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_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 _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])