Stationary heat conduction in a 2D truss

The truss of elasticity_2D, conducting heat instead of carrying load. Each bar conducts along its own axis, so the heat routes through the members.

import torch

from torchfem import TrussHeat
from torchfem.materials import IsotropicConductivity1D

torch.set_default_dtype(torch.float64)

Model setup

# Create material
material = IsotropicConductivity1D(50.0)

n1 = torch.linspace(0.0, 4.0, 5)
n2 = torch.linspace(0.0, 1.0, 2)
n1, n2 = torch.stack(torch.meshgrid(n1, n2, indexing="xy"))
nodes = torch.stack([n1.ravel(), n2.ravel()], dim=1)

elements = torch.tensor(
    [
        [0, 1],
        [1, 2],
        [2, 3],
        [3, 4],
        [5, 6],
        [6, 7],
        [7, 8],
        [8, 9],
        [1, 5],
        [0, 6],
        [2, 6],
        [1, 7],
        [3, 7],
        [2, 8],
        [4, 8],
        [3, 9],
        [1, 6],
        [2, 7],
        [3, 8],
        [4, 9],
    ]
)

# Create truss
truss = TrussHeat(nodes, elements, material)

# Set boundary conditions: cold at the left end, hot at the right
truss.constraints[[0, 5]] = True
truss.constraints[[4, 9]] = True
truss.temperatures[[4, 9]] = 100.0

# Visualize truss
truss.plot(node_labels=True)

Solve

temp, rfl, q, temp_grad, _ = truss.solve()

Visualize the axial heat flux

A bar between two nodes of equal temperature carries none, so the vertical members drop out and the heat travels along the chords and diagonals.

truss.plot(element_property={"Heat flux |q|": q.abs()})