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Jukka Aho
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docs/src/thermo_elastic_walkthrough.md | 55 ++++++++++++++++++++++++++++++++++ 1 file changed, 55 insertions(+)
56 lines
2.0 KiB
Markdown
56 lines
2.0 KiB
Markdown
# [Thermo-elasticity: multi-field walkthrough](@id thermo_elastic_walkthrough)
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This page is a **narrative companion** to
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[`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),
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which is the executable contract for the coupled `u` + `T` path through the
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DOF-based assembler.
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## What you assemble
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`ThermoElasticKernel` couples vertex displacement `u` (3 DOFs per node) with
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vertex temperature `T` (1 DOF per node). The global stiffness has blocks
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`K_uu`, `K_TT`, and (when the coupling coefficient `β ≠ 0`) off-diagonal
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`K_uT` / `K_Tu`. With `β = 0` the kernel is block-diagonal and matches
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independent elasticity and heat solves on the same mesh.
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## Minimal code (block-diagonal smoke)
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The following uses the same material stack as the regression test, a small
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`Hex8` box, and `DOFBasedCOOCache` (the multi-field kernel is wired through this
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cache type rather than the narrow `create_cache` overload used for
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`ContinuumKernel` alone).
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```julia
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using JuliaFEM
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using SparseArrays
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mesh = create_structured_box_mesh(Hex8;
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xmin = 0.0, xmax = 1.0, nx = 2,
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ymin = 0.0, ymax = 1.0, ny = 2,
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zmin = 0.0, zmax = 1.0, nz = 2,
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)
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mech = LinearElastic(E = 210e9, ν = 0.3)
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therm = HeatConductivity(k = 50.2)
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β = 0.0
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kernel = ThermoElasticKernel(ContinuumFormulation{FullThreeD}(), mech, therm, β)
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S = @DOFSet{u::DOF{Displacement{3}, Vertex},
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T::DOF{Temperature, Vertex}}
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elements, handler = create_elements!(mesh, Element{Hex8, Lagrange{1}, S})
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asm = DOFBasedCOOAssembler()
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cache = DOFBasedCOOCache(elements, handler, mesh, kernel)
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assemble!(cache, asm, kernel, mesh)
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K, f = extract_system(cache)
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@assert size(K, 1) == size(K, 2) == 108
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@assert nnz(K) == 5488
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```
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## Where to read next
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- Kernel source and coupling equations: `src/domains/thermo_elastic/kernel.jl`.
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- Compile-time DOF layout: `local_dof_layout(Element{Hex8, Lagrange{1}, S})`.
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- Matrix-free parity with `K * x`: same test file as above.
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