Linear triangle elements

The linear triangle is a three-node constant-strain triangle (CST) for 2D plane stress. Each node contributes ux and uy displacement DOFs, with corresponding fx and fy nodal forces.

Use nusa.model.LinearTriangleModel with nusa.element.LinearTriangle.

Element properties

A CST element requires a material with Young’s modulus E and Poisson’s ratio nu, plus an explicitly specified thickness:

material = Material(E=200e9, nu=0.3)
element = LinearTriangle(
    (n1, n2, n3),
    material=material,
    thickness=0.1,
)

The canonical element result contains constant strain and stress components:

strain_xx
strain_yy
strain_xy
stress_xx
stress_yy
stress_xy

Example: single CST element

The following example builds a single triangular element, constrains two nodes, applies an in-plane load, solves the model, and plots nodal fields.

 1# -*- coding: utf-8 -*-
 2# ***********************************
 3#  Author: Pedro Jorge De Los Santos
 4#  E-mail: delossantosmfq@gmail.com
 5#  License: MIT License
 6# ***********************************
 7
 8import matplotlib.pyplot as plt
 9
10from nusa import LinearTriangle, LinearTriangleModel, Material, Node, plot_model
11
12
13def build_model():
14    model = LinearTriangleModel("Single CST")
15
16    n1 = Node((0.0, 0.0))
17    n2 = Node((1.0, 0.5))
18    n3 = Node((0.0, 1.0))
19
20    material = Material(E=200e9, nu=0.3)
21    model.add_nodes([n1, n2, n3])
22    model.add_element(
23        LinearTriangle((n1, n2, n3), material=material, thickness=0.1)
24    )
25    model.add_constraint(n1, ux=0.0, uy=0.0)
26    model.add_constraint(n3, ux=0.0, uy=0.0)
27    model.add_force(n2, (1000.0, 0.0))
28    return model
29
30
31def main():
32    model = build_model()
33    plot_model(model)
34
35    result = model.solve()
36    result.plot_nodal_field("ux")
37    result.plot_nodal_field("stress_xx")
38    plt.show()
39
40
41if __name__ == "__main__":
42    main()

Element and nodal fields

Element fields are read directly from the canonical element results:

result.element_field("stress_xx")

Nodal fields can be recovered from element values:

result.nodal_field("stress_xx")

For the current CST implementation, element scalar fields are recovered to nodes using arithmetic averaging over adjacent elements.

Derived fields

NuSA also provides selected derived nodal fields:

result.nodal_field("displacement_magnitude")
result.nodal_field("von_mises_stress")

Legacy short aliases such as sxx and seqv are still accepted by the post-processing helpers, while the canonical names are preferred in new code.

Visualization

Problem geometry, loads, and constraints are plotted from the model:

from nusa import plot_model

plot_model(model)

Solved scalar fields are plotted from the result:

result.plot_nodal_field("stress_xx")
result.plot_element_field("stress_xx")

This distinction is especially useful for continuum problems because the mesh belongs to the problem definition while stress/strain fields belong to a particular analysis result.