FEM.Geometry package¶

Meshing and geometry definitions

Submodules¶

FEM.Geometry.Geometree module¶

DEPRECATED

This class was my introduction to OctTrees. I implemented all geometry with this class. Then, I realized SciPy has a KDTree implementation, faster and better. IDK what to tink about it

class FEM.Geometry.Geometree.Geometree(boundary, n: int = 1, depth: int = 1)¶

Bases: object

add_point(p: tuple) → bool¶

contains(p: tuple) → bool¶

draw(ax)¶

draw_points(ax)¶

graph_query_range(p, r)¶

min_search_size = -1¶

query_first_point_set()¶

query_range(quadrant, plot=False, ax=None) → bool¶

query_range_point_radius(p, r=None, plot=False, ax=None)¶

subdivide() → None¶

class FEM.Geometry.Geometree.Quadrant3D(p: tuple, dim: tuple)¶

Bases: object

boxes_disjoint(e)¶

contains(e) → bool¶

draw(ax)¶

draw_(ax)¶

intesects_quadrant(e) → bool¶

subdivide() → list¶

class FEM.Geometry.Geometree.Quadrant3DSpherical(p: tuple, r: tuple)¶

Bases: Quadrant3D

contains(e) → bool¶

FEM.Geometry.Geometry module¶

Geometry definitions.

class FEM.Geometry.Geometry.Delaunay(vertices: list, params: str, nvn: int = 1, holes_dict=None, fillets=None, fast=False, extra_segs=None)¶

Bases: Geometry2D

Generate Delaunay triangulation using Triangle

Parameters:

vertices (list) – matrix containing the domain vertices coordinates
params (str) – Triangulation parameters, use the aux function _strdelaunay
nvn (int, optional) – Number of variables per node. Defaults to 1.
holes_dict (list, optional) – A list of holes dicts. Defaults to None.
fillets (list, optional) – A list of fillets. Defaults to None.
fast (bool, optional) – If True, the created elements will have have the fast propertie (see Element class docs)

extrude(h: float = 1.0, m: int = 5, **kargs) → Geometry3D¶

class FEM.Geometry.Geometry.Geometry(dictionary: list, gdls: list, types: list, nvn: int = 1, regions: list[Region] | None = None, fast=False)¶

Bases: object

Define a general geometry structure

Parameters:

dictionary (list) – Matrix with element definitions. Each row is an element. The gdl are defined in columns
gdls (list) – List of domain coordinates
types (list) – Types of each element
nvn (int, optional) – Nunmber of variables per node. Defaults to 1.
regions (list, optional) – List of domain regions. Defaults to [].
fast (bool) – If True, the created elements will have have the fast propertie (see Element class docs)

addRegions(regions: list[Region]) → None¶

Adds regions to an already created geometry

Parameters:: regions (list[Region]) – Regions to be created

calculateCentroids() → None¶: Calculate elements centroids

calculateRegions() → None¶: Calculates the nodes of the geometry regions

cbFromRegion(region: int, value: float, nv: int = 1) → list¶

Generate a list of boundary conditions from specified boundary.

Parameters:

region (int) – region number
value (float) – Value of the bc
nv (int, optional) – Variable number, starts with 1. Defaults to 1.

Returns:

List of boundary conditions that can be concatenated or assigned to the geometry

Return type:

list

cbeAllRegions(value: float) → None¶

Set all regions boundary conditions to the specified value to all the variables.

Parameters:: value (float) – Value of the boundary condition

detectNonLocal(lr: float) → list¶

Detect adjacent elements between a distance Lr. Uses KDTrees

Parameters:: lr (float) – Distance to detect adjacent elements
Returns:: Non local element dictionary
Return type:: list

detectNonLocalLegacy(lr: float) → list¶

Detect adjacent elements between a distance Lr. Uses iterative approach :param lr: Distance to detect adjacent elements :type lr: float

Returns:: Non local element dictionary
Return type:: list

exportJSON(filename: str | None = None) → str¶

Export geometry definition as JSON file or JSON string

Parameters:: filename (str, optional) – If given, a JSON file is created. Defaults to None.
Returns:: JSON string
Return type:: str

generateElements() → None¶: Generate elements structure

giveElementsOfRegion(region: int, centroid=False) → list¶

Give elements over a region

Parameters:

region (int) – region number. Start with 0
centroid (bool) – To use the centroid as find method. Defaults to false. Use the nodes

Returns:

List of elements in the specified region

Return type:

list

giveNodesOfRegion(region: int) → ndarray¶

Give nodes over a region

Parameters:: region (int) – region number. Start with 0
Returns:: List of nodes in the specified region
Return type:: np.ndarray

giveRegions() → list¶

Returns a list of regions coordinates matrix

Returns:: List of regions coordinates matrix
Return type:: list

classmethod importJSON(filename: str, **kargs) → Geometry¶

Import geometry definition from JSON file

Parameters:: filename (str) – Path to the JSON file
Returns:: Geometry generated using the JSON file
Return type:: Geometry

initialize() → None¶: Calculates the total number of GDL’s and generates the elements structure

maskFromRegions() → None¶: Create the display mask from geometry regions

setCbe(cbe: list) → None¶

This method have to be used to assign essential boundary conditions. Thes method prevents to assign duplicated boundary conditions

Parameters:: cbe (list) – Boundary conditions to be applied

show() → None¶: Creates a geometry graph

class FEM.Geometry.Geometry.Geometry1D(dictionary: list, gdls: list, types: list, nvn: int = 1, fast=False)¶

Bases: Geometry

Define an 1D geometry structure

Parameters:

dictionary (list) – Matrix with element definitions. Each row is an element. The gdl are defined in columns
gdls (list) – List of domain coordinates
types (list) – Types of each element
nvn (int, optional) – Nunmber of variables per node. Defaults to 1.
fast (bool, optional) – If True, the created elements will have have the fast propertie (see Element class docs)

show() → None¶: Create a geometry graph

class FEM.Geometry.Geometry.Geometry2D(dictionary: list, gdls: list, types: list, nvn: int = 1, regions: list[Region] | None = None, fast=False)¶

Bases: Geometry

Creates a 2D geometry

Parameters:

dictionary (list) – Matrix with element definitions. Each row is an element. The gdl are defined in columns
gdls (list) – List of domain coordinates
types (list) – Types of each element
nvn (int, optional) – Nunmber of variables per node. Defaults to 1.
regions (list[Region], optional) – List of regions to apply in the geometry. Defaults to None.
fast (bool, optional) – If True, the created elements will have have the fast propertie (see Element class docs)

cbOnHole(hole: int, value: float, nv: int = 1, sa: float = 0, ea: float = 6.283185307179586) → list¶

Generate a list of boundary conditions from specified hole.

Parameters:

hole (int) – Hole index in wich load will be applied
value (float) – Value of the bc
nv (int, optional) – Variable number, starts with 1. Defaults to 1.
sa (float, optional) – Start face angle. Defaults to 0.
ea (float, optional) – Finish face angle. Defaults to \(2\pi\).

Returns:

List of boundary conditions that can be concatenated or assigned to the geometry

Return type:

list

generateBCFromCoords(x: float, y: float, value: float = 0, nv: int = 1) → list¶

Generates boundary conditions by coordinates. The boundary condition is applied to the nearest node

Parameters:

x (float) – X coordinate of point
y (float) – Y coordinate of point
value (float, optional) – Value of the boundary condition. Defaults to 0.
nv (int, optional) – Variable number. The first variable is 1. Defaults to 1.

Returns:

Matrix of boundary coordinates that can be concatenated

Return type:

list

generateRegionFromCoords(p0: list, p1: list) → None¶

Generates a geometry Region1D by specified coordinates

Parameters:

p0 (list) – region start point
p1 (list) – region end point

loadOnHole(hole: int, sa: float = 0, ea: float = 6.283185307179586, fx: Callable | None = None, fy: Callable | None = None) → None¶

Assign loads over a hole.

Parameters:

hole (int) – Hole index in wich load will be applied
sa (float, optional) – Start face angle. Defaults to 0.
ea (float, optional) – Finish face angle. Defaults to \(2\pi\).
fx (Callable, optional) – Load Function x component. Defaults to None.
fy (Callable, optional) – Load Function y component. Defaults to None.

loadOnRegion(region: int, fx: Callable | None = None, fy: Callable | None = None, add=None) → None¶

Assign a load over a geometry region.

The start point of region is the 0 point of load The end point of region is the end point of load

Load must be defined as a function (normal or lambda)

Parameters:

region (int) – region in wich load will be applied
fx (Callable, optional) – Load Function x component. Defaults to None.
fy (Callable, optional) – Load Function y component. Defaults to None.

loadOnRegionVF(region: int, f: Callable | None = None, add=None) → None¶

Assign a load over a geometry region.

The start point of region is the 0 point of load The end point of region is the end point of load

Load must be defined as a function (normal or lambda)

Parameters:

region (int) – region in wich load will be applied
f (Callable, optional) – Load Function. Defaults to None.

normalLoadOnRegion(region: int, f: Callable | None = None, add=None) → None¶

Assign a load over a geometry region.

The start point of region is the 0 point of load The end point of region is the end point of load

Load must be defined as a function (normal or lambda)

Parameters:

region (int) – region in wich load will be applied
f (Callable, optional) – Load Function. Defaults to None.

revolve(m=10, theta=6.283185307179586, **kargs)¶

show(texto: int = 10, bolita: int = 0, draw_segs: bool = True, draw_labels: bool = False, draw_bc: bool = False, label_bc: bool = False) → None¶

Create a geometry graph

Parameters:

texto (int, optional) – Text size. Defaults to 10.
bolita (int, optional) – Node size. Defaults to 0.
draw_segs (bool, optional) – To draw or not draw the regions. Defaults to True.
draw_labels (bool, optional) – To draw or not draw element labels. Defaults to False.
draw_bc (bool, optional) – To draw boundary conditions. Defaults to False.
label_bc (bool, optional) – To draw labels on boundary conditions. Defaults to False.

class FEM.Geometry.Geometry.Geometry3D(dictionary: list, gdls: list, types: list, nvn: int = 1, regions: list[Region] | None = None, fast=False)¶

Bases: Geometry

Creates a 3D geometry

Parameters:

dictionary (list) – Matrix with element definitions. Each row is an element. The gdl are defined in columns
gdls (list) – List of domain coordinates
types (list) – Types of each element
nvn (int, optional) – Nunmber of variables per node. Defaults to 1.
regions (list[Region], optional) – List of regions to apply in the geometry. Defaults to None.
fast (bool, optional) – If True, the created elements will have have the fast propertie (see Element class docs)

detectBoundaryElements(plot=False)¶

detectBoundaryElementsLegacy()¶

isBoundary(e)¶

show() → None¶: Creates a geometry graph

class FEM.Geometry.Geometry.Lineal(lenght: float, n: int, o: int, nvn: int = 1)¶

Bases: Geometry1D

Generate a evenly spaced elements domain

Parameters:

lenght (float) – Domain lenght
n (int) – Number of elements
o (int) – Element order, can be 1 or 2
nvn (int, optional) – Number of variables per node. Defaults to 1.

class FEM.Geometry.Geometry.Orimetry(dictionary: list, gdls: list, types: list, regions: list[Region] | None = None)¶

Bases: Geometry3D

docstring for Orimetry

initialize() → None¶: Calculates the total number of GDL’s and generates the elements structure

FEM.Geometry.Region module¶

Defines geometry region. Regions are used to set boundary conditions and loads to 2D and 3D problems

class FEM.Geometry.Region.Region(coords: ndarray, desc: str = '')¶

Bases: object

Creates a general region

Parameters:: coords (np.ndarray) – Coordinates matrix of therefion. Each row is a coordinate, each column is a dimension.

setNodesOfRegion(geometry: Geometry, tol: float = 1e-05) → None¶

Calculates the nodes of the geometry which are inside the region.

Parameters:

geometry (Geometry) – Input geometry
tol (float, optional) – Near tolerance. Defaults to 10**(-5).

class FEM.Geometry.Region.Region1D(coords: ndarray, **kargs)¶

Bases: Region

Creates a line region (1D element)

Parameters:: coords (np.ndarray) – Coordinate matrix. Must be of two rows and 2 or 3 columns. 2 columns for 2D region, 3 columns for 3D region.

isBetween(p: ndarray, tol: float = 1e-05) → bool¶

Check if a given point is inside the region.

Parameters:

p (np.ndarray) – Point to be tested
tol (float, optional) – Tolerance for check. Defaults to 1*10**(-5).

Returns:

True if the point is inside the region

Return type:

bool

class FEM.Geometry.Region.Region2D(coords: ndarray, **kargs)¶

Bases: Region

Creates a square region (2D element)

Parameters:: coords (np.ndarray) – Coordinate matrix. Must be of four rows and 3 columns.

isBetween(p: ndarray, tol: float = 1e-05) → bool¶

Check if a given point is inside the region.

Parameters:

p (np.ndarray) – Point to be tested
tol (float, optional) – Tolerance for check. Defaults to 1*10**(-5).

Returns:

True if the point is inside the region

Return type:

bool

pointToPlaneDistance(p: ndarray) → float¶

Calculates the distance from a given point to the region.

Parameters:: p (np.ndarray) – Point to be tested
Returns:: Distance between the plane and the point
Return type:: float