Shell stationary heat problem

Compute the stationary temperature distribution in a curved shell.

import torch

from torchfem.data import get_data
from torchfem.io import import_shell
from torchfem.materials import IsotropicConductivity2D

# Set default data type to double precision
torch.set_default_dtype(torch.float64)

# Wall thickness t and vessel radius R
t = 6.0
R = 100.0

Static heat equation on a curved surface

# Material model
material = IsotropicConductivity2D(kappa=6.0e-3)

# Import one octant of a pressure vessel, closed by three symmetry planes
vessel = import_shell(get_data("copv.vtu"), material, thickness=t)
nodes = vessel.nodes

# Hot boss at the dome apex
boss = nodes[:, 1:].norm(dim=1) < 0.2 * R
vessel.constraints[boss] = True
vessel.temperatures[boss, 0] = 150.0

# Cooled cradle at mid-length
cradle = nodes[:, 0] >= -0.001
vessel.constraints[cradle] = True
vessel.temperatures[cradle, 0] = 20.0

# The symmetry planes carry no flux, which needs no boundary condition

# Solve
temp, rfl, hf, temp_grad, _ = vessel.solve()

vessel.plot(node_property={"Temperature": temp}, colormap="magma")