def two_bars(self, young, density, area, length):
X = torch.tensor([[0, 0], [length, 0], [length, length]])
conn = torch.tensor([[0, 1], [1, 2]], dtype=int)
nodes = Nodes(X)
mat = BasicMaterial(lambda e: young * e, density)
els = Truss(conn, nodes, area, mat)
return Model(nodes, els)
def nodes(self, seed, length, dim):
num_nodes = 3
return Nodes(
X=length * torch.rand(num_nodes, dim),
u=length * torch.rand(num_nodes, dim),
v=length * torch.rand(num_nodes, dim),
)
def __init__(self, nodes=None, elements=None, time=0, damping=0):
self.nodes = Nodes(nodes) if isinstance(nodes, torch.Tensor) else nodes
self.elements = [] if elements is None else [elements]
self.loads = []
self.constraints = []
self.damping = damping
self.time = time
def nodes(self, seed, length, angle, rand_strain):
"""Three nodes mirrored vertically."""
origin = length * 100 * torch.rand(2)
p1 = origin + torch.tensor([length * cos(angle), length * sin(angle)])
p2 = origin + torch.tensor([length * cos(angle), -length * sin(angle)])
X = torch.stack([origin, p1, p2])
# logitudinal stretch
u1 = rand_strain * (X[1] - X[0])
u2 = rand_strain * (X[2] - X[0])
u = torch.stack([torch.zeros(2), u1, u2])
return Nodes(X, u)
def pyramid_truss(self, length, area, young, density=1):
X = torch.tensor([[0, 0, 0], [0, 1, 0], [1, 1, 0], [1, 0, 0],
[1, 1, 1]])
X = (X + 100.0) * length
u = torch.rand(8, 3) * length / 2.0
v = torch.rand(8, 3) * length / 2.0
nodes = Nodes(X, u, v)
conn = torch.tensor(
[[0, 1], [1, 2], [2, 3], [3, 0], [0, 2], [1, 4], [2, 4], [3, 4]],
dtype=int,
)
material = BasicMaterial(lambda e: young * e, density)
elements = Truss(conn, nodes, area, material)
model = Model(nodes, elements) # zero damping
return model
def test_single_bar_force(self, length, area, young, rtol):
# assign a random initial position and normalize to length
X = torch.rand((2, 3)) + 100
X = length * X / (X[1] - X[0]).norm()
# align the bar to z direction and stretch it
strain = 0.1
u = torch.stack([
torch.zeros(3),
X[0] - X[1] + length * torch.tensor([0, 0, 1 + strain])
])
nodes = Nodes(X, u)
mat = BasicMaterial(lambda e: young * e)
conn = torch.tensor([[0, 1]], dtype=int)
elements = Truss(conn, nodes, area, mat)
model = Model(nodes, elements)
assert model.force()[1, 2] == pytest.approx(-strain * young * area,
rel=rtol)
def nodes(self):
return Nodes(torch.rand(3, 2))
def test_default_state(self):
nodes = Nodes(torch.rand(10, 2))
assert nodes.X.size() == nodes.u.size()
assert nodes.X.size() == nodes.v.size()
assert torch.allclose(nodes.u, torch.zeros(10, 2))
assert torch.allclose(nodes.v, torch.zeros(10, 2))
def test_current_position(self):
nodes = Nodes(torch.rand(10, 2))
assert torch.allclose(nodes.x(), nodes.X)
nodes.u = torch.rand(10, 2)
assert torch.allclose(nodes.x(), nodes.X + nodes.u)
def test_len(self):
nodes = Nodes(torch.rand(10, 2))
assert len(nodes) == 10