mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-08-18 19:30:10 +00:00
Jukka Aho
147 lines
4.5 KiB
Julia
147 lines
4.5 KiB
Julia
# This file is a part of JuliaFEM.
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# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
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using JuliaFEM
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using JuliaFEM.Test
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#=
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In [36]: C = Matrix([[0], [30], [15]]) # node coordinates
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In [37]: A = Matrix([P.subs({x: C[i,0]}).T for i in range(len(P))])
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In [38]: N = P.T*A.inv()
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In [39]: Me = integrate(N.T*N, (x, 0, 30))
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In [40]: De = diag(*integrate(N, (x, 0, 30)))
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In [41]: Me
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Out[41]:
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Matrix([
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[ 4, -1, 2],
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[-1, 4, 2],
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[ 2, 2, 16]])
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In [42]: De
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Out[42]:
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Matrix([
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[5, 0, 0],
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[0, 5, 0],
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[0, 0, 20]])
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=#
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@testset "dirichlet problem in 1 dimension" begin
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element = Element(Seg2, [1, 2])
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element["geometry"] = Vector{Float64}[[0.0, 0.0], [6.0, 0.0]]
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element["temperature 1"] = 0.0
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p1 = Problem(Dirichlet, "test problem 1", 1, "temperature")
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p1.properties.dual_basis = false
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p2 = Problem(Dirichlet, "test problem 2", 1, "temperature")
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p2.properties.dual_basis = true
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assemble!(p1, element)
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assemble!(p2, element)
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C1 = full(p1.assembly.C1)
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C2 = full(p1.assembly.C2)
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@test isapprox(C1, C2)
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@test isapprox(C1, [2.0 1.0; 1.0 2.0])
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C1 = full(p2.assembly.C1)
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C2 = full(p2.assembly.C2)
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@test isapprox(C1, C2)
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@test isapprox(C1, [3.0 0.0; 0.0 3.0])
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element = Element(Seg3, [1, 2, 3])
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element["geometry"] = Vector{Float64}[[0.0, 0.0], [30.0, 0.0], [15.0, 0.0]]
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element["temperature 1"] = 0.0
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p1 = Problem(Dirichlet, "quadratic 1", 1, "temperature")
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p1.properties.dual_basis = false
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p2 = Problem(Dirichlet, "quadratic 1", 1, "temperature")
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p2.properties.dual_basis = true
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assemble!(p1, element)
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assemble!(p2, element)
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C1 = full(p1.assembly.C1)
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C2 = full(p1.assembly.C2)
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@test isapprox(C1, C2)
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@test isapprox(C1, [4.0 -1.0 2.0; -1.0 4.0 2.0; 2.0 2.0 16.0])
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C1 = full(p2.assembly.C1)
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C2 = full(p2.assembly.C2)
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@test isapprox(C1, C2)
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@test isapprox(C1, [5.0 0.0 0.0; 0.0 5.0 0.0; 0.0 0.0 20.0])
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end
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#=
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@testset "dirichlet problem using tri3 surface element" begin
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element = Tri3([1, 2, 3])
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element["geometry"] = Node[[0.0, 0.0, 0.0], [1.0, 0.0, 0.0], [0.0, 1.0, 0.0]]
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element["temperature"] = 0.0
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problem = Problem(Dirichlet, "test problem", 1, "temperature")
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push!(problem, element)
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assemble!(problem, 0.0)
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C1 = full(problem.assembly.C1)
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C2 = full(problem.assembly.C2)
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@test isapprox(C1, C2)
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@test isapprox(C1, 1/24*[2 1 1; 1 2 1; 1 1 2])
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end
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@testset "dirichlet problem in 2 dimensions" begin
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element = Seg2([1, 2])
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element["geometry"] = Node[[1.0, 1.0], [0.0, 1.0]]
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element["displacement 1"] = 0.0
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element["displacement 2"] = 0.0
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problem = Problem(Dirichlet, "test problem", 2, "displacement")
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push!(problem, element)
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assemble!(problem, 0.0)
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C1 = full(problem.assembly.C1)
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C2 = full(problem.assembly.C2)
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g = full(problem.assembly.g)
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@test isapprox(C1, C2)
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C1_expected = 1/6*[2 0 1 0; 0 2 0 1; 1 0 2 0; 0 1 0 2]
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@test isapprox(C1, C1_expected)
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@test isapprox(g, [0.0, 0.0, 0.0, 0.0])
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end
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@testset "dirichlet problem in 2 dimensions, with 1 dof fixed" begin
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element = Seg2([1, 2])
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element["geometry"] = Node[[1.0, 1.0], [0.0, 1.0]]
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element["displacement 2"] = 0.0
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problem = Problem(Dirichlet, "test problem", 2, "displacement")
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push!(problem, element)
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assemble!(problem, 0.0)
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C1 = full(problem.assembly.C1)
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C2 = full(problem.assembly.C2)
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g = full(problem.assembly.g)
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@test isapprox(C1, C2)
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C1_expected = 1/6*[
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0 0 0 0
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0 2 0 1
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0 0 0 0
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0 1 0 2]
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@test isapprox(C1, C1_expected)
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@test isapprox(g, [0.0, 0.0, 0.0, 0.0])
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end
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=#
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@testset "test analytical boundary condition" begin
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X = Dict{Int64, Vector{Float64}}(
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1 => [0.0, 0.0],
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2 => [1.0, 0.0])
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element = Element(Seg2, [1, 2])
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update!(element, "geometry", X)
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update!(element, "displacement 1", 0.0)
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f(xi, time) = begin
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info("function call at xi = $xi, time = $time")
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X = element("geometry", xi, time)
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info("geometry at xi, X = $X")
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val = X[1]*time
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info("result for field at xi = $val")
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return val
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end
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update!(element, "displacement 2", f)
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p = Problem(Dirichlet, "test boundary", 2, "displacement")
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push!(p, element)
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assemble!(p, 0.0)
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g1 = full(p.assembly.g, 4, 1)
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@test isapprox(g1, [0.0, 0.0, 0.0, 0.0])
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empty!(p.assembly)
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assemble!(p, 1.0)
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g2 = full(p.assembly.g, 4, 1)
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C2 = full(p.assembly.C2, 4, 4)
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u = C2 \ g2
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info("u = $u")
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@test isapprox(u, [0.0, 0.0, 0.0, 1.0])
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end
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