def test_coords(self):
nodes = [Node(1, 0, 0), Node(2, 0.05, 0)]
dofs = np.array([0, 1])
element_1d = Element1D(1, nodes, 1, dofs)
self.assertEqual(element_1d.nodes[0].coordinates, [0, 0])
self.assertEqual(element_1d.nodes[1].coordinates, [0.05, 0])
def test_m_matrix(self):
nodes = [Node(1, 0, 0), Node(2, 0.05, 0)]
dofs = np.array([0, 1])
element_1d = Element1D(1, nodes, 1, dofs)
m_e = element_1d.m_matrix()
self.assertAlmostEqual(m_e[0][0], 0.01666667)
self.assertAlmostEqual(m_e[0][1], 0.00833333)
self.assertAlmostEqual(m_e[1][0], 0.00833333)
self.assertAlmostEqual(m_e[1][1], 0.01666667)
def test_k_matrix(self):
nodes = [Node(1, 0, 0), Node(2, 0.05, 0)]
dofs = np.array([0, 1])
element_1d = Element1D(1, nodes, 1, dofs)
k_e = element_1d.k_matrix()
self.assertEqual(k_e[0][0], 20.0)
self.assertEqual(k_e[0][1], -20.0)
self.assertEqual(k_e[1][0], -20.0)
self.assertEqual(k_e[1][1], 20.0)
def test_get_solution_point_from_solution_vector(self):
nodes = [Node(1, 0, 0), Node(2, 0.05, 0)]
dofs = np.array([0, 1])
element_1d = Element1D(1, nodes, 1, dofs)
local_u_FEM = [3.0, 0.01]
u = element_1d.get_solution_point_from_solution_vector(
0.05, local_u_FEM)
self.assertEqual(u, 0.01)
def test_integrate_uAnlytical_squared(self):
nodes = [Node(1, 0, 0), Node(2, 0.05, 0)]
dofs = np.array([0, 1])
element_1d = Element1D(1, nodes, 1, dofs)
def u_an(x, t):
return sin(2 * pi * x) * sin(2 * pi * t)
integral = element_1d.integrate_uAnlytical_squared(u_an, 0.01)
self.assertAlmostEqual(integral, 0.010179115314613244)
def test_element1D_instance_is_created(self):
nodes = [Node(1, 0, 0), Node(2, 0.05, 0)]
dofs = np.array([0, 1])
element_1d = Element1D(1, nodes, 1, dofs)
self.assertEqual(element_1d.id, 1)
self.assertEqual(element_1d.nodes[0].id, 1)
self.assertEqual(element_1d.nodes[0]._x, 0)
self.assertEqual(element_1d.nodes[0]._y, 0)
self.assertEqual(element_1d.nodes[1].id, 2)
self.assertEqual(element_1d.nodes[1]._x, 0.05)
self.assertEqual(element_1d.nodes[1]._y, 0)
def test_integrate_uAnlytical_minus_uFEM_squared(self):
nodes = [Node(1, 0, 0), Node(2, 0.05, 0)]
dofs = np.array([0, 1])
element_1d = Element1D(1, nodes, 1, dofs)
local_u_FEM = [3.0, 0.01]
def u_an(x, t):
return sin(2 * pi * x) * sin(2 * pi * t)
integral = element_1d.integrate_uAnlytical_minus_uFEM_squared(
u_an, local_u_FEM, 1)
self.assertAlmostEqual(integral, 240.80266666666665)
def test_f_vector(self):
nodes = [Node(1, 0, 0), Node(2, 0.05, 0)]
dofs = np.array([0, 1])
element_1d = Element1D(1, nodes, 1, dofs)
def force_global_function(x, t):
return 2 * pi * cos(2 * pi * t) * sin(
2 * pi * x) + 4 * pi * pi * sin(2 * pi * t) * sin(2 * pi * x)
f_e = element_1d.f_vector(force_global_function, 0)
self.assertAlmostEqual(f_e[0], 0.01635941)
self.assertAlmostEqual(f_e[1], 0.03258397)