def main():
height = 100
width = 600
delta = width / height
# Create the mesh to solve linear elasticity on.
mesh = Mesh("meshes/bridge.xml")
scale_mesh(mesh, width, height)
# Define the function space
V = VectorFunctionSpace(mesh, "P", 1)
# Mark boundary subdomians
boundary_parts = MeshFunction("size_t", mesh, mesh.topology().dim() - 1)
boundary_parts.set_all(0)
# Tolarance of boundary near checks.
tol = 2e-4
class BottomBoundary(SubDomain):
""" Constrain the bottom to not move. """
def inside(self, x, on_boundary):
return ((near(x[0], 0.1, 10) or near(x[0], width - 0.1, 10)) and
near(x[1], 0, tol))
gamma_bottom = BottomBoundary()
class PointLoad(SubDomain):
""" Add a point load to the top center. """
def inside(self, x, on_boundary):
return (near(x[0], width / 2.0, width / 50) and
near(x[1], height, tol))
gamma_point = PointLoad()
gamma_point.mark(boundary_parts, 2)
B = Constant((0.0, 0.0)) # Body force per unit volume
T = Constant((0.0, delta * 0)) # Point load on the boundary
# Boundary conditions on the subdomains
bct = DirichletBC(V, Constant((0.0, 0.0)), gamma_bottom, method="pointwise")
bcp = DirichletBC(V, T, gamma_point, method="pointwise")
bcs = [bct, bcp]
dss = ds(subdomain_data=boundary_parts)
L = lambda v: dot(B, v) * dx + dot(T, v) * dss(2)
u = linear_elasticity(V, L, bcs)
File("output/MBB/displacement.pvd") << u
# Compute magnitude of displacement
V = FunctionSpace(mesh, "P", 1)
u_magnitude = sqrt(dot(u, u))
u_magnitude = project(u_magnitude, V)
File("output/MBB/magnitude.pvd") << u_magnitude
print("min/max u: {:g}, {:g}".format(
u_magnitude.vector().get_local().min(),
u_magnitude.vector().get_local().max()))
# Save solution to file in VTK format
File("output/MBB/von_mises.pvd") << von_Mises_stress(mesh, u)
class MBBBoundaryConditions(BoundaryConditions):
def get_fixed(self):
width, height, tol = self.width, self.height, self.tol
class BottomBoundary(SubDomain):
""" Constrain the bottom to not move. """
def inside(self, x, on_boundary):
return ((near(x[0], 0.1, 2e1) or near(x[0], width - 0.1, 2e1))
and near(x[1], 0, tol))
return [BottomBoundary()]
def get_forces(self):
width, height, tol = self.width, self.height, self.tol
class PointLoad(SubDomain):
""" Add a point load to the top center. """
def inside(self, x, on_boundary):
return (near(x[0], width / 2.0, width / 50)
and near(x[1], height, tol))
return [PointLoad()], [Constant((0.0, -2e-1))]
if __name__ == "__main__":
width, height, tol = 600, 100, 5e-2
bc = MBBBoundaryConditions(width, height, tol)
mesh = Mesh("meshes/bridge.xml")
scale_mesh(mesh, width, height)
run_simulation(mesh, bc, "MBB/bridge-single-load-", E=1e1)
def main():
height = 100
width = 600
delta = width / height
# Create the mesh to solve linear elasticity on.
mesh = Mesh("meshes/bridge.xml")
scale_mesh(mesh, width, height)
# Define the function space
V = VectorFunctionSpace(mesh, "P", 1)
# Mark boundary subdomians
boundary_parts = MeshFunction("size_t", mesh, mesh.topology().dim() - 1)
boundary_parts.set_all(0)
# Tolarance of boundary near checks.
tol = 2e-4
class BottomBoundary(SubDomain):
""" Constrain the bottom to not move. """
def inside(self, x, on_boundary):
return ((near(x[0], 0.1, 10) or near(x[0], width - 0.1, 10))
and near(x[1], 0, tol))
gamma_bottom = BottomBoundary()
class PointLoad(SubDomain):
""" Add a point load to the top center. """
def inside(self, x, on_boundary):
return (near(x[0], width / 2.0, width / 50)
and near(x[1], height, tol))
gamma_point = PointLoad()
gamma_point.mark(boundary_parts, 2)
B = Constant((0.0, 0.0)) # Body force per unit volume
T = Constant((0.0, delta * 0)) # Point load on the boundary
# Boundary conditions on the subdomains
bct = DirichletBC(V,
Constant((0.0, 0.0)),
gamma_bottom,
method="pointwise")
bcp = DirichletBC(V, T, gamma_point, method="pointwise")
bcs = [bct, bcp]
dss = ds(subdomain_data=boundary_parts)
L = lambda v: dot(B, v) * dx + dot(T, v) * dss(2)
u = linear_elasticity(V, L, bcs)
File("output/MBB/displacement.pvd") << u
# Compute magnitude of displacement
V = FunctionSpace(mesh, "P", 1)
u_magnitude = sqrt(dot(u, u))
u_magnitude = project(u_magnitude, V)
File("output/MBB/magnitude.pvd") << u_magnitude
print("min/max u: {:g}, {:g}".format(
u_magnitude.vector().get_local().min(),
u_magnitude.vector().get_local().max()))
# Save solution to file in VTK format
File("output/MBB/von_mises.pvd") << von_Mises_stress(mesh, u)
def inside(self, x, on_boundary):
return near(x[0], width, tol) and near(x[1], height / 3., tol)
return [PointLoad()], [Constant((0.0, -3e-1))]
if __name__ == "__main__":
bc = LBracketBoundaryConditions(1, 1, 5e-2)
# Create the mesh to solve linear elasticity on.
large_quad = mshr.Polygon(
[Point(0, 0), Point(1, 0),
Point(1, 1), Point(0, 1)])
small_quad = mshr.Polygon([
Point(1 / 3., 1 / 3.),
Point(1, 1 / 3.),
Point(1, 1),
Point(1 / 3., 1)
])
domain = large_quad - small_quad
mesh = mshr.generate_mesh(domain, 30)
run_simulation(mesh, bc, "L-bracket/v100-")
mesh = Mesh("meshes/L-bracket-v20.xml")
scale_mesh(mesh, 1, 1)
run_simulation(mesh, bc, "L-bracket/v20-")
mesh = Mesh("meshes/L-bracket-v10.xml")
scale_mesh(mesh, 1, 1)
run_simulation(mesh, bc, "L-bracket/v10-")