num = np.dot(Cga - Cga0, xv)
dCag_an = np.dot(derCag, dqv)
dCga_an = np.dot(derCga, dqv)
er_ag_new = np.max(np.abs(dCag_num - dCag_an))
er_ga_new = np.max(np.abs(dCga_num - dCga_an))
dCab_num = np.dot(Cab - Cab0, xv)
dCba_num = np.dot(Cba - Cba0, xv)
dCab_an = np.dot(derCab, dfv)
dCba_an = np.dot(derCba, dfv)
er_ab_new = np.max(np.abs(dCab_num - dCab_an))
er_ba_new = np.max(np.abs(dCba_num - dCba_an))
dCag_num_euler = np.dot(Cag_euler - Cag0_euler, xv)
dCga_num_euler = np.dot(Cga_euler - Cga0_euler, xv)
dCag_an_euler = np.dot(derCag_euler, dev)
dCga_an_euler = np.dot(derCga_euler, dev)
er_ag_euler_new = np.max(np.abs(dCag_num_euler - dCag_an_euler))
er_ga_euler_new = np.max(np.abs(dCga_num_euler - dCga_an_euler))
assert er_ga_new < er_ga, 'der_Cquat_by_v error not converging to 0'
assert er_ag_new < er_ag, 'der_CquatT_by_v error not converging to 0'
assert er_ab_new < er_ab, 'der_Ccrv_by_v error not converging to 0'
assert er_ba_new < er_ba, 'der_CcrvT_by_v error not converging to 0'
assert er_ga_euler_new < er_ga_euler, 'der_Ceuler_by_v error not converging to 0'
assert er_ag_euler_new < er_ag_euler, 'der_Peuler_by_v error not converging to 0'
er_ag = er_ag_new
er_ga = er_ga_new
er_ab = er_ab_new
er_ba = er_ba_new
er_ag_euler = er_ag_euler_new
er_ga_euler = er_ga_euler_new
assert er_ga < A[-2], 'der_Cquat_by_v error too large'
assert er_ag < A[-2], 'der_CquatT_by_v error too large'
assert er_ab < A[-2], 'der_Ccrv_by_v error too large'
assert er_ba < A[-2], 'der_CcrvT_by_v error too large'
assert er_ag_euler < A[-2], 'der_Peuler_by_v error too large'
assert er_ga_euler < A[-2], 'der_Ceuler_by_v error too large'
