def test_material_nonenriched_element():
"""test if material is properly asigned for non enriched elements when in
xfem analysis with 3 elements
"""
class Mesh():
def __init__(self):
self.nodes = {
1: [0, 0, 0],
2: [1, 0, 0],
3: [1, 1, 0],
4: [0, 1, 0],
5: [2, 0, 0],
6: [2, 1, 0],
7: [3, 0, 0],
8: [3, 1, 0]
}
self.elements = {
1: [3, 2, 11, 10, 1, 2, 3, 4],
2: [3, 2, 11, 10, 2, 5, 6, 3],
3: [3, 2, 11, 10, 5, 7, 8, 6]
}
msh = Mesh()
func = lambda x, y: x - 0.5
zls = skmech.xfem.ZeroLevelSet(func, [0, 3], [0, 1], num_div=[50, 50])
mat = skmech.Material(E={-1: 2.22, 1: 1.11}, nu={-1: 0.3, 1: 0.3})
model = skmech.Model(msh, zerolevelset=zls, material=mat, thickness=0.01)
E = {}
for eid, [etype, *_] in model.elements.items():
ele = skmech.constructor(eid, etype, model)
E[eid] = ele.E
assert E[3] == 1.11
assert E[1] == [2.22, 1.11, 1.11, 2.22]
assert E[2] == [1.11, 1.11, 1.11, 1.11]
def test_dof3():
"""test dof for 4 zero level sets in separate 4 elements
also tests for matrix material properties.
"""
class Mesh():
def __init__(self):
self.nodes = {
1: [0, 0, 0],
2: [1, 0, 0],
3: [1, 1, 0],
4: [0, 1, 0],
5: [2, 0, 0],
6: [2, 1, 0],
7: [2, 2, 0],
8: [1, 2, 0],
9: [0, 2, 0]
}
self.elements = {
1: [3, 2, 11, 10, 1, 2, 3, 4],
2: [3, 2, 11, 10, 2, 5, 6, 3],
3: [3, 2, 11, 10, 3, 6, 7, 8],
4: [3, 2, 11, 10, 4, 3, 8, 9]
}
msh = Mesh()
func1 = lambda x, y: (x - 0)**2 + (y - 0)**2 - .2**2
func2 = lambda x, y: (x - 2)**2 + (y - 0)**2 - .2**2
func3 = lambda x, y: (x - 2)**2 + (y - 2)**2 - .2**2
func4 = lambda x, y: (x - 0)**2 + (y - 2)**2 - .2**2
zls = [skmech.xfem.ZeroLevelSet(func1, [0, 2], [0, 2], num_div=[50, 50]),
skmech.xfem.ZeroLevelSet(func2, [0, 2], [0, 2], num_div=[50, 50]),
skmech.xfem.ZeroLevelSet(func3, [0, 2], [0, 2], num_div=[50, 50]),
skmech.xfem.ZeroLevelSet(func4, [0, 2], [0, 2], num_div=[50, 50])]
# -1 is reinforcement, 1 is matrix
mat = skmech.Material(E={-1: 2e11, 1: 1e11}, nu={-1: 0.3, 1: 0.3},
case='stress')
model = skmech.Model(msh, zerolevelset=zls, material=mat,
thickness=0.01)
E = {}
dof = {}
for eid, [etype, *_] in model.elements.items():
ele = skmech.constructor(eid, etype, model)
dof[eid] = ele.dof
E[eid] = ele.E
assert dof[1] == [1, 2, 3, 4, 5, 6, 7, 8, 19, 20, 21, 22, 23, 24, 25,
26, 27, 28, 29, 30, 35, 36, 43, 44, 45, 46]
assert dof[2] == [3, 4, 9, 10, 11, 12, 5, 6, 21, 22, 23, 24, 27, 28, 29,
30, 31, 32, 33, 34, 35, 36, 37, 38, 43, 44]
assert dof[3] == [5, 6, 11, 12, 13, 14, 15, 16, 23, 24, 29, 30, 33, 34, 35,
36, 37, 38, 39, 40, 41, 42, 43, 44, 47, 48]
assert dof[4] == [7, 8, 5, 6, 15, 16, 17, 18, 23, 24, 25, 26, 29, 30, 35,
36, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50]
assert E[1] == [2e11, 1e11, 1e11, 1e11]
assert E[2] == [1e11, 2e11, 1e11, 1e11]
assert E[3] == [1e11, 1e11, 2e11, 1e11]
assert E[4] == [1e11, 1e11, 1e11, 2e11]
def test_neumann():
class Mesh():
pass
msh = Mesh()
msh.nodes = {1: [0, 0, 0], 2: [14, 0, 0], 3: [6, 6, 0], 4: [0, 6, 0]}
msh.elements = {1: [1, 2, 5, 4, 2, 3], 2: [3, 2, 0, 0, 1, 2, 3, 4]}
mat = skmech.Material(E={0: 10000}, nu={0: 0.2})
trac = {5: (3 / 5, 4 / 5)}
model = skmech.Model(mesh=msh, material=mat, traction=trac,
num_quad_points=2)
Pt = skmech.neumann(model)
assert list(Pt) == [0., 0., 3., 4., 3., 4., 0., 0.]
def test_dof2():
"""test dof for two zero level sets in 2 elements"""
class Mesh():
def __init__(self):
self.nodes = {
1: [0, 0, 0],
2: [1, 0, 0],
3: [1, 1, 0],
4: [0, 1, 0],
5: [2, 0, 0],
6: [2, 1, 0],
}
self.elements = {
1: [3, 2, 11, 10, 1, 2, 3, 4],
2: [3, 2, 11, 10, 2, 5, 6, 3],
}
msh = Mesh()
func = lambda x, y: x - 0.5
func2 = lambda x, y: (-x + 1.5)
zls = [skmech.xfem.ZeroLevelSet(func, [0, 2], [0, 1], num_div=[50, 50]),
skmech.xfem.ZeroLevelSet(func2, [0, 2], [0, 1], num_div=[50, 50])]
mat = skmech.Material(E={-1: 2e11, 1: 1e11}, nu={-1: 0.3, 1: 0.3},
case='strain')
model = skmech.Model(msh, zerolevelset=zls, material=mat,
thickness=0.01)
assert model.xfem.enr_elements == [1, 2]
assert model.xfem.enr_nodes == [1, 2, 3, 4, 5, 6]
assert model.xfem.zls[0].enr_nodes == [1, 2, 3, 4]
assert model.xfem.zls[1].enr_nodes == [2, 3, 5, 6]
assert model.xfem.zls[0].enr_node_dof == {1: [13, 14], 2: [15, 16],
3: [17, 18], 4: [19, 20]}
assert model.xfem.zls[1].enr_node_dof == {2: [21, 22], 3: [23, 24],
5: [25, 26], 6: [27, 28]}
dof = {}
for eid, [etype, *_] in model.elements.items():
ele = skmech.constructor(eid, etype, model)
dof[eid] = ele.dof
# element dof numbering following CCW for standards and following
# the sorted enr node order for each zero level set
assert dof[1] == [1, 2, 3, 4, 5, 6, 7, 8,
13, 14, 15, 16, 17, 18, 19, 20, # first zls
21, 22, 23, 24] # second
assert dof[2] == [3, 4, 9, 10, 11, 12, 5, 6,
15, 16, 17, 18, # node 2, 3 enr dof for first zls
21, 22, 23, 24, 25, 26, 27, 28] # nodes 2,3,5,6 2nd zls
def test_dof():
"""test dof for 2 zero level set thtat don't share an element with 4 ele"""
class Mesh():
def __init__(self):
self.nodes = {
1: [0, 0, 0],
2: [1, 0, 0],
3: [1, 1, 0],
4: [0, 1, 0],
5: [2, 0, 0],
6: [2, 1, 0],
7: [3, 0, 0],
8: [3, 1, 0],
9: [4, 0, 0],
10: [4, 1, 0]
}
self.elements = {
1: [3, 2, 11, 10, 1, 2, 3, 4],
2: [3, 2, 11, 10, 2, 5, 6, 3],
3: [3, 2, 11, 10, 5, 7, 8, 6],
4: [3, 2, 11, 10, 7, 9, 10, 8]
}
msh = Mesh()
func = lambda x, y: x - 0.5
func2 = lambda x, y: (-x + 3.5)
zls = [skmech.xfem.ZeroLevelSet(func, [0, 4], [0, 1], num_div=[50, 50]),
skmech.xfem.ZeroLevelSet(func2, [0, 4], [0, 1], num_div=[50, 50])]
mat = skmech.Material(E={-1: 2e11, 1: 1e11}, nu={-1: 0.3, 1: 0.3},
case='strain')
model = skmech.Model(msh, zerolevelset=zls, material=mat,
thickness=0.01)
assert model.xfem.enr_elements == [1, 2, 3, 4]
dof = {}
for eid, [etype, *_] in model.elements.items():
ele = skmech.constructor(eid, etype, model)
dof[eid] = ele.dof
assert dof[1] == [1, 2, 3, 4, 5, 6, 7, 8,
21, 22, 23, 24, 25, 26, 27, 28]
assert dof[4] == [13, 14, 17, 18, 19, 20, 15, 16,
29, 30, 31, 32, 33, 34, 35, 36]
msh.nodes = {
1: [0, 0, 0],
2: [1, 0, 0],
3: [1, 1, 0],
4: [0, 1, 0],
5: [.5, 0, 0],
6: [1, .5, 0],
7: [.5, 1, 0],
8: [0, .5, 0],
9: [.4, .6]
}
msh.elements = {
1: [15, 2, 12, 1, 1], # nodes for dirichlet boundary
13: [1, 2, 3, 30, 1, 5],
14: [1, 2, 3, 30, 5, 2],
3: [1, 2, 7, 2, 3, 7],
4: [1, 2, 7, 2, 7, 4],
9: [3, 2, 11, 10, 1, 5, 9, 8], # quad elements
10: [3, 2, 11, 10, 5, 2, 6, 9],
11: [3, 2, 11, 10, 9, 6, 3, 7],
12: [3, 2, 11, 10, 8, 9, 7, 4]
}
displ = {12: (0, 0), 3: (None, 0), 7: (0, .1)}
mat = skmech.Material(E={11: 1000}, nu={11: 0.0})
model = skmech.Model(msh, material=mat, displacement=displ)
u = skmech.statics.solver(model)
fig, ax = plt.subplots()
skmech.plot.geometry(model.nodes, model.elements, ax)
skmech.plot.deformed(model.nodes, model.elements, u, ax, magf=1)
plt.show()
def test_element_stiffness():
"""test element material"""
class Mesh():
def __init__(self):
self.nodes = {
1: [0, 0, 0],
2: [.2, 0, 0],
3: [.2, .2, 0],
4: [0, 0.2, 0],
5: [.4, 0, 0],
6: [.6, 0, 0],
7: [.6, .2, 0],
8: [.4, .2, 0],
}
self.elements = {
10: [15, 2, 12, 1, 1],
20: [15, 2, 13, 4, 4],
13: [1, 2, 3, 30, 6, 7],
30: [1, 2, 7, 2, 3, 7],
4: [1, 2, 7, 2, 7, 4],
1: [3, 2, 11, 10, 1, 2, 3, 4],
2: [3, 2, 11, 10, 2, 5, 8, 3],
3: [3, 2, 11, 10, 5, 6, 7, 8],
}
msh = Mesh()
func = lambda x, y: x - 0.3
zls = skmech.xfem.ZeroLevelSet(func, [0, .6], [0, .2], num_div=[100, 100])
mat = skmech.Material(E={-1: 2e11, 1: 1e11}, nu={-1: 0.3, 1: 0.3},
case='strain')
model = skmech.Model(msh, zerolevelset=zls, material=mat,
thickness=0.01)
k = {}
emat = {}
for eid, [etype, *_] in model.elements.items():
ele = skmech.constructor(eid, etype, model)
emat[eid] = ele.E
k[eid] = ele.stiffness_matrix()[ele.id_m] # extract non augmentbed
# This is done when computing element stifness matrix
# assert emat[3] == [109890109890.1099,
# 109890109890.1099,
# 109890109890.1099,
# 109890109890.1099]
# assert emat[2] == [219780219780.2198,
# 109890109890.1099,
# 109890109890.1099,
# 219780219780.2198]
k_std_ele1 = np.array(
[[1.154, 0.481, -0.769, 0.096, -0.577, -0.481, 0.192, -0.096],
[0.481, 1.154, -0.096, 0.192, -0.481, -0.577, 0.096, -0.769],
[-0.769, -0.096, 1.154, -0.481, 0.192, 0.096, -0.577, 0.481],
[0.096, 0.192, -0.481, 1.154, -0.096, -0.769, 0.481, -0.577],
[-0.577, -0.481, 0.192, -0.096, 1.154, 0.481, -0.769, 0.096],
[-0.481, -0.577, 0.096, -0.769, 0.481, 1.154, -0.096, 0.192],
[0.192, 0.096, -0.577, 0.481, -0.769, -0.096, 1.154, -0.481],
[-0.096, -0.769, 0.481, -0.577, 0.096, 0.192, -0.481, 1.154]])
assert np.allclose(k[1][:8, :8] / 1e9, k_std_ele1, atol=1e-2)
k_enr_ele1 = np.array(
[[129.915, 0., 49.573, -0.], [-0., 70.085, -0., -18.803],
[49.573, -0., 129.915, 0.], [0., -18.803, 0., 70.085]])
# TODO check that! maybe something related to the material plane strain plane stress
assert np.allclose(k[1][8:, 8:] / 1e9 * 3600, k_enr_ele1, atol=1e-2)
3: [1, 1, 0],
4: [0, 1, 0],
5: [.5, 0, 0],
6: [1, .5, 0],
7: [.5, 1, 0],
8: [0, .5, 0],
9: [.4, .6]
}
msh.elements = {
1: [15, 2, 12, 1, 1],
2: [15, 2, 13, 2, 2],
3: [1, 2, 7, 2, 2, 6],
4: [1, 2, 7, 2, 6, 3],
7: [1, 2, 5, 4, 4, 8],
8: [1, 2, 5, 4, 8, 1],
9: [3, 2, 11, 10, 1, 5, 9, 8],
10: [3, 2, 11, 10, 5, 2, 6, 9],
11: [3, 2, 11, 10, 9, 6, 3, 7],
12: [3, 2, 11, 10, 8, 9, 7, 4]
}
material = skmech.Material(E={11: 10000}, nu={11: 0.3})
traction = {5: (-1, 0), 7: (1, 0)}
displacement_bc = {12: (0, 0)}
model = skmech.Model(msh,
material=material,
traction=traction,
imposed_displ=imposed_displacement,
displacement_bc=displacement_bc,
num_quad_points=2)
