Mesh example: More geometry

This example is from from Calfem for Pyhon Mesh Manual (Mesh_Ex_02.py)

Creating geometry from B-Splines and circle arcs. Also shows how to set ID numbers for geometry entities and how to specify element density.

import numpy as np

import calfem.geometry as cfg
import calfem.mesh as cfm
import calfem.vis_mpl as cfv

Define geometry

All mesh generation starts by creating a Geometry object.

g = cfg.Geometry()

Add points

In this example we set the IDs manually.

g.point([-2,  0], ID=0)

elSize determines the size of the elements near this point.

g.point([0,  1], ID=1, el_size=5)

elSize is 1 by default. Larger number means less dense mesh. Size means the length of the sides of the elements.

g.point([1,  0], 2, el_size=5)
g.point([0, -2], 3)
g.point([0,  0], 4, el_size=5)
g.point([.5, .2], 5)
g.point([-.5, .5], 6)
g.point([-.7, -.5], 7)

Add curves

The 3 points that define the circle arc are [start, center, end]. The arc must be smaller than Pi.

g.circle([1, 4, 2], 2)

BSplines are similar to Splines, but do not necessarily pass through the control points.

g.bspline([5, 6, 7, 5], 5)
g.bspline([1, 0, 3, 2], 4)

Add surfaces

g.surface([4, 2], [[5]])

Markers do not have to be set when the curve is created. It can be done afterwards. Set marker=80 for curves 2 and 4:

for curveID in [2, 4]:
    g.curve_marker(curveID, 80)

Generate mesh

Create a mesh object and set its attributes.

mesh = cfm.GmshMesh(g)

mesh.el_type = 3
mesh.dofs_per_node = 2
mesh.el_size_factor = 0.05

Create the finite element mesh using the create() method of the mesh object.

coords, edof, dofs, bdofs, elementmarkers = mesh.create()

Info    : GMSH -> Python-module

Visualise mesh

Draw geometry

%matplotlib inline
# %matplotlib widget

cfv.figure(fig_size=(8,8))
cfv.draw_geometry(
    g,
    label_curves=True,
    title="Example 2 - Geometry"
)

Draw mesh

cfv.figure(fig_size=(8,8))
cfv.draw_mesh(
    coords=coords,
    edof=edof,
    dofs_per_node=mesh.dofs_per_node,
    el_type=mesh.el_type,
    filled=True,
    title="Example 2 - Mesh"
)