mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-09-28 20:46:58 +00:00
56 lines
2.0 KiB
Markdown
56 lines
2.0 KiB
Markdown
|
# [Thermo-elasticity: multi-field walkthrough](@id thermo_elastic_walkthrough)
|
|||
|
|
|
|||
|
|
This page is a **narrative companion** to
|
|||
|
|
[`test/domains/thermo_elastic/test_thermo_elastic_kernel.jl`](https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/test/domains/thermo_elastic/test_thermo_elastic_kernel.jl),
|
|||
|
|
which is the executable contract for the coupled `u` + `T` path through the
|
|||
|
|
DOF-based assembler.
|
|||
|
|
|
|||
|
|
## What you assemble
|
|||
|
|
|
|||
|
|
`ThermoElasticKernel` couples vertex displacement `u` (3 DOFs per node) with
|
|||
|
|
vertex temperature `T` (1 DOF per node). The global stiffness has blocks
|
|||
|
|
`K_uu`, `K_TT`, and (when the coupling coefficient `β ≠ 0`) off-diagonal
|
|||
|
|
`K_uT` / `K_Tu`. With `β = 0` the kernel is block-diagonal and matches
|
|||
|
|
independent elasticity and heat solves on the same mesh.
|
|||
|
|
|
|||
|
|
## Minimal code (block-diagonal smoke)
|
|||
|
|
|
|||
|
|
The following uses the same material stack as the regression test, a small
|
|||
|
|
`Hex8` box, and `DOFBasedCOOCache` (the multi-field kernel is wired through this
|
|||
|
|
cache type rather than the narrow `create_cache` overload used for
|
|||
|
|
`ContinuumKernel` alone).
|
|||
|
|
|
|||
|
|
```julia
|
|||
|
|
using JuliaFEM
|
|||
|
|
using SparseArrays
|
|||
|
|
|
|||
|
|
mesh = create_structured_box_mesh(Hex8;
|
|||
|
|
xmin = 0.0, xmax = 1.0, nx = 2,
|
|||
|
|
ymin = 0.0, ymax = 1.0, ny = 2,
|
|||
|
|
zmin = 0.0, zmax = 1.0, nz = 2,
|
|||
|
|
)
|
|||
|
|
|
|||
|
|
mech = LinearElastic(E = 210e9, ν = 0.3)
|
|||
|
|
therm = HeatConductivity(k = 50.2)
|
|||
|
|
β = 0.0
|
|||
|
|
kernel = ThermoElasticKernel(ContinuumFormulation{FullThreeD}(), mech, therm, β)
|
|||
|
|
|
|||
|
|
S = @DOFSet{u::DOF{Displacement{3}, Vertex},
|
|||
|
|
T::DOF{Temperature, Vertex}}
|
|||
|
|
elements, handler = create_elements!(mesh, Element{Hex8, Lagrange{1}, S})
|
|||
|
|
|
|||
|
|
asm = DOFBasedCOOAssembler()
|
|||
|
|
cache = DOFBasedCOOCache(elements, handler, mesh, kernel)
|
|||
|
|
assemble!(cache, asm, kernel, mesh)
|
|||
|
|
K, f = extract_system(cache)
|
|||
|
|
|
|||
|
|
@assert size(K, 1) == size(K, 2) == 108
|
|||
|
|
@assert nnz(K) == 5488
|
|||
|
|
```
|
|||
|
|
|
|||
|
|
## Where to read next
|
|||
|
|
|
|||
|
|
- Kernel source and coupling equations: `src/domains/thermo_elastic/kernel.jl`.
|
|||
|
|
- Compile-time DOF layout: `local_dof_layout(Element{Hex8, Lagrange{1}, S})`.
|
|||
|
|
- Matrix-free parity with `K * x`: same test file as above.
|