def test_static_deflection(self):
x = array([0.0, 4.0, 10.0])
EI = 144.0
# Using the z axis as the transverse direction gives the same
# sign convention as Reddy uses in 2D, namely that rotations
# are positive clockwise.
fe = BeamFE(x, density=10, EA=0, EIy=EI, EIz=0)
fe.set_boundary_conditions('C', 'F')
fe.set_dofs([False, False, True, False, True, False])
element = ModalElementFromFE('elem', fe)
# Distributed load, linearly interpolated
load = np.zeros((3, 3))
load[-1, 2] = -100 # Load in z direction at tip
element.apply_distributed_loading(load)
defl = -element.applied_stress / np.diag(element.K)
# Check against directly calculating static deflection from FE
Q = fe.distribute_load(interleave(load, 6))
defl_fe, reactions_fe = fe.static_deflection(Q)
assert_aae(dot(element.shapes, defl), defl_fe, decimal=2)
def test_static_deflection(self):
x = array([0.0, 4.0, 10.0])
EI = 144.0
# Using the z axis as the transverse direction gives the same
# sign convention as Reddy uses in 2D, namely that rotations
# are positive clockwise.
fe = BeamFE(x, density=10, EA=0, EIy=EI, EIz=0)
fe.set_boundary_conditions('C', 'F')
fe.set_dofs([False, False, True, False, True, False])
element = ModalElementFromFE('elem', fe)
# Distributed load, linearly interpolated
load = np.zeros((3, 3))
load[-1, 2] = -100 # Load in z direction at tip
element.apply_distributed_loading(load)
defl = -element.applied_stress / np.diag(element.K)
# Check against directly calculating static deflection from FE
Q = fe.distribute_load(interleave(load, 6))
defl_fe, reactions_fe = fe.static_deflection(Q)
assert_aae(dot(element.shapes, defl), defl_fe, decimal=2)
def test_rigid_element_reference_loading(self):
# Make an element with no modes (rigid)
fe = BeamFE(np.linspace(0, 1, 11), density=1, EA=0, EIy=1, EIz=0)
fe.set_boundary_conditions('C', 'F')
fe.set_dofs([False, False, True, False, True, False])
element = ModalElementFromFE('elem', fe, 0)
# Distributed load, linearly interpolated
load = np.zeros((11, 3))
load[:, 2] = -100 # Uniform load in z direction
element.apply_distributed_loading(load)
assert_aae(element.applied_stress, [])
assert_aae(element.applied_forces[0:6], [0, 0, -100 * 1, 0, 50, 0])
assert_aae(element.applied_forces[6:12], 0)
# Distributed load, triangle at tip
load = np.zeros((11, 3))
load[-1, 2] = -100 # tapered load in z direction
element.applied_forces[:] = 0 # reset
element.apply_distributed_loading(load)
F = -100 * 0.1 / 2
assert_aae(element.applied_forces[0:6],
[0, 0, F, 0, -F * (0.9 + 0.1 * 2 / 3), 0])
assert_aae(element.applied_forces[6:12], 0)
def test_rigid_element_reference_loading(self):
# Make an element with no modes (rigid)
fe = BeamFE(np.linspace(0, 1, 11), density=1, EA=0, EIy=1, EIz=0)
fe.set_boundary_conditions('C', 'F')
fe.set_dofs([False, False, True, False, True, False])
element = ModalElementFromFE('elem', fe, 0)
# Distributed load, linearly interpolated
load = np.zeros((11, 3))
load[:, 2] = -100 # Uniform load in z direction
element.apply_distributed_loading(load)
assert_aae(element.applied_stress, [])
assert_aae(element.applied_forces[0:6], [0, 0, -100 * 1, 0, 50, 0])
assert_aae(element.applied_forces[6:12], 0)
# Distributed load, triangle at tip
load = np.zeros((11, 3))
load[-1, 2] = -100 # tapered load in z direction
element.applied_forces[:] = 0 # reset
element.apply_distributed_loading(load)
F = -100 * 0.1 / 2
assert_aae(element.applied_forces[0:6],
[0, 0, F, 0, -F * (0.9 + 0.1 * 2 / 3), 0])
assert_aae(element.applied_forces[6:12], 0)
