def _generate_mesh_using_symmetry(self, ntheta, nphi, clip_free_surface,
mesh_name):
if clip_free_surface:
if self.geometric_center[2] < -self.radius: # fully immersed
theta_max = np.pi
elif self.geometric_center[2] < self.radius:
theta_max = np.arccos(self.geometric_center[2] / self.radius)
else:
raise ValueError(
"Impossible to mesh the immersed hull of a sphere completely out of the water"
)
else:
theta_max = np.pi
theta = np.linspace(0.0, theta_max, ntheta + 1)
points_on_a_meridian = (self.radius * np.stack(
[np.sin(theta),
np.zeros_like(theta), -np.cos(theta)], axis=1) +
self.geometric_center)
symmetry_axis = Axis(vector=[0, 0, 1], point=self.geometric_center)
return AxialSymmetricMesh.from_profile(points_on_a_meridian,
axis=symmetry_axis,
nphi=nphi,
name=mesh_name)
def _generate_clever_sphere_mesh(self,
ntheta=10,
nphi=10,
clip_free_surface=False,
name=None):
if clip_free_surface:
if self.geometric_center[2] < -self.radius: # fully immersed
theta_max = np.pi
elif self.geometric_center[2] < self.radius:
theta_max = np.arccos(self.geometric_center[2] / self.radius)
else:
raise Exception("Sphere out of the water")
else:
theta_max = np.pi
theta = np.linspace(0.0, theta_max, ntheta + 1)
circle_profile = np.zeros((ntheta + 1, 3), dtype=float)
circle_profile[:, 0] = np.sin(theta)
circle_profile[:, 2] = -np.cos(theta)
circle_profile *= self.radius
return AxialSymmetricMesh.from_profile(circle_profile,
nphi=nphi,
name=f"{name}_mesh")
def test_odd_axial_symmetry():
"""Buoy with odd number of slices."""
def shape(z):
return 0.1 * (-(z + 1)**2 + 16)
buoy = FloatingBody(
AxialSymmetricMesh.from_profile(shape,
z_range=np.linspace(-5.0, 0.0, 9),
nphi=5))
buoy.add_translation_dof(direction=(0, 0, 1), name="Heave")
problem = RadiationProblem(body=buoy, omega=2.0)
result1 = solver_with_sym.solve(problem)
full_buoy = FloatingBody(buoy.mesh.merged())
full_buoy.add_translation_dof(direction=(0, 0, 1), name="Heave")
problem = RadiationProblem(body=full_buoy, omega=2.0)
result2 = solver_with_sym.solve(problem)
volume = buoy.mesh.volume
assert np.isclose(result1.added_masses["Heave"],
result2.added_masses["Heave"],
atol=1e-4 * volume * problem.rho)
assert np.isclose(result1.radiation_dampings["Heave"],
result2.radiation_dampings["Heave"],
atol=1e-4 * volume * problem.rho)
def __init__(self,
length=10.0,
radius=1.0,
center=(0, 0, 0),
nx=10,
ntheta=10,
nr=2,
clever=True,
name=None):
self.length = length
self.radius = radius
self.geometric_center = np.asarray(center, dtype=float)
if name is None:
name = f"cylinder_{next(Mesh._ids)}"
open_cylinder = AxialSymmetricMesh.from_profile(
lambda z: radius,
z_range=np.linspace(-length / 2, length / 2, nx + 1),
nphi=ntheta)
if nr > 0:
top_side = Disk(radius=radius,
center=(0, 0, length / 2),
axial_symmetry=True,
normal=(0, 0, 1),
resolution=(nr, ntheta),
name=f"top_side_of_{name}").mesh
bottom_side = top_side.copy(name=f"bottom_side_of_{name}_mesh")
bottom_side.mirror(xOy_Plane)
mesh = AxialSymmetricMesh.join_meshes(open_cylinder, top_side,
bottom_side)
else:
mesh = open_cylinder
if not clever:
mesh = mesh.merged()
mesh.merge_duplicates()
mesh.heal_triangles()
mesh.translate(center)
mesh.name = f"{name}_mesh"
FloatingBody.__init__(self, mesh=mesh, name=name)
def __init__(self,
radius=1.0,
resolution=(3, 5),
center=(0, 0, 0),
normal=(1, 0, 0),
reflection_symmetry=False,
axial_symmetry=False,
name=None):
assert radius > 0, "Radius of the disk mesh should be given as a positive value."
assert len(
resolution
) == 2, "Resolution of a disk should be given as a couple a values."
assert all([
h > 0 for h in resolution
]), "Resolution of the disk mesh should be given as positive values."
assert all([
i == int(i) for i in resolution
]), "Resolution of a disk should be given as integer values."
assert len(
center
) == 3, "Position of the center of a disk should be given a 3-ple of values."
self.radius = float(radius)
self.geometric_center = np.asarray(center, dtype=float)
nr, ntheta = resolution
if reflection_symmetry and ntheta % 2 == 1:
raise ValueError(
"To use the reflection symmetry of the mesh, "
"it should have an even number of panels in this direction.")
if reflection_symmetry and axial_symmetry:
raise NotImplementedError(
"Disk generators with both symmetries have not been implemented."
)
if name is None:
name = f"disk_{next(Mesh._ids)}"
LOG.debug(
f"New disk body of radius {radius} and resolution ({nr}, {ntheta}), named {name}."
)
if reflection_symmetry:
half_mesh = Disk.generate_disk_mesh(radius=self.radius,
theta_max=np.pi / 2,
nr=nr,
ntheta=ntheta // 2,
name=f"half_of_{name}_mesh")
mesh = ReflectionSymmetricMesh(half_mesh,
plane=xOz_Plane,
name=f"{name}_mesh")
elif axial_symmetry:
mesh_slice = Disk.generate_disk_mesh(radius=self.radius,
theta_max=np.pi / ntheta,
nr=nr,
ntheta=1,
name=f"slice_of_{name}_mesh")
mesh_slice.rotate_around_center_to_align_vectors(
(0, 0, 0), e_x, e_z
) # Convoluted way to avoid a warning message in AxialSymmetry...
mesh = AxialSymmetricMesh(mesh_slice,
axis=Oz_axis,
nb_repetitions=ntheta - 1,
name=f"{name}_mesh")
mesh.rotate_around_center_to_align_vectors((0, 0, 0), e_z, e_x)
else:
mesh = Disk.generate_disk_mesh(radius=self.radius,
nr=nr,
ntheta=ntheta,
name=f"{name}_mesh")
mesh.rotate_around_center_to_align_vectors(
(0, 0, 0), mesh.faces_normals[0], normal)
mesh.translate(center)
FloatingBody.__init__(self, mesh=mesh, name=name)
def __init__(self,
length=10.0,
radius=1.0,
center=(0, 0, 0),
nx=10,
ntheta=10,
nr=2,
clever=True,
name=None):
"""Generate the mesh of a vertical cylinder.
Parameters
----------
length : float, optional
length of the cylinder
radius : float, optional
radius of the cylinder
center : 3-ple or array of shape (3,), optional
position of the geometric center of the cylinder
nx : int, optional
number of circular slices
ntheta : int, optional
number of panels along a circular slice of the cylinder
nr : int, optional
number of panels along a radius on the extremities of the cylinder
clever : bool, optional
if True, uses the mesh symmetries
name : str, optional
a string naming the floating body
"""
self.length = length
self.radius = radius
self.geometric_center = np.asarray(center, dtype=np.float)
if name is None:
name = f"cylinder_{next(Mesh._ids)}"
open_cylinder = AxialSymmetricMesh.from_profile(
lambda z: radius,
z_range=np.linspace(-length / 2, length / 2, nx + 1),
nphi=ntheta)
if nr > 0:
top_side = Disk(radius=radius,
center=(0, 0, length / 2),
axial_symmetry=True,
normal=(0, 0, 1),
resolution=(nr, ntheta),
name=f"top_side_of_{name}").mesh
bottom_side = top_side.copy(name=f"bottom_side_of_{name}_mesh")
bottom_side.mirror(xOy_Plane)
mesh = AxialSymmetricMesh.join_meshes(open_cylinder, top_side,
bottom_side)
else:
mesh = open_cylinder
if not clever:
mesh = mesh.merged()
mesh.merge_duplicates()
mesh.heal_triangles()
mesh.translate(center)
mesh.name = f"{name}_mesh"
FloatingBody.__init__(self, mesh=mesh, name=name)