mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-08-17 19:09:04 +00:00
Jukka Aho
288 lines
8.8 KiB
Julia
288 lines
8.8 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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importall Base
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import JuliaFEM: get_basis, get_dbasis
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type TestElement <: AbstractElement
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end
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function get_basis(element::Element{TestElement}, xi, time)
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1/4*[
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(1-xi[1])*(1-xi[2])
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(1+xi[1])*(1-xi[2])
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(1+xi[1])*(1+xi[2])
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(1-xi[1])*(1+xi[2])]'
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end
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function get_dbasis(element::Element{TestElement}, xi, time)
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1/4*[
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-(1-xi[2]) (1-xi[2]) (1+xi[2]) -(1+xi[2])
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-(1-xi[1]) -(1+xi[1]) (1+xi[1]) (1-xi[1])]
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end
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function length(element::Element{TestElement})
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return 4
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end
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function size(element::Element{TestElement})
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return (2, 4)
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end
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function get_element()
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element = Element(TestElement, [1, 2, 3, 4])
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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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3 => [1.0, 1.0],
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4 => [0.0, 1.0])
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T = Dict{Int64, Float64}(
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1 => 1.0,
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2 => 2.0,
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3 => 3.0,
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4 => 4.0)
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u1 = Dict{Int64, Vector{Float64}}(
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1 => [0.0, 0.0],
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2 => [0.0, 0.0],
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3 => [1/4, 0.0],
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4 => [0.0, 0.0])
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u2 = Dict{Int64, Vector{Float64}}(
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1 => [0.0, 0.0],
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2 => [1.0, -1.0],
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3 => [2.0, 3.0],
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4 => [0.0, 0.0])
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update!(element, "geometry", X)
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update!(element, "temperature", T)
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update!(element, "displacement1", u1)
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update!(element, "displacement2", u2)
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return element
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end
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@testset "spatial interpolation in basis" begin
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element = get_element()
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@test isapprox(element([0.0, 0.0], 0.0), 1/4*[1 1 1 1])
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@test isapprox(element([0.0, 0.0], 1.0), 1/4*[1 1 1 1])
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end
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@testset "gradient of shape functions" begin
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element = get_element()
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grad = element([0.0, 0.0], 0.0, Val{:Grad})
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@test isapprox(grad, 1/2*[-1 1 1 -1; -1 -1 1 1])
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end
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@testset "interpolation of scalar field in spatial domain" begin
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# in unit square: T(X,t) = t*(1 + X[1] + 3*X[2] - 2*X[1]*X[2])
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element = get_element()
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T_known(X) = 1 + X[1] + 3*X[2] - 2*X[1]*X[2]
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T_interpolated = element("temperature", [0.0, 0.0], 0.0)
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@test isapprox(T_interpolated, T_known([0.5, 0.5]))
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end
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@testset "interpolation of gradient of scalar field in spatial domain" begin
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# in unit square: grad(T)(X) = [1-2X[2], 3-2*X[1]]
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element = get_element()
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gradT = element("temperature", [0.0, 0.0], 0.0, Val{:Grad})
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gradT_expected(X) = [1-2*X[2] 3-2*X[1]]
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@test isapprox(gradT, gradT_expected([0.5, 0.5]))
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end
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@testset "test interpolation of vector field" begin
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# in unit square, u(X,t) = [1/4*t*X[1]*X[2], 0, 0]
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element = get_element()
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u = element("displacement1", [0.0, 0.0], 0.0)
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# x = X+u
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u_expected(X) = [1/4*X[1]*X[2], 0]
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# @test isapprox(x, [9/16, 1/2])
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@test isapprox(u, u_expected([0.5, 0.5]))
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end
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@testset "interpolation of gradient of vector_field" begin
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# in unit square, u(X) = t*[X[1]*(X[2]+1), X[1]*(4*X[2]-1)]
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# => u_i,j = t*[X[2]+1 X[1]; 4*X[2]-1 4*X[1]]
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element = get_element()
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# displacement = Field(
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# (0.5, Vector[[0.0, 0.0], [0.5, -0.5], [1.0, 1.5], [0.0, 0.0]]),
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# (1.5, Vector[[0.0, 0.0], [1.5, -1.5], [3.0, 4.5], [0.0, 0.0]]))
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gradu = element("displacement2", [0.0, 0.0], 0.0, Val{:Grad})
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gradu_expected(X) = [X[2]+1 X[1]; 4*X[2]-1 4*X[1]]
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@test isapprox(gradu, gradu_expected([0.5, 0.5]))
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end
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#= TODO: Fix test
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@testset "linear time extrapolation of field" begin
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#T_known(X,t) = t*(1 + X[1] + 3*X[2] - 2*X[1]*X[2])
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T = DVTV()
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update!(T, 0.0 => [0.0, 0.0, 0.0, 0.0])
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update!(T, 1.0 => [1.0, 2.0, 3.0, 4.0])
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@test T(-1.0) == -1.0*[1.0, 2.0, 3.0, 4.0]
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@test T( 3.0) == 3.0*[1.0, 2.0, 3.0, 4.0]
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# when going to \pm infinity, return the last one.
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@test T(-Inf) == 0.0*[1.0, 2.0, 3.0, 4.0]
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@test T(+Inf) == 1.0*[1.0, 2.0, 3.0, 4.0]
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end
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=#
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#= TODO: Fix test
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@testset "constant time extrapolation of field" begin
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#T_known(X,t) = t*(1 + X[1] + 3*X[2] - 2*X[1]*X[2])
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T = DVTV()
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update!(T, 0.0 => [0.0, 0.0, 0.0, 0.0])
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update!(T, 1.0 => [1.0, 2.0, 3.0, 4.0])
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@test isapprox(T(-1.0, Val{:constant}), [0.0, 0.0, 0.0, 0.0])
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@test isapprox(T( 3.0, Val{:constant}), [1.0, 2.0, 3.0, 4.0])
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end
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=#
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#= TODO: Fix test
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@testset "time extrapolation of field with only one timestep" begin
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T = DVTV()
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update!(T, 0.0 => [1.0, 2.0, 3.0, 4.0])
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@test isapprox(T(1.0), [1.0, 2.0, 3.0, 4.0])
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end
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=#
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#= TODO: Fix test
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@testset "interpolation in temporal direction" begin
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field = DCTV()
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update!(field, 0.0 => 0.0)
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update!(field, 2.0 => 1.0)
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update!(field, 4.0 => 2.0)
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@test isapprox(field(-Inf), 0.0)
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@test isapprox(field( 0.0), 0.0)
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@test isapprox(field( 1.0), 0.5)
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@test isapprox(field( 2.0), 1.0)
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@test isapprox(field( 3.0), 1.5)
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@test isapprox(field( 4.0), 2.0)
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@test isapprox(field(+Inf), 2.0)
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end
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=#
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#= TODO: Fix test
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@testset "time derivative interpolation in temporal basis in constant velocity" begin
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field = DCTV()
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update!(field, 0.0 => 0.0)
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update!(field, 2.0 => 1.0)
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update!(field, 4.0 => 2.0)
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@test isapprox(field(+Inf, Val{:diff}), 0.5)
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@test isapprox(field(-Inf, Val{:diff}), 0.5)
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@test isapprox(field( 0.0, Val{:diff}), 0.5)
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@test isapprox(field( 0.5, Val{:diff}), 0.5)
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@test isapprox(field( 1.0, Val{:diff}), 0.5)
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@test isapprox(field( 1.5, Val{:diff}), 0.5)
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@test isapprox(field( 2.0, Val{:diff}), 0.5)
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end
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=#
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#= TODO: Fix test
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@testset "time derivative interpolation in temporal basis in variable velocity" begin
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pos = DCTV()
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for ti in linspace(0, 2, 5)
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update!(pos, ti => 1/2*ti^2)
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end
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# => ((0.0,0.0),(0.5,0.125),(1.0,0.5),(1.5,1.125),(2.0,2.0))
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velocity = pos(1.0, Val{:diff})
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v1 = (0.500 - 0.125)/0.5
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v2 = (1.125 - 0.500)/0.5
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@test isapprox(velocity, mean([v1, v2])) # = 1.00
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velocity = pos(2.0, Val{:diff})
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@test isapprox(velocity, (2.0-1.125)/0.5) # = 1.75
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end
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=#
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function test_time_derivative_gradient_interpolation_of_field()
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# in unit square, u(X) = t*[X[1]*(X[2]+1), X[1]*(4*X[2]-1)]
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# => u_i,j = t*[X[2]+1 X[1]; 4*X[2]-1 4*X[1]]
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# => d(u_i,j)/dt = [X[2]+1 X[1]; 4*X[2]-1 4*X[1]]
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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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3 => [1.0, 1.0],
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4 => [0.0, 1.0])
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u1 = Dict{Int64, Vector{Float64}}(
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1 => [0.0, 0.0],
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2 => [0.5, -0.5],
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3 => [1.0, 1.5],
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4 => [0.0, 0.0])
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u2 = Dict{Int64, Vector{Float64}}(
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1 => [0.0, 0.0],
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2 => [1.5, -1.5],
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3 => [3.0, 4.5],
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4 => [0.0, 0.0])
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element = Element(TestElement, [1, 2, 3, 4])
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update!(element, "geometry", X)
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update!(element, "displacement", 0.5 => u1)
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update!(element, "displacement", 1.5 => u2)
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xi = [0.0, 0.0]
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time = 1.2
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diffgradu = element("displacement", xi, time, Val{:diff}, Val{:Grad})
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diffgradu_expected(X, t) = [X[2]+1 X[1]; 4*X[2]-1 4*X[1]]
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@test diffgradu == diffgradu_expected([0.5, 0.5], 1.2)
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end
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@testset "some continuum mechanics interpolations" 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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3 => [1.0, 1.0],
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4 => [0.0, 1.0])
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u1 = Dict{Int64, Vector{Float64}}(
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1 => [0.0, 0.0],
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2 => [0.0, 0.0],
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3 => [0.0, 0.0],
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4 => [0.0, 0.0])
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u2 = Dict{Int64, Vector{Float64}}(
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1 => [0.0, 0.0],
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2 => [0.0, 0.0],
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3 => [1/4, 0.0],
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4 => [0.0, 0.0])
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element = Element(Quad4, [1, 2, 3, 4])
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update!(element, "geometry", X)
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update!(element, "displacement", 0.0 => u1)
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update!(element, "displacement", 1.0 => u2)
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# from my old home works
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X = element("geometry", [0.0, 0.0], 1.0)
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u = element("displacement", [0.0, 0.0], 1.0)
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x = X + u
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x_expected = [9/16, 1/2]
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gradu = element("displacement", [0.0, 0.0], 1.0, Val{:Grad})
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epsilon = 1/2*(gradu + gradu')
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rotation = 1/2*(gradu - gradu')
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k = 0.25
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epsilon_expected = [
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X[2]*k 1/2*X[1]*k
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1/2*X[1]*k 0]
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rotation_expected = [
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0 k/2*X[1]
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-k/2*X[1] 0]
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F = I + gradu
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F_expected = [
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X[2]*k+1 X[1]*k
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0 1]
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C = F'*F
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C_expected = [
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(X[2]*k+1)^2 (X[2]*k+1)*X[1]*k
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(X[2]*k+1)*X[1]*k X[1]^2*k^2+1]
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E = 1/2*(F'*F - I)
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E_expected = [
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1/2*(X[2]*k + 1)^2-1/2 1/2*(X[2]*k+1)*X[1]*k
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1/2*(X[2]*k + 1)*X[1]*k 1/2*X[1]^2*k^2]
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U = 1/sqrt(trace(C) + 2*sqrt(det(C)))*(C + sqrt(det(C))*I)
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# U_expected = [1.24235 0.13804; 0.13804 1.02149]
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@test isapprox(x, x_expected)
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@test isapprox(epsilon, epsilon_expected)
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@test isapprox(rotation, rotation_expected)
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@test isapprox(F, F_expected)
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@test isapprox(C, C_expected)
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@test isapprox(E, E_expected)
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# TODO: Fix test
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# @test isapprox(U, U_expected)
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end
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