Create a mesh#

A mesh is a discrete representation of the simulation domain. Meshes are produced by Mesher (which wraps Gmsh) and are accessible in the EasyFEA.FEM module.

Note

To import an existing mesh file instead of creating one from scratch, see Import a mesh.

Geometry objects#

Mesh generation relies on manipulating the geometric objects listed below, which are available in the EasyFEA.Geoms namespace:

Class

Description

Point

Single point; optional fillet radius r

Line

Straight segment between two points

Circle

Full circle defined by center and diameter

CircleArc

Circular arc (from radius, center, or on-circle point)

Points

Closed polygon / spline from a list of points

Contour

Closed loop assembled from Line, CircleArc, and/or Points

Domain

Axis-aligned rectangle or box defined by two corners

meshSize on any geometry object sets the local target element size. isHollow=True (the default) means the geometry defines a hole or boundary only; isHollow=False means it defines a filled region.

Tip

All examples below use Display (matplotlib) for inline output. For interactive 3D visualization, replace Display.Plot_Mesh(mesh) with PyVista.Plot_Mesh(mesh) — see Post-process simulation results.

2D mesh#

Mesh_2D() meshes the surface of the geometry, with optional inclusions (holes, filled regions), cracks, and local refinement.

Simple rectangle#

from EasyFEA import Display, ElemType
from EasyFEA.Geoms import Domain

domain = Domain((0, 0), (100, 20), meshSize=5.0)
mesh = domain.Mesh_2D([], ElemType.TRI3)
Display.Plot_Mesh(mesh)
Display.Plot_Tags(mesh)

<Axes: xlabel='$x$', ylabel='$y$'>
../_images/create_mesh_0_1.png ../_images/create_mesh_0_2.png

Rectangle with a circular hole#

from EasyFEA import Display, ElemType
from EasyFEA.Geoms import Domain, Circle

domain = Domain((0, 0), (100, 50), meshSize=5.0)
hole   = Circle(center=(50, 25), diam=20, meshSize=1.0, isHollow=True)

mesh = domain.Mesh_2D([hole], ElemType.TRI3)
Display.Plot_Mesh(mesh)

<Axes: title={'center': 'TRI3: Ne = 1256, Nn = 690'}, xlabel='$x$', ylabel='$y$'>
../_images/create_mesh_1_1.png

Structured quad mesh#

By setting isOrganised=True, you obtain a structured mesh that requires a structurable polygon consisting of four or three segments:

from EasyFEA import Display, ElemType
from EasyFEA.Geoms import Domain

domain = Domain((0, 0), (100, 20), meshSize=5.0)
mesh = domain.Mesh_2D([], ElemType.QUAD4, isOrganised=True)
Display.Plot_Mesh(mesh)

<Axes: title={'center': 'QUAD4: Ne = 80, Nn = 105'}, xlabel='$x$', ylabel='$y$'>
../_images/create_mesh_2_1.png

3D mesh by extrusion#

Mesh_Extrude() creates a 3D volume by extruding a 2D surface along a direction vector.

from EasyFEA import Display, ElemType
from EasyFEA.Geoms import Domain

domain = Domain((0, 0), (100, 20), meshSize=5.0)
mesh = domain.Mesh_Extrude(
    extrude=(0, 0, 10),   # extrusion direction and length
    layers=[3],            # number of layers along the extrusion
    elemType=ElemType.HEXA8,
    isOrganised=True,
)
Display.Plot_Mesh(mesh)

<Axes3D: title={'center': 'HEXA8: Ne = 240, Nn = 420'}, xlabel='$x$', ylabel='$y$', zlabel='$z$'>
../_images/create_mesh_3_1.png

3D mesh by revolution#

Mesh_Revolve() sweeps a 2D cross-section around an axis to create an axisymmetric volume.

from EasyFEA import Display, ElemType
from EasyFEA.Geoms import Domain, Line, Point

cross_section = Domain((5, 0), (8, 8), meshSize=2.0)

# revolution axis: Y-axis
axis = Line((0, 0), (0, 1))

mesh = cross_section.Mesh_Revolve(
    axis=axis,
    angle=270,
    layers=[30],    # number of angular divisions
    elemType=ElemType.PRISM6,
)
Display.Plot_Mesh(mesh)

<Axes3D: title={'center': 'PRISM6: Ne = 540, Nn = 496'}, xlabel='$x$', ylabel='$y$', zlabel='$z$'>
../_images/create_mesh_4_1.png

Element types#

The types of isoparametric geometric elements that can be used to discretize the domain are available in the ElemType class.