Geometry from Coordinates

The following example demonstrates how geometry objects can be created from a list of points, facets, holes and control points.

A straight angle section with a plate at its base is created from a list of points and facets.

The bottom plate is assigned a separate control point meaning two discrete regions are created. Creating separate regions allows the user to control the mesh size in each region and assign material properties to different regions.

Import Modules

We start by importing the CompoundGeometry() object to create the geometry, and the Section() object for analysis.

from sectionproperties.analysis import Section
from sectionproperties.pre import CompoundGeometry

Create Geometry

We will define some parameters that describe the geometry of the section.

w_a = 1  # width of angle leg
w_p = 2  # width of bottom plate
d = 2  # depth of section
t = 0.1  # thickness of section

We can now build a list of points, facets and control points.

# list of points describing the geometry
points = [
    (w_p * -0.5, 0),  # bottom plate
    (w_p * 0.5, 0),
    (w_p * 0.5, t),
    (w_p * -0.5, t),
    (t * -0.5, t),  # inverted angle section
    (t * 0.5, t),
    (t * 0.5, d - t),
    (w_a - 0.5 * t, d - t),
    (w_a - 0.5 * t, d),
    (t * -0.5, d),
]

# list of facets (edges) describing the geometry connectivity
facets = [
    (0, 1),  # bottom plate
    (1, 2),
    (2, 3),
    (3, 0),
    (4, 5),  # inverted angle section
    (5, 6),
    (6, 7),
    (7, 8),
    (8, 9),
    (9, 4),
]

# list of control points (points within each region)
control_points = [
    (0, t * 0.5),  # bottom plate
    (0, d - t),  # inverted angle section
]

We can now use the CompoundGeometry.from_points() method to build our geometry. We use the CompoundGeometry variation of this method as we have two distinct regions. If there was only one region (i.e. one control point), we would use the Geometry version of this method.

geom = CompoundGeometry.from_points(
    points=points,
    facets=facets,
    control_points=control_points,
)
geom.plot_geometry()

<Axes: title={'center': 'Cross-Section Geometry'}>

Create Mesh and Section

For this mesh, we use a smaller refinement for the bottom plate region.

geom.create_mesh(mesh_sizes=[0.0005, 0.001])

sec = Section(geometry=geom)
sec.plot_mesh(materials=False)

<Axes: title={'center': 'Finite Element Mesh'}>

Perform an Analysis

We perform geometric, warping and plastic analyses.

sec.calculate_geometric_properties()
sec.calculate_warping_properties()
sec.calculate_plastic_properties()

Plot Centroids

We can plot the calculated centroids using the plot_centroids() method.

sec.plot_centroids()

<Axes: title={'center': 'Centroids'}>

Because we performed geometric, warping and plastic analyses we see the following results in the above plot:

• Geometric analysis - elastic centroid, principal axes

• Warping analysis - shear centre

• Plastic analysis - plastic centroids