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JuliaFEM.jl/test/test_mortar_2d.jl
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Julia

# This file is a part of JuliaFEM.
# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
using JuliaFEM
using JuliaFEM.Testing
function get_test_model()
X = Dict{Int, Vector{Float64}}(
1 => [0.0, 0.0], 2 => [2.0, 0.0],
3 => [0.0, 1.0], 4 => [2.0, 1.0],
5 => [0.0, 1.0], 6 => [1.3, 1.0],
7 => [0.0, 2.0], 8 => [1.3, 2.0],
9 => [1.3, 1.0], 10 => [2.0, 1.0],
11 => [1.3, 2.0], 12 => [2.0, 2.0])
T = Dict{Int, Vector{Float64}}(
7 => [0.0, 288.0], 8 => [0.0, 288.0],
11 => [0.0, 288.0], 12 => [0.0, 288.0])
# volume elements, three bodies
e1 = Element(Quad4, [1, 2, 4, 3])
e2 = Element(Quad4, [5, 6, 8, 7])
e3 = Element(Quad4, [9, 10, 12, 11])
update!([e1, e2, e3], "geometry", X)
update!([e1, e2, e3], "youngs modulus", 288.0)
update!([e1, e2, e3], "poissons ratio", 1/3)
b1 = Element(Seg2, [7, 8])
b2 = Element(Seg2, [11, 12])
update!([b1, b2], "geometry", X)
update!([b1, b2], "displacement traction force", T)
body1 = Problem(Elasticity, "body 1", 2)
body1.properties.formulation = :plane_stress
push!(body1, e1)
body2 = Problem(Elasticity, "body 2", 2)
body2.properties.formulation = :plane_stress
push!(body2, e2, b1)
body3 = Problem(Elasticity, "body 3", 2)
body3.properties.formulation = :plane_stress
push!(body3, e3, b2)
# boundary elements for dirichlet dx=0
dx1 = Element(Seg2, [1, 3])
dx2 = Element(Seg2, [5, 7])
update!([dx1, dx2], "geometry", X)
update!([dx1, dx2], "displacement 1", 0.0)
bc1 = Problem(Dirichlet, "dx=0", 2, "displacement")
push!(bc1, dx1, dx2)
# boundary elements for dirichlet dy=0
dy1 = Element(Seg2, [1, 2])
update!(dy1, "geometry", X)
update!(dy1, "displacement 2", 0.0)
bc2 = Problem(Dirichlet, "dy=0", 2, "displacement")
push!(bc2, dy1)
# mortar boundary between body 1 and body 2
mel1 = Element(Seg2, [3, 4])
sel1 = Element(Seg2, [5, 6])
update!([mel1, sel1], "geometry", X)
update!(sel1, "master elements", [mel1])
bc3 = Problem(Mortar, "interface between body 1 and 2", 2, "displacement")
push!(bc3, mel1, sel1)
# mortar boundary between body 1 and body 3
sel2 = Element(Seg2, [9, 10])
update!(sel2, "geometry", X)
update!(sel2, "master elements", [mel1])
bc4 = Problem(Mortar, "interface between body 1 and 3", 2, "displacement")
push!(bc4, mel1, sel2)
# mortar boundary between body 2 and body 3
sel3 = Element(Seg2, [6, 8])
mel2 = Element(Seg2, [9, 11])
update!([sel3, mel2], "geometry", X)
update!(sel3, "master elements", [mel2])
bc5 = Problem(Mortar, "interface between body 2 and 3", 2, "displacement")
push!(bc5, sel3, mel2)
return body1, body2, body3, bc1, bc2, bc3, bc4, bc5
end
#= TODO: Fix test
@testset "test 2d mortar problem with three bodies and shared nodes" begin
body1, body2, body3, bc1, bc2, bc3, bc4, bc5 = get_test_model()
solver = Solver(Linear)
push!(solver, body1, body2, body3, bc1, bc2, bc3, bc4, bc5)
solver()
X = e3("geometry", [1.0, 1.0], 0.0)
u = e3("displacement", [1.0, 1.0], 0.0)
info("displacement at $X: $u")
u_expected = [-1/3, 1.0]
@test isapprox(u, u_expected)
end
=#