def test_FY_load_rotated(self):
# tests a clamped beam for vertical load at the tip
import random
P = random.randrange(1, 200)
L = self.beam3.l
EI = self.beam3.EI
_t = HB.transfer_matrix(alpha=self.rotation_angle,
asdegree=False,
blocks=1,
blocksize=2)
_load = _t * np.matrix([[0, P]]).T
self.beam_as_structure_2.add_single_dynam_to_node(nodeID=2,
dynam={
'FX': _load[0],
'FY': _load[1]
},
clear=True)
self.beam_as_structure_2.solver['linear static'].solve()
disps = self.beam_as_structure_2.results[
'linear static'].element_displacements(
local=True,
beam=self.beam_as_structure_2.beams[0],
asvector=True)
_expected = np.matrix([
[0.0],
[0.0],
[0.0],
[0.0],
[(P * L**3) / (3 * EI)], # vertical displacement at the end
[(P * L**2) / (2 * EI)]
]) # rotation at the end
self.assertTrue(np.allclose(disps, _expected, atol=ATOL))
def test_nodal_displacements_12(self):
# same as _11, but the beams are rotated 60 degree clockwise
# assertion #1: single Axial force on Node 2, the element is rotated, so are the loads.
# but then at the end the resulting displacements are rotated back and we get the same results as in test _1
# structure #1: 3 elements in a row along the global X axis
_ux = 0.5 # unit in x direction; instead of 1 as unit we have cos(60) to account for the rotation
_uy = -math.sqrt(
3
) / 2. # unit in x direction; instead of 1 as unit we have cos(60) to account for the rotation
n1 = Node.Node(ID=1, coords=(0, 0))
n2 = Node.Node(ID=2, coords=(100 * _ux, 100 * _uy))
n3 = Node.Node(ID=3, coords=(200 * _ux, 200 * _uy))
n4 = Node.Node(ID=4, coords=(300 * _ux, 300 * _uy))
# definition of the beams is unchanged
b1 = HB.HermitianBeam2D(E=210000., ID=1, I=833.33, A=100., i=n1, j=n2)
b2 = HB.HermitianBeam2D(E=210000., ID=2, I=833.33, A=100., i=n2, j=n3)
b3 = HB.HermitianBeam2D(E=210000., ID=3, I=833.33, A=100., i=n3, j=n4)
structure = Structure.Structure(beams=[b1, b2, b3],
supports={1: ['ux', 'uy', 'rotz']})
# two loads instead of one as these are in the global system
structure.add_single_dynam_to_node(nodeID=4,
dynam={'FX': _ux},
clear=True)
structure.add_single_dynam_to_node(nodeID=4, dynam={'FY': _uy})
# since the elements were previously rotated by -60 degrees, now we rotate the results by 60 degrees back...
T = HB.transfer_matrix(60, asdegree=True, blocks=len(structure.nodes))
structure.solver['linear static'].solve()
disps = structure.results['linear static'].global_displacements(
asvector=True)
disps = T * disps
_expected = np.matrix([
[0.0],
[0.0],
[0.0],
[4.76190476e-06], # same as in _1
[0.00000000e+00],
[0.00000000e+00],
[9.52380952e-06],
[0.00000000e+00],
[0.00000000e+00],
[1.42857143e-05],
[0.00000000e+00],
[0.00000000e+00]
])
self.assertTrue(np.allclose(disps, _expected, atol=ATOL))
def test_element_stiffness_matrix_rotated(self):
k_asinteger = np.matrix([[1, 0, 0, -1, 0, 0], [0, 12, 6, 0, -12, 6],
[0, 6, 4, 0, -6, 2], [-1, 0, 0, 1, 0, 0],
[0, -12, -6, 0, 12, -6], [0, 6, 2, 0, -6, 4]])
_tm = HB.transfer_matrix(alpha=self.rotation_angle,
asdegree=False,
blocks=2,
blocksize=3)
k_asinteger = _tm * k_asinteger * _tm.T
self.assertTrue(
np.allclose(k_asinteger,
self.beam3.matrix_in_global(mtrx=self.beam3.Ke)))
self.assertTrue(
np.allclose(self.beam3.matrix_in_global(mtrx=self.beam3.Ke),
self.beam4.matrix_in_global(mtrx=self.beam4.Ke)))