Analysis and visualization of a multi-mesh model

This example combines quadrilateral and triangular elements that share the same node array. Each element block has its own assembly, while their sum is used to solve a single mechanical problem.

Results requested from the assembly sum are stored in a fedoo.MultiMesh. Fedoo can therefore visualize all element blocks directly with one fedoo.DataSet.plot() call.

import fedoo as fd
import numpy as np

Build a mesh containing different element types

A MultiMesh owns one common node array and an ordered collection of element blocks. Named entries make each submesh easy to retrieve later. The tuple associated with each name contains its element type and connectivity.

nodes = np.array(
    [
        [0.0, 0.0],
        [1.0, 0.0],
        [0.0, 1.0],
        [1.0, 1.0],
        [0.5, 1.866],
    ]
)
mesh = fd.MultiMesh(
    nodes,
    {
        "quadrilateral": ("quad4", np.array([[0, 1, 3, 2]])),
        "triangle": ("tri3", np.array([[2, 3, 4]])),
    },
    node_sets={"left": np.array([0, 2]), "right": np.array([1, 3])},
    name="mixed_mesh",
)

# Define equations as usual (constitutivelaw + weakform)
fd.ModelingSpace("2Dstress")
material = fd.constitutivelaw.ElasticIsotrop(2e5, 0.3)
wf = fd.weakform.StressEquilibrium(material)

# Create a global assembly
# Assemblies are created on the individual element blocks and then combined
# into the assembly used by the problem.
assembly1 = fd.Assembly.create(wf, mesh["quadrilateral"])
assembly2 = fd.Assembly.create(wf, mesh["triangle"])
assembly = assembly1 + assembly2

# Define a new static problem
pb = fd.problem.Linear(assembly)

# Clamp the left side and prescribe a horizontal displacement on the right.
pb.bc.add("Dirichlet", mesh.node_sets["left"], "Disp", 0)
pb.bc.add("Dirichlet", mesh.node_sets["right"], "DispX", 0.5)


# Solve problem
pb.solve()

Extract and plot multi-mesh results

get_results collects the fields from both elementary assemblies. The resulting dataset retains the quadrilateral and triangular submeshes and their element data independently. Nevertheless, the complete model can be drawn directly with the usual Fedoo plotting function.

results = pb.get_results(["Stress", "Disp", "Strain"])
plotter = results.plot(
    "Stress",
    component="vm",
    data_type="Node",
    show=False,
    show_edges=True,
    show_nodes=True,
    title="Von Mises stress on a MultiMesh",
)
plotter.show()