mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-09-11 22:21:52 +00:00
Jukka Aho
121 lines
4.7 KiB
Julia
121 lines
4.7 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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module BasisTests
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using JuliaFEM.Test
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using JuliaFEM: get_basis, grad, FieldSet, Field, Quad4
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"""basic continuum interpolations"""
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function test_basic_interpolations()
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element = Quad4([1, 2, 3, 4])
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element["geometry"] = Vector[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 1.0]]
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element["temperature"] = ([0.0, 0.0, 0.0, 0.0], [1.0, 2.0, 3.0, 4.0])
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element["displacement"] = (
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Vector[[0.0, 0.0], [0.0, 0.0], [0.00, 0.0], [0.0, 0.0]],
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Vector[[0.0, 0.0], [0.0, 0.0], [0.25, 0.0], [0.0, 0.0]])
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# from my old home works
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basis = get_basis(element)
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dbasis = grad(basis)
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@test isapprox(basis("geometry", [0.0, 0.0], 1.0) + basis("displacement", [0.0, 0.0], 1.0), [9/16, 1/2])
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gradu = dbasis("displacement", [0.0, 0.0], 1.0)
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epsilon = 1/2*(gradu + gradu')
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rotation = 1/2*(gradu - gradu')
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X = basis("geometry", [0.0, 0.0], 1.0)
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k = 0.25
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epsilon_wanted = [X[2]*k 1/2*X[1]*k; 1/2*X[1]*k 0]
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rotation_wanted = [0 k/2*X[1]; -k/2*X[1] 0]
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@test isapprox(epsilon, epsilon_wanted)
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@test isapprox(rotation, rotation_wanted)
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F = I + gradu
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@test isapprox(F, [X[2]*k+1 X[1]*k; 0 1])
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C = F'*F
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@test isapprox(C, [(X[2]*k+1)^2 (X[2]*k+1)*X[1]*k; (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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@test isapprox(E, [1/2*(X[2]*k + 1)^2-1/2 1/2*(X[2]*k+1)*X[1]*k; 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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@test isapprox(U, [1.24235 0.13804; 0.13804 1.02149])
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end
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function test_interpolation_in_temporal_basis()
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info("testing interpolation on temporal basis")
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temporalbasis = TemporalBasis((t) -> [1-t, t], (t) -> [-1, 1])
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@test temporalbasis(0.2) == [0.8, 0.2]
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i1 = Increment([0.0])
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i2 = Increment([1.0])
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i3 = Increment([2.0])
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t1 = TimeStep(0.0, Increment[i1])
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t2 = TimeStep(2.0, Increment[i2])
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t3 = TimeStep(4.0, Increment[i3])
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field = Field(TimeStep[t1, t2, t3])
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@test call(field, temporalbasis, -Inf) == [0.0]
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@test call(field, temporalbasis, 0.0) == [0.0]
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@test call(field, temporalbasis, 1.0) == [0.5]
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@test call(field, temporalbasis, 2.0) == [1.0]
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@test call(field, temporalbasis, 3.0) == [1.5]
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@test call(field, temporalbasis, 4.0) == [2.0]
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@test call(field, temporalbasis, +Inf) == [2.0]
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@test call(field, temporalbasis, +Inf, Val{:derivative}) == [0.5]
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@test call(field, temporalbasis, -Inf, Val{:derivative}) == [0.5]
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@test call(field, temporalbasis, 0.0, Val{:derivative}) == [0.5]
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@test call(field, temporalbasis, 0.5, Val{:derivative}) == [0.5]
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@test call(field, temporalbasis, 1.0, Val{:derivative}) == [0.5]
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@test call(field, temporalbasis, 1.5, Val{:derivative}) == [0.5]
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@test call(field, temporalbasis, 2.0, Val{:derivative}) == [0.5]
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fs = FieldSet()
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t = collect(linspace(0, 2, 5))
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x = 1/2*t.^2
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x2 = tuple(collect(zip(t, x))...)
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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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fs["particle"] = x2
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position = call(fs["particle"], temporalbasis, 1.0)[1]
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@test isapprox(position, 0.50)
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velocity = call(fs["particle"], temporalbasis, 2.0, Val{:derivative})[1]
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@test isapprox(velocity, (2.0-1.125)/0.5) # = 1.75
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velocity = call(fs["particle"], temporalbasis, 1.0, Val{:derivative})[1]
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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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info("v1 = $v1, v2 = $v2")
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info(mean([v1, v2]))
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@test isapprox(velocity, mean([v1, v2])) # = 1.00
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# FIXME, returns wrong type.
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@test isa(position, Increment) == true
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@test isa(velocity, Increment) == true
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end
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function test_interpolation_in_spatial_basis()
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info("testing interpolation on spatial basis")
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basis(xi) = 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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dbasis(xi) = 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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spatialbasis = SpatialBasis(basis, dbasis)
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@test spatialbasis.basis([0.0, 0.0]) == 1/4*[1 1 1 1]
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fs = FieldSet()
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fs["geometry"] = Vector{Float64}[[0.0,0.0], [1.0,0.0], [1.0,1.0], [0.0,1.0]]
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fs["displacement"] = (0.0, zeros(2, 4)), (1.0, Vector[[0.0, 0.0], [0.0, 0.0], [0.25, 0.0], [0.0, 0.0]])
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X = call(last(fs["geometry"]), spatialbasis, [0.0, 0.0])
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u = call(last(fs["displacement"]), spatialbasis, [0.0, 0.0])
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x = X+u
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@test X ≈ 1/2*[1, 1]
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@test x ≈ [9/16, 1/2]
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gradu = call(last(fs["displacement"]), spatialbasis, [0.0, 0.0], last(fs["geometry"]), Val{:gradient})
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@test gradu ≈ [0.125 0.125; 0.0 0.0]
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end
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end
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