def QuadBallSphericalArc(center=(0., 0., 0.),
inner_radius=9.,
outer_radius=10.,
n=10,
nthick=1,
element_type="hex",
cut_threshold=None,
portion=1. / 8.):
"""Similar to QuadBall but hollow and creates only 1/8th or 1/4th or 1/2th of the sphere.
Starting and ending angles are not supported. Radial division (nthick: to be consistent
with SphericalArc method of Mesh class) is supported
input:
cut_threshold [float] cutting threshold for element removal since this function is based
QuadBall. Ideal value is zero, so prescribe a value as close to zero
as possible, however that might not always be possible as the cut
might take remove some wanted elements [default = -0.01]
portion [float] portion of the sphere to take. Can only be 1/8., 1/4., 1/2.
"""
assert inner_radius < outer_radius
mm = QuadBallSurface(n=n, element_type=element_type)
offset = outer_radius * 2.
if cut_threshold is None:
cut_threshold = -0.01
if portion == 1. / 8.:
mm.RemoveElements(
np.array([[cut_threshold, cut_threshold, cut_threshold],
[offset, offset, offset]]))
elif portion == 1. / 4.:
mm.RemoveElements(
np.array([[cut_threshold, cut_threshold, -offset],
[offset, offset, offset]]))
elif portion == 1. / 2.:
mm.RemoveElements(
np.array([[cut_threshold, -offset, -offset],
[offset, offset, offset]]))
else:
raise ValueError("The value of portion can only be 1/8., 1/4. or 1/2.")
radii = np.linspace(inner_radius, outer_radius, nthick + 1)
mesh = Mesh()
mesh.element_type = "hex"
mesh.nelem = 0
mesh.nnode = 0
for i in range(nthick):
mm1, mm2 = deepcopy(mm), deepcopy(mm)
if not np.isclose(radii[i], 1):
mm1.points *= radii[i]
if not np.isclose(radii[i + 1], 1):
mm2.points *= radii[i + 1]
if i == 0:
elements = np.hstack(
(mm1.elements, mm1.nnode + mm2.elements)).astype(np.int64)
mesh.elements = np.copy(elements)
mesh.points = np.vstack((mm1.points, mm2.points))
else:
elements = np.hstack(
(mesh.elements[(i - 1) * mm2.nelem:i * mm2.nelem, 4:],
mesh.nnode + mm2.elements)).astype(np.int64)
mesh.elements = np.vstack((mesh.elements, elements))
mesh.points = np.vstack((mesh.points, mm2.points))
mesh.nelem = mesh.elements.shape[0]
mesh.nnode = mesh.points.shape[0]
mesh.elements = np.ascontiguousarray(mesh.elements, dtype=np.int64)
mesh.nelem = mesh.elements.shape[0]
mesh.nnode = mesh.points.shape[0]
mesh.GetBoundaryFaces()
mesh.GetBoundaryEdges()
mesh.points[:, 0] += center[0]
mesh.points[:, 1] += center[1]
mesh.points[:, 2] += center[2]
return mesh
print("The problem requires 2D analyses. Solving", number_of_planar_surfaces, "2D problems")
for niter in range(number_of_planar_surfaces):
pmesh = Mesh()
if mesh.element_type == "tet":
pmesh.element_type = "tri"
no_face_vertices = 3
elif mesh.element_type == "hex":
pmesh.element_type = "quad"
no_face_vertices = 4
else:
raise ValueError("Curvilinear mesher for element type {} not yet implemented".format(mesh.element_type))
pmesh.elements = mesh.faces[planar_mesh_faces[planar_mesh_faces[:,1]==surface_flags[niter,0],0],:]
pmesh.nelem = np.int64(surface_flags[niter,1])
pmesh.GetBoundaryEdges()
unique_edges = np.unique(pmesh.edges).astype(nodesDBC.dtype)
# Dirichlet2D = np.zeros((unique_edges.shape[0],3))
# nodesDBC2D = np.zeros(unique_edges.shape[0]).astype(np.int64)
unique_elements, inv = np.unique(pmesh.elements, return_inverse=True)
unique_elements = unique_elements.astype(nodesDBC.dtype)
aranger = np.arange(unique_elements.shape[0],dtype=np.uint64)
pmesh.elements = aranger[inv].reshape(pmesh.elements.shape)
# counter = 0
# for i in unique_edges:
# nodesDBC2D[counter] = np.where(nodesDBC==i)[0][0]
# Dirichlet2D[counter,:] = Dirichlet[nodesDBC2D[counter],:]
# counter += 1
# nodesDBC2D = nodesDBC2D.astype(np.int64)
