Mesh#

class planestress.pre.mesh.Mesh[source]#

Bases: object

Class for a plane-stress mesh.

Variables:

nodes (npt.NDArray[np.float64]) – List of nodes describing the mesh, e.g. [[x1, y1], [x2, y2], ... ].
elements (list[FiniteElement]) – List of finite element objects in the mesh.
line_elements (list[LineElement]) – List of line element objects in the mesh.
triangulation (list[tuple[int, int, int]]) – List of indexes defining the triangles in the mesh (quads & higher order elements converted to triangles) for plotting purposes.
materials (list[Material]) – List of material objects for each region in the mesh.
tagged_nodes (list[TaggedNode]) – List of nodes tagged in the mesh.
tagged_lines (list[TaggedLine]) – List of lines tagged in the mesh.
nodes_str_tree (shapely.STRtree) – A shapely.STRtree of the nodes in the mesh.
tagged_nodes_str_tree (shapely.STRtree) – A shapely.STRtree of the tagged nodes in the mesh.
tagged_lines_str_tree (shapely.STRtree) – A shapely.STRtree of the tagged lines in the mesh.
bbox (tuple[float, float, float, float, float, float]) – Bounding box of the model geometry (xmin, ymin, zmin, xmax, ymax, zmax).

Methods

`check_nearest_tol`	Checks if the point 1 is relatively close to point 2.
`create_mesh`	Creates a mesh from geometry using gmsh.
`create_triangulation`	Creates a list of triangle indexes that are used for plotting purposes.
`get_finite_element_by_tag`	Returns a `FiniteElement` given an element tag.
`get_line_element_by_tag`	Returns a `LineElement` given an element tag.
`get_node_idx_by_coordinates`	Returns the node index at or nearest to the point (`x`, `y`).
`get_tagged_line`	Returns a `TaggedLine` given a line tag.
`get_tagged_line_by_coordinates`	Returns a `TaggedLine` closest to the line defined by two points.
`get_tagged_node`	Returns a `TaggedNode` given a node tag.
`get_tagged_node_by_coordinates`	Returns a `TaggedNode` at or nearest to the point (`x`, `y`).
`num_nodes`	Returns the number of nodes in the mesh.
`plot_mesh`	Plots the finite element mesh.
`save_mesh`	Saves the generated gmsh to the `Mesh` object.

Attributes

`nodes`
`elements`
`line_elements`
`triangulation`
`materials`
`tagged_nodes`
`tagged_lines`
`nodes_str_tree`
`tagged_nodes_str_tree`
`tagged_lines_str_tree`
`bbox`

create_mesh(points: list[Point], facets: list[Facet], curve_loops: list[CurveLoop], surfaces: list[Surface], materials: list[Material], embedded_geometry: list[Point | Facet], mesh_sizes: list[float], quad_mesh: bool, mesh_order: int, serendipity: bool, mesh_algorithm: int, subdivision_algorithm: int, fields: list[Field], verbosity: int = 0) → None[source]#

Creates a mesh from geometry using gmsh.

Parameters:

points (list[Point]) – List of Point objects.
facets (list[Facet]) – List of Facet objects.
curve_loops (list[CurveLoop]) – List of CurveLoop objects.
surfaces (list[Surface]) – List of Surface objects.
materials (list[Material]) – A list of Material objects for each region in the mesh.
embedded_geometry (list[Point | Facet]) – List of embedded points and lines.
mesh_sizes (list[float]) – A list of the characteristic mesh lengths for each region in the mesh.
quad_mesh (bool) – If set to True, recombines the triangular mesh to create quadrilaterals.
mesh_order (int) – Order of the mesh, 1 - linear or 2 - quadratic.
serendipity (bool) – If set to True, creates serendipity elements for quadrilateral meshes.
mesh_algorithm (int) – Gmsh mesh algorithm, see https://gmsh.info/doc/texinfo/gmsh.html#index-Mesh_002eAlgorithm
subdivision_algorithm (int) – Gmsh subdivision algorithm, see https://gmsh.info/doc/texinfo/gmsh.html#index-Mesh_002eSubdivisionAlgorithm
fields (list[Field]) – A list of Field objects, describing mesh refinement fields.
verbosity (int) – Gmsh verbosity level, see https://gmsh.info/doc/texinfo/gmsh.html#index-General_002eVerbosity. Defaults to 0.

save_mesh(materials: list[Material], surface_orientated: list[bool]) → None[source]#

Saves the generated gmsh to the Mesh object.

Parameters:

materials (list[Material]) – List of material objects.
surface_orientated (list[bool]) – List describing if surface is correctly oriented.

Raises:

ValueError – If there is an unsupported gmsh element type in the mesh.

create_triangulation() → None[source]#

Creates a list of triangle indexes that are used for plotting purposes.

Elements that are not three-noded triangles need to be further subdivided into triangles to allow for the use of triangular plotting functions in post-processing.

num_nodes() → int[source]#

Returns the number of nodes in the mesh.

Returns:: Number of nodes in the mesh.
Return type:: int

check_nearest_tol(point1: tuple[float, float], point2: tuple[float, float]) → bool[source]#

Checks if the point 1 is relatively close to point 2.

The acceptable tolerance is taken to be 1% of the minimum dimension of the bounding box.

Parameters:

point1 (tuple[float, float]) – Location of point 1 (x, y).
point2 (tuple[float, float]) – Location of point 2 (x, y).

Returns:

True if point 1 is relatively close to point 2.

Return type:

bool

get_node_idx_by_coordinates(x: float, y: float) → int[source]#

Returns the node index at or nearest to the point (x, y).

Parameters:

x (float) – x location of the node to find.
y (float) – y location of the node to find.

Raises:

ValueError – If the point is not close to a node.

Returns:

Index of the node closest to (x, y).

Return type:

int

get_tagged_node(tag: int) → TaggedNode[source]#

Returns a TaggedNode given a node tag.

Parameters:: tag (int) – Node tag.
Raises:: ValueError – If there is no TaggedNode with a tag equal to tag.
Returns:: Tagged node identified by tag.
Return type:: TaggedNode

get_tagged_node_by_coordinates(x: float, y: float) → TaggedNode[source]#

Returns a TaggedNode at or nearest to the point (x, y).

Parameters:

x (float) – x location of the tagged node to find.
y (float) – y location of the tagged node to find.

Raises:

ValueError – If the point is not close to a tagged node.

Returns:

Tagged node closest to (x, y).

Return type:

TaggedNode

get_tagged_line(tag: int) → TaggedLine[source]#

Returns a TaggedLine given a line tag.

Parameters:: tag (int) – Line tag.
Raises:: ValueError – If there is no TaggedLine with a tag equal to tag.
Returns:: Tagged line identified by tag.
Return type:: TaggedLine

get_tagged_line_by_coordinates(point1: tuple[float, float], point2: tuple[float, float]) → TaggedLine[source]#

Returns a TaggedLine closest to the line defined by two points.

Raises:

ValueError – If the line is not close to a tagged line.

Parameters:

point1 (tuple[float, float]) – First point (x, y) of the tagged line to find.
point2 (tuple[float, float]) – Second point (x, y) of the tagged line to find.

Returns:

Tagged line closest to the line defined by two points.

Return type:

TaggedLine

get_line_element_by_tag(tag: int) → LineElement[source]#

Returns a LineElement given an element tag.

Parameters:: tag (int) – Line element tag.
Raises:: ValueError – If there is no LineElement with a tag equal to tag.
Returns:: Line element identified by tag.
Return type:: LineElement

get_finite_element_by_tag(tag: int) → FiniteElement[source]#

Returns a FiniteElement given an element tag.

Parameters:: tag (int) – Finite element tag.
Raises:: ValueError – If there is no FiniteElement with a tag equal to tag.
Returns:: Finite element identified by tag.
Return type:: FiniteElement

plot_mesh(title: str, materials: bool, node_indexes: bool, element_indexes: bool, alpha: float, ux: npt.NDArray[np.float64] | None = None, uy: npt.NDArray[np.float64] | None = None, **kwargs: Any) → matplotlib.axes.Axes[source]#

Plots the finite element mesh.

Plots a deformed mesh if ux and/or uy is provided. In this case, the undeformed mesh is also plotted with alpha=0.2 and materials is set to False.

Parameters:

title (str) – Plot title.
materials (bool) – If set to True shades the elements with the specified material colors.
node_indexes (bool) – If set to True, plots the indexes of each node.
element_indexes (bool) – If set to True, plots the indexes of each element.
alpha (float) – Transparency of the mesh outlines, \(0 \leq \alpha \leq 1\).
ux (npt.NDArray[np.float64] | None) – Deformation component in the x direction. Defaults to None.
uy (npt.NDArray[np.float64] | None) – Deformation component in the y direction. Defaults to None.
kwargs (dict[str, Any]) – Other keyword arguments are passed to plotting_context().

Returns:

Matplotlib axes object.

Return type:

matplotlib.axes.Axes