def setUp(self):
# FE model for beam
x = linspace(0, self.length, 20)
fe = BeamFE(x, density=self.density, EA=0, EIy=1, EIz=0)
fe.set_boundary_conditions('C', 'F')
self.beam = ModalElementFromFE('beam', fe, 0)
# Set loading - in negative Z direction
load = np.zeros((len(x), 3))
load[:, 2] = -self.force
self.beam.loading = load
# Hinge with axis along Y axis
self.hinge = Hinge('hinge', [0, 1, 0])
self.hinge.internal_torque = self.hinge_torque
# Build system
self.system = System()
self.system.add_leaf(self.hinge)
self.hinge.add_leaf(self.beam)
self.system.setup()
if not self.free_beam:
# Prescribe hinge to be fixed
self.system.prescribe(self.hinge)
# Initial calculations
self.recalc()
def test_distal_node_velocity_due_to_hinge_rotation_has_correct_axis(self):
h = Hinge('hinge', [0, 0, 1])
h.vstrain[0] = 4.5 # rad/s
h.calc_kinematics()
assert_array_equal(h.F_vp, eye(6)) # distal node moves with prox
assert_array_equal(h.F_ve[:3, 0], zeros(3)) # hinge ang vel is
assert_array_equal(h.F_ve[3:, 0], [0, 0, 1]) # about axis
assert_array_equal(h.F_v2, zeros(6)) # no quadratic force, base fixed
def test_distal_node_velocity_due_to_hinge_rotation_has_correct_axis(self):
h = Hinge('hinge', [0, 0, 1])
h.vstrain[0] = 4.5 # rad/s
h.calc_kinematics()
assert_array_equal(h.F_vp, eye(6)) # distal node moves with prox
assert_array_equal(h.F_ve[:3, 0], zeros(3)) # hinge ang vel is
assert_array_equal(h.F_ve[3:, 0], [0, 0, 1]) # about axis
assert_array_equal(h.F_v2, zeros(6)) # no quadratic force, base fixed
def test_distal_node_is_rotated_by_90deg_about_correct_axis(self):
h = Hinge('hinge', [0, 0, 1])
h.rp = array([3.5, 9.21, 8.6])
h.Rp = eye(3)
# Test distal transform
h.calc_distal_pos()
assert_array_equal(h.rd, h.rp)
assert_array_equal(h.Rd, h.Rp)
h.xstrain[0] = pi / 2
h.calc_distal_pos()
assert_array_equal(h.rd, h.rp) # always coincident
# New unit vectors X -> y, Y -> -x, Z -> z
assert_array_almost_equal(h.Rd, c_[[0, 1, 0], [-1, 0, 0], [0, 0, 1]])
class hinged_beam_tests(unittest.TestCase):
density = 5.0
length = 20.0
force = 34.2 # N/m
hinge_torque = 0.0
free_beam = False
def setUp(self):
# FE model for beam
x = linspace(0, self.length, 20)
fe = BeamFE(x, density=self.density, EA=0, EIy=1, EIz=0)
fe.set_boundary_conditions('C', 'F')
self.beam = ModalElementFromFE('beam', fe, 0)
# Set loading - in negative Z direction
load = np.zeros((len(x), 3))
load[:, 2] = -self.force
self.beam.loading = load
# Hinge with axis along Y axis
self.hinge = Hinge('hinge', [0, 1, 0])
self.hinge.internal_torque = self.hinge_torque
# Build system
self.system = System()
self.system.add_leaf(self.hinge)
self.hinge.add_leaf(self.beam)
self.system.setup()
if not self.free_beam:
# Prescribe hinge to be fixed
self.system.prescribe(self.hinge)
# Initial calculations
self.recalc()
def recalc(self):
self.system.update_kinematics() # Set up nodal values initially
self.system.update_matrices()
self.system.solve_accelerations() # Calculate accelerations of DOFs
self.system.update_kinematics() # Update nodal values based on DOFs
self.system.update_matrices()
self.system.solve_reactions() # Solve reactions incl d'Alembert
def test_additional_post_transform_of_90deg_is_applied(self):
h = Hinge('hinge', [0, 0, 1], post_transform=rotmat_x(pi / 2))
h.rp = array([3.5, 9.21, 8.6])
h.Rp = eye(3)
# Test distal transform with post transform
h.calc_distal_pos()
assert_array_equal(h.rd, h.rp)
# just post transform
assert_array_almost_equal(h.Rd, c_[[1, 0, 0], [0, 0, 1], [0, -1, 0]])
h.xstrain[0] = pi / 2
h.calc_distal_pos()
assert_array_equal(h.rd, h.rp) # always coincident
# rotate about z then x
assert_array_almost_equal(h.Rd, c_[[0, 1, 0], [0, 0, 1], [1, 0, 0]])
def test_distal_node_is_rotated_by_90deg_about_correct_axis(self):
h = Hinge('hinge', [0, 0, 1])
h.rp = array([3.5, 9.21, 8.6])
h.Rp = eye(3)
# Test distal transform
h.calc_distal_pos()
assert_array_equal(h.rd, h.rp)
assert_array_equal(h.Rd, h.Rp)
h.xstrain[0] = pi / 2
h.calc_distal_pos()
assert_array_equal(h.rd, h.rp) # always coincident
# New unit vectors X -> y, Y -> -x, Z -> z
assert_array_almost_equal(h.Rd, c_[[0, 1, 0], [-1, 0, 0], [0, 0, 1]])
def test_interal_torque(self):
# NB minus sign because convention for applied_stress is that
# stiffness loads are positive.
h = Hinge('hinge', [0, 0, 1])
# Constant loading
h.internal_torque = 3.4
h.calc_external_loading()
assert_array_equal(h.applied_forces, 0)
assert_array_equal(h.applied_stress, [-3.4])
# Loading function
h.internal_torque = lambda element, t: 5.4
h.calc_external_loading()
assert_array_equal(h.applied_forces, 0)
assert_array_equal(h.applied_stress, [-5.4])
def test_additional_post_transform_of_90deg_is_applied(self):
h = Hinge('hinge', [0, 0, 1], post_transform=rotmat_x(pi / 2))
h.rp = array([3.5, 9.21, 8.6])
h.Rp = eye(3)
# Test distal transform with post transform
h.calc_distal_pos()
assert_array_equal(h.rd, h.rp)
# just post transform
assert_array_almost_equal(h.Rd, c_[[1, 0, 0], [0, 0, 1], [0, -1, 0]])
h.xstrain[0] = pi / 2
h.calc_distal_pos()
assert_array_equal(h.rd, h.rp) # always coincident
# rotate about z then x
assert_array_almost_equal(h.Rd, c_[[0, 1, 0], [0, 0, 1], [1, 0, 0]])
def test_interal_torque(self):
# NB minus sign because convention for applied_stress is that
# stiffness loads are positive.
h = Hinge('hinge', [0, 0, 1])
# Constant loading
h.internal_torque = 3.4
h.calc_external_loading()
assert_array_equal(h.applied_forces, 0)
assert_array_equal(h.applied_stress, [-3.4])
# Loading function
h.internal_torque = lambda element, t: 5.4
h.calc_external_loading()
assert_array_equal(h.applied_forces, 0)
assert_array_equal(h.applied_stress, [-5.4])
def __init__(self, structure_config):
s = structure_config
#### Load details of flexible elements ####
if "definition" in s["tower"]:
if "mass" in s["tower"]:
raise ValueError("Both tower definition and explicit mass!")
self.tower_definition = Tower(s["tower"]["definition"])
assert np.all(self.tower_definition.stn_pos[:, :2] == 0) # vert.
z_tower = self.tower_definition.stn_pos[:, 2]
self.tower_modes = ModesFromScratch(
z_tower - z_tower[0],
self.tower_definition.density,
1,
self.tower_definition.EIy,
self.tower_definition.EIz,
)
else:
self.tower_definition = None
self.tower_modes = None
if "blade" in s:
self.blade_modes = load_modes_from_Bladed(s["blade"]["definition"])
else:
self.blade_modes = None
#### Create the elements ####
# Free joint represents the rigid-body motion of the platform
free_joint = FreeJoint("base")
# This is the rigid-body mass of the platform structure
conn_platform = RigidConnection("conn-platform", offset=s["platform"]["CoM"])
platform = RigidBody("platform", mass=s["platform"]["mass"], inertia=np.diag(s["platform"]["inertia"]))
free_joint.add_leaf(conn_platform)
conn_platform.add_leaf(platform)
# Make a rigid body to represent the added mass
# (approximate to zero frequency)
# XXX this is skipping the coupling matrix
# A = whales_model.A(0)
# added_mass = RigidBody('added-mass', mass=np.diag(A[:3, :3]),
# inertia=A[3:, 3:])
# Flexible tower or equivalent rigid body
if self.tower_modes:
# move base of tower 10m up, and rotate so tower x-axis is vertical
conn_tower = RigidConnection("conn-tower", offset=[0, 0, z_tower[0]], rotation=rotmat_y(-pi / 2))
tower = DistalModalElementFromScratch("tower", self.tower_modes, s["tower"]["number of normal modes"])
else:
# move tower to COG
conn_tower = RigidConnection("conn-tower", offset=s["tower"]["CoM"])
tower = RigidBody("tower", s["tower"]["mass"], np.diag(s["tower"]["inertia"]))
free_joint.add_leaf(conn_tower)
conn_tower.add_leaf(tower)
# The nacelle -- rigid body
# rotate back so nacelle inertia is aligned with global coordinates
if self.tower_modes:
nacoff = s["nacelle"]["offset from tower top"]
conn_nacelle = RigidConnection(
"conn-nacelle", offset=dot(rotmat_y(pi / 2), nacoff), rotation=rotmat_y(pi / 2)
)
tower.add_leaf(conn_nacelle)
else:
conn_nacelle = RigidConnection("conn-nacelle", offset=np.array([0, 0, s["nacelle"]["height"]]))
free_joint.add_leaf(conn_nacelle)
nacelle = RigidBody(
"nacelle", mass=s["nacelle"]["mass"], inertia=np.diag(s["nacelle"].get("inertia", np.zeros(3)))
)
conn_nacelle.add_leaf(nacelle)
# The rotor hub -- currently just connections (no mass)
# rotate so rotor centre is aligned with global coordinates
if self.tower_modes:
rotoff = s["rotor"]["offset from tower top"]
conn_rotor = RigidConnection("conn-rotor", offset=dot(rotmat_y(pi / 2), rotoff), rotation=rotmat_y(pi / 2))
tower.add_leaf(conn_rotor)
else:
conn_rotor = RigidConnection("conn-rotor", offset=np.array([0, 0, s["nacelle"]["height"]]))
free_joint.add_leaf(conn_rotor)
# The drive shaft rotation (rotation about x)
shaft = Hinge("shaft", [1, 0, 0])
conn_rotor.add_leaf(shaft)
# The blades
if self.blade_modes:
rtlen = s["rotor"]["root length"]
Ryx = dot(rotmat_y(-pi / 2), rotmat_x(-pi / 2)) # align blade modes
for i in range(3):
R = rotmat_x(i * 2 * pi / 3)
root = RigidConnection("root%d" % (i + 1), offset=dot(R, [0, 0, rtlen]), rotation=dot(R, Ryx))
blade = ModalElement("blade%d" % (i + 1), self.blade_modes)
shaft.add_leaf(root)
root.add_leaf(blade)
else:
rotor = RigidBody("rotor", s["rotor"]["mass"], np.diag(s["rotor"]["inertia"]))
shaft.add_leaf(rotor)
# Build system
self.system = System(free_joint)
# Constrain missing DOFs -- tower torsion & extension not complete
if self.tower_modes:
self.system.prescribe(tower, vel=0, part=[0, 3])
def _make_random_hinge(rdm):
return Hinge('hinge',
hinge_axis=random_rotation_matrix(rdm)[:, 0],
post_transform=random_rotation_matrix(rdm))
def __init__(self, structure_config):
s = structure_config
#### Load details of flexible elements ####
if 'definition' in s['tower']:
if 'mass' in s['tower']:
raise ValueError("Both tower definition and explicit mass!")
self.tower_definition = Tower(s['tower']['definition'])
assert np.all(self.tower_definition.stn_pos[:, :2] == 0) # vert.
z_tower = self.tower_definition.stn_pos[:, 2]
self.tower_modes = ModesFromScratch(
z_tower - z_tower[0],
self.tower_definition.density, 1,
self.tower_definition.EIy, self.tower_definition.EIz)
else:
self.tower_definition = None
self.tower_modes = None
if 'blade' in s:
self.blade_modes = load_modes_from_Bladed(s['blade']['definition'])
else:
self.blade_modes = None
#### Create the elements ####
# Free joint represents the rigid-body motion of the platform
free_joint = FreeJoint('base')
# This is the rigid-body mass of the platform structure
conn_platform = RigidConnection('conn-platform',
offset=s['platform']['CoM'])
platform = RigidBody('platform',
mass=s['platform']['mass'],
inertia=np.diag(s['platform']['inertia']))
free_joint.add_leaf(conn_platform)
conn_platform.add_leaf(platform)
# Make a rigid body to represent the added mass
# (approximate to zero frequency)
# XXX this is skipping the coupling matrix
#A = whales_model.A(0)
# added_mass = RigidBody('added-mass', mass=np.diag(A[:3, :3]),
# inertia=A[3:, 3:])
# Flexible tower or equivalent rigid body
if self.tower_modes:
# move base of tower 10m up, and rotate so tower x-axis is vertical
conn_tower = RigidConnection(
'conn-tower', offset=[0, 0, z_tower[0]],
rotation=rotmat_y(-pi/2))
tower = DistalModalElementFromScratch(
'tower', self.tower_modes,
s['tower']['number of normal modes'])
else:
# move tower to COG
conn_tower = RigidConnection(
'conn-tower', offset=s['tower']['CoM'])
tower = RigidBody('tower', s['tower']['mass'],
np.diag(s['tower']['inertia']))
free_joint.add_leaf(conn_tower)
conn_tower.add_leaf(tower)
# The nacelle -- rigid body
# rotate back so nacelle inertia is aligned with global coordinates
if self.tower_modes:
nacoff = s['nacelle']['offset from tower top']
conn_nacelle = RigidConnection('conn-nacelle',
offset=dot(rotmat_y(pi/2), nacoff),
rotation=rotmat_y(pi/2))
tower.add_leaf(conn_nacelle)
else:
conn_nacelle = RigidConnection(
'conn-nacelle',
offset=np.array([0, 0, s['nacelle']['height']]))
free_joint.add_leaf(conn_nacelle)
nacelle = RigidBody(
'nacelle',
mass=s['nacelle']['mass'],
inertia=np.diag(s['nacelle'].get('inertia', np.zeros(3))))
conn_nacelle.add_leaf(nacelle)
# The rotor hub -- currently just connections (no mass)
# rotate so rotor centre is aligned with global coordinates
if self.tower_modes:
rotoff = s['rotor']['offset from tower top']
conn_rotor = RigidConnection('conn-rotor',
offset=dot(rotmat_y(pi/2), rotoff),
rotation=rotmat_y(pi/2))
tower.add_leaf(conn_rotor)
else:
conn_rotor = RigidConnection(
'conn-rotor',
offset=np.array([0, 0, s['nacelle']['height']]))
free_joint.add_leaf(conn_rotor)
# The drive shaft rotation (rotation about x)
shaft = Hinge('shaft', [1, 0, 0])
conn_rotor.add_leaf(shaft)
# The blades
if self.blade_modes:
rtlen = s['rotor']['root length']
Ryx = dot(rotmat_y(-pi/2), rotmat_x(-pi/2)) # align blade modes
for i in range(3):
R = rotmat_x(i*2*pi/3)
root = RigidConnection('root%d' % (i+1),
offset=dot(R, [0, 0, rtlen]),
rotation=dot(R, Ryx))
blade = ModalElement('blade%d' % (i+1), self.blade_modes)
shaft.add_leaf(root)
root.add_leaf(blade)
else:
rotor = RigidBody('rotor', s['rotor']['mass'],
np.diag(s['rotor']['inertia']))
shaft.add_leaf(rotor)
# Build system
self.system = System(free_joint)
# Constrain missing DOFs -- tower torsion & extension not complete
if self.tower_modes:
self.system.prescribe(tower, vel=0, part=[0, 3])
