mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-10-03 06:41:30 +00:00
Jukka Aho
85 lines
3.2 KiB
Julia
85 lines
3.2 KiB
Julia
# This file is a part of JuliaFEM.
|
||
# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
|
||
|
||
"""
|
||
`HellingerReissnerKernel`: displacement + piecewise-constant symmetric stress
|
||
on the DOF-based assembler.
|
||
|
||
1. Global `K` is numerically symmetric.
|
||
2. `K_uu` is zero (no displacement Laplace term in classical HR).
|
||
3. `K_σσ` equals `-vol · (G M⁻¹ G)` on the stress block.
|
||
4. `assemble!` allocates 0 bytes after warmup.
|
||
"""
|
||
|
||
using Test
|
||
using JuliaFEM
|
||
using JuliaFEM: HellingerReissnerKernel, ContinuumFormulation, FullThreeD
|
||
using JuliaFEM: DOFBasedCOOAssembler, DOFBasedCOOCache, assemble!, extract_system
|
||
using JuliaFEM: create_unit_cube_mesh, create_elements!, @DOFSet, DOF, Displacement, Vertex
|
||
using LinearAlgebra
|
||
using Tensors
|
||
|
||
function _hex8_unit_cube_single_element()
|
||
return create_unit_cube_mesh(Hex8; nx = 1, ny = 1, nz = 1)
|
||
end
|
||
|
||
@testset "HellingerReissnerKernel symmetry + empty displacement block" begin
|
||
mesh = _hex8_unit_cube_single_element()
|
||
mat = LinearElastic(E = 210e9, ν = 0.3)
|
||
S = @DOFSet{u::DOF{Displacement{3}, Vertex}, sig::DOF{SymmetricTensor{2,3}, Cell}}
|
||
elem, handler = create_elements!(mesh, Element{Hex8, Lagrange{1}, S})
|
||
k = HellingerReissnerKernel(ContinuumFormulation{FullThreeD}(), mat)
|
||
asm = DOFBasedCOOAssembler()
|
||
cache = DOFBasedCOOCache(elem, handler, mesh, k)
|
||
assemble!(cache, asm, k, mesh)
|
||
K, _ = extract_system(cache)
|
||
|
||
R = K - transpose(K)
|
||
@test norm(R) <= 1e-8 * max(1.0, norm(K))
|
||
|
||
n_u = 3 * length(mesh.nodes)
|
||
Kuu = K[1:n_u, 1:n_u]
|
||
@test norm(Kuu) <= 1e-10 * max(1.0, norm(K))
|
||
end
|
||
|
||
@testset "HellingerReissnerKernel K_σσ vs −vol·(G M⁻¹ G)" begin
|
||
mesh = _hex8_unit_cube_single_element()
|
||
mat = LinearElastic(E = 210e9, ν = 0.3)
|
||
S = @DOFSet{u::DOF{Displacement{3}, Vertex}, sig::DOF{SymmetricTensor{2,3}, Cell}}
|
||
elem, handler = create_elements!(mesh, Element{Hex8, Lagrange{1}, S})
|
||
k = HellingerReissnerKernel(ContinuumFormulation{FullThreeD}(), mat)
|
||
asm = DOFBasedCOOAssembler()
|
||
cache = DOFBasedCOOCache(elem, handler, mesh, k)
|
||
assemble!(cache, asm, k, mesh)
|
||
K, _ = extract_system(cache)
|
||
|
||
n_u = 3 * length(mesh.nodes)
|
||
Kss = K[(n_u + 1):end, (n_u + 1):end]
|
||
vol = 1.0 # unit cube
|
||
ref = -vol * k.σσ
|
||
@test size(Kss) == (6, 6)
|
||
@test norm(Kss - ref) / max(norm(ref), 1.0) < 1e-12
|
||
end
|
||
|
||
@testset "HellingerReissnerKernel assemble! zero allocations" begin
|
||
mesh = _hex8_unit_cube_single_element()
|
||
mat = LinearElastic(E = 210e9, ν = 0.3)
|
||
S = @DOFSet{u::DOF{Displacement{3}, Vertex}, sig::DOF{SymmetricTensor{2,3}, Cell}}
|
||
elem, handler = create_elements!(mesh, Element{Hex8, Lagrange{1}, S})
|
||
k = HellingerReissnerKernel(ContinuumFormulation{FullThreeD}(), mat)
|
||
asm = DOFBasedCOOAssembler()
|
||
cache = DOFBasedCOOCache(elem, handler, mesh, k)
|
||
for _ in 1:3
|
||
assemble!(cache, asm, k, mesh)
|
||
end
|
||
GC.gc()
|
||
@test (@allocated assemble!(cache, asm, k, mesh)) == 0
|
||
end
|
||
|
||
@testset "HellingerReissnerKernel API guards" begin
|
||
mat = LinearElastic(E = 210e9, ν = 0.3)
|
||
k = HellingerReissnerKernel(ContinuumFormulation{FullThreeD}(), mat)
|
||
@test dofs_per_node(k) == 5
|
||
@test_throws ErrorException get_field(k)
|
||
end
|