import dolfinx as df
import numpy as np
import pint
import ufl
from mpi4py import MPI
from petsc4py.PETSc import ScalarType
from fenicsxconcrete.experimental_setup.base_experiment import Experiment
from fenicsxconcrete.util import Parameters, ureg
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class CantileverBeam(Experiment):
"""Sets up a cantilever beam, clamped on one side and loaded with gravity
Attributes:
parameters : parameter dictionary with units
p : parameter dictionary without units
"""
def __init__(self, parameters: dict[str, pint.Quantity] | None = None):
"""initializes the object, for the rest, see base class
Args:
parameters: dictionary containing the required parameters for the experiment set-up
see default_parameters for a first guess
"""
super().__init__(parameters)
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def setup(self) -> None:
"""defines the mesh for 2D or 3D
Raises:
ValueError: if dimension (self.p["dim"]) is not 2 or 3
"""
if self.p["dim"] == 2:
self.mesh = df.mesh.create_rectangle(
comm=MPI.COMM_WORLD,
points=[(0.0, 0.0), (self.p["length"], self.p["height"])],
n=(self.p["num_elements_length"], self.p["num_elements_height"]),
cell_type=df.mesh.CellType.quadrilateral,
)
elif self.p["dim"] == 3:
self.mesh = df.mesh.create_box(
comm=MPI.COMM_WORLD,
points=[
(0.0, 0.0, 0.0),
(self.p["length"], self.p["width"], self.p["height"]),
],
n=[
self.p["num_elements_length"],
self.p["num_elements_width"],
self.p["num_elements_height"],
],
cell_type=df.mesh.CellType.hexahedron,
)
else:
raise ValueError(f'wrong dimension: {self.p["dim"]} is not implemented for problem setup')
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@staticmethod
def default_parameters() -> dict[str, pint.Quantity]:
"""sets up a working set of parameter values as example
Returns:
dictionary with a working set of the required parameter
"""
setup_parameters = {}
setup_parameters["length"] = 1 * ureg("m")
setup_parameters["height"] = 0.3 * ureg("m")
setup_parameters["width"] = 0.3 * ureg("m") # only relevant for 3D case
setup_parameters["dim"] = 3 * ureg("")
setup_parameters["num_elements_length"] = 10 * ureg("")
setup_parameters["num_elements_height"] = 3 * ureg("")
setup_parameters["num_elements_width"] = 3 * ureg("") # only relevant for 3D case
return setup_parameters
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def create_displacement_boundary(self, V) -> list:
"""defines displacement boundary as fixed at bottom
Args:
V: function space
Returns:
list of dirichlet boundary conditions
"""
# fenics will individually call this function for every node and will note the true or false value.
def clamped_boundary(x):
return np.isclose(x[0], 0)
displacement_bcs = []
zero = np.zeros(self.p["dim"])
displacement_bcs.append(
df.fem.dirichletbc(
np.array(zero, dtype=ScalarType),
df.fem.locate_dofs_geometrical(V, clamped_boundary),
V,
)
)
return displacement_bcs
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def create_body_force(self, v: ufl.argument.Argument) -> ufl.form.Form:
"""defines body force
Args:
v: test function
Returns:
form for body force
"""
force_vector = np.zeros(self.p["dim"])
force_vector[-1] = -self.p["rho"] * self.p["g"] # works for 2D and 3D
f = df.fem.Constant(self.mesh, ScalarType(force_vector))
L = ufl.dot(f, v) * ufl.dx
return L