mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
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Jukka Aho
40 lines
1.5 KiB
Julia
40 lines
1.5 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: get_basis, grad, FieldSet, Field, Quad4
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using FactCheck
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facts("basic continuum interpolations") do
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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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@fact 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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@fact epsilon --> roughly(epsilon_wanted)
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@fact rotation --> roughly(rotation_wanted)
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F = I + gradu
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@fact F --> [X[2]*k+1 X[1]*k; 0 1]
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C = F'*F
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@fact 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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@fact 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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#@fact U --> roughly([1.24235 0.13804; 0.13804 1.02149])
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end
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