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Calculate shape functions using FEMBasis.jl
A lot of code is moved to FEMBasis.jl regarding calculating basis / shape functions of finite elements. * add FEMBasis to REQUIRE * remove obsolete files * remove obsolete test files * make integration point iterable * loosen type definitions * get length of element rather from basis than connectivity * calculate midpoint of reference element * wrong input argument to eval_basis! fixed
This commit is contained in:
Jukka Aho
@@ -1,287 +0,0 @@
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# 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.Testing
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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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@@ -1,65 +0,0 @@
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# 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.Testing
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importall Base
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import JuliaFEM: get_basis, get_dbasis, get_integration_points
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type MyQuad4 <: AbstractElement
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end
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function get_basis(element::Element{MyQuad4}, ip, time)
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1/4*[(1-ip[1])*(1-ip[2]) (1+ip[1])*(1-ip[2]) (1+ip[1])*(1+ip[2]) (1-ip[1])*(1+ip[2])]
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end
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function get_dbasis(element::Element{MyQuad4}, ip, time)
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1/4*[-(1-ip[2]) (1-ip[2]) (1+ip[2]) -(1+ip[2])
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-(1-ip[1]) -(1+ip[1]) (1+ip[1]) (1-ip[1])]
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end
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function get_integration_points(element::MyQuad4)
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[
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(1.0, 1.0/sqrt(3.0)*[-1, -1]),
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(1.0, 1.0/sqrt(3.0)*[ 1, -1]),
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(1.0, 1.0/sqrt(3.0)*[ 1, 1]),
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(1.0, 1.0/sqrt(3.0)*[-1, 1])
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]
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end
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function length(element::Element{MyQuad4})
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return 4
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end
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function size(element::Element{MyQuad4})
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return (2, 4)
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end
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@testset "test new element" begin
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el = Element(MyQuad4, Int[])
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el["geometry"] = Vector{Float64}[[0.0,0.0], [1.0,0.0], [1.0,1.0], [0.0,1.0]]
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el["displacement"] = Vector{Float64}[[0.0,0.0], [0.0,0.0], [1.0,0.0], [0.0,0.0]]
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@test isapprox(el("geometry", [0.0, 0.0], 0.0), [0.5, 0.5])
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@test isapprox(el("displacement", [0.0, 0.0], 0.0), [0.25, 0.0])
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el["temperature thermal conductivity"] = 6.0
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dim = length(el)
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K = zeros(dim, dim)
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A = 0.0
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time = 0.0
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for ip in get_integration_points(el)
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dN = el(ip, time, Val{:Grad})
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detJ = el(ip, time, Val{:detJ})
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w = ip.weight*detJ
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c = el("temperature thermal conductivity", ip, time)
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K += w*c*dN'*dN
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A += w
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end
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@test isapprox(A, 1.0)
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K_expected = [
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4.0 -1.0 -2.0 -1.0
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-1.0 4.0 -1.0 -2.0
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-2.0 -1.0 4.0 -1.0
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-1.0 -2.0 -1.0 4.0]
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@test isapprox(K, K_expected)
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end
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@@ -1,28 +0,0 @@
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# 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.Testing
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@testset "NSeg interpolate" begin
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element = Element(NSeg, [1, 2])
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@test element([0.0], 0.0) == [0.5 0.5]
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@test size(element) == (1, 2)
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@test is_nurbs(element)
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element2 = Element(Seg2, [1, 2])
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@test !is_nurbs(element2)
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end
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@testset "NSurf interpolate" begin
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element = Element(NSurf, [1, 2, 3, 4])
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@test element([0.0, 0.0], 0.0) == [0.25 0.25 0.25 0.25]
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@test size(element) == (2, 4)
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@test is_nurbs(element)
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end
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@testset "NSolid interpolate" begin
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element = Element(NSolid, [1, 2, 3, 4, 5, 6, 7, 8])
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@test element([0.0, 0.0, 0.0], 0.0) == [0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125]
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@test size(element) == (3, 8)
|
||||
@test is_nurbs(element)
|
||||
end
|
||||
@@ -1,89 +0,0 @@
|
||||
# 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
|
||||
|
||||
ALL_ELEMENTS = [
|
||||
Seg2, Seg3,
|
||||
Tri3, Tri6, Tri7,
|
||||
Quad4, Quad8, Quad9,
|
||||
Tet4, Tet10,
|
||||
Wedge6,
|
||||
Hex8, Hex20, Hex27
|
||||
]
|
||||
|
||||
info("basic data for elements implemented so far:")
|
||||
for element_type in [Poi1; ALL_ELEMENTS]
|
||||
element = Element(element_type, Int[])
|
||||
element_length = length(element)
|
||||
element_size = size(element)
|
||||
element_description = description(element)
|
||||
info("Element $element_type, description = $element_description, length = $element_length, size = $element_size")
|
||||
end
|
||||
|
||||
|
||||
ALL_ELEMENTS_NODES = [
|
||||
[1,2], [1,2,3],
|
||||
[1,2,3], [1,2,3,4,5,6], [1,2,3,4,5,6,7],
|
||||
[1,2,3,4], [1,2,3,4,5,6,7,8], [1,2,3,4,5,6,7,8,9],
|
||||
[1,2,3,4], [1,2,3,4,5,6,7,8,9,10],
|
||||
[1,2,3,4,5,6],
|
||||
[1,2,3,4,5,6,7,8],
|
||||
[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,15,17,18,19,20],
|
||||
[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,15,17,18,19,20,
|
||||
21,22,23,24,25,26,27]
|
||||
]
|
||||
|
||||
@testset "Evaluating basis" begin
|
||||
for (T, nod) in zip(ALL_ELEMENTS,ALL_ELEMENTS_NODES)
|
||||
el = Element(T,nod)
|
||||
nnodes = length(el)
|
||||
for (i, X) in enumerate(get_reference_coordinates(T))
|
||||
Ni = vec(el(X))
|
||||
expected = zeros(nnodes)
|
||||
expected[i] = 1.0
|
||||
@test isapprox(Ni, expected)
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
function get_volume{T<:AbstractElement}(::Type{T},nodes)
|
||||
X = get_reference_coordinates(T)
|
||||
element = Element(T,nodes)
|
||||
update!(element, "geometry", X)
|
||||
V = 0.0
|
||||
for ip in get_integration_points(element)
|
||||
V += ip.weight*element(ip, 0.0, Val{:detJ})
|
||||
end
|
||||
return V
|
||||
end
|
||||
|
||||
RESULTS = [2.0, 2.0, 0.5, 0.5, 0.5, 2.0^2, 2.0^2,
|
||||
2.0^2, 1/6, 1/6, 1.0, 2.0^3, 2.0^3, 2.0^3,]
|
||||
|
||||
@testset "Calculate reference element length/area/volume" begin
|
||||
for (T, nod, res) in zip(ALL_ELEMENTS,ALL_ELEMENTS_NODES,
|
||||
RESULTS)
|
||||
@test isapprox(get_volume(T,nod), res)
|
||||
end
|
||||
end
|
||||
|
||||
SIZES = [(1,2), (1,3), (2,3), (2,6), (2,7), (2,4),
|
||||
(2,8), (2,9), (3,4), (3,10), (3,6), (3,8),
|
||||
(3,20), (3,27)]
|
||||
|
||||
@testset "element size" begin
|
||||
for (T, nod, res) in zip(ALL_ELEMENTS,ALL_ELEMENTS_NODES, SIZES)
|
||||
@test size(Element(T,nod)) == res
|
||||
end
|
||||
end
|
||||
|
||||
@testset "element length" begin
|
||||
for i in 1:length(ALL_ELEMENTS)
|
||||
typ = ALL_ELEMENTS[i]
|
||||
vec = ALL_ELEMENTS_NODES[i]
|
||||
el = Element(typ,vec)
|
||||
@test length(el) == length(vec)
|
||||
end
|
||||
end
|
||||
@@ -41,7 +41,7 @@ using JuliaFEM.Testing
|
||||
|
||||
# Postprocess.
|
||||
# Interpolate temperature field along boundary of Γ₁ at time t=1.0
|
||||
xi = [0.0, -1.0]
|
||||
xi = (0.0, )
|
||||
X = el2("geometry", xi, 1.0)
|
||||
T = el2("temperature", xi, 1.0)
|
||||
info("Temperature at point X = $X is T = $T")
|
||||
|
||||
Reference in New Issue
Block a user