mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-09-22 02:40:51 +00:00
Jukka Aho
1844530303
force vector, autodiff takes care of linearization - elasticity equations are now solved using e.g. principle of minimum potential energy. syntax is quite good, see notebook. - updated how to interpolate fields, by introducing function spaces. syntax is now good. still have to figure out how to do time derivatives - etc. etc. tutorial is broken at the moment, i took of get_lhs and get_rhs because they didn't really work.
51 lines
2.1 KiB
Julia
51 lines
2.1 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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element = Quad4([1, 2, 3, 4])
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geometry_field = Field(0.0, Vector[]) # Create empty field at time t=0.0
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push!(geometry_field, [ 0.0, 0.0]) # push some values for field
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push!(geometry_field, [ 1.0, 0.0])
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push!(geometry_field, [ 1.0, 1.0])
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push!(geometry_field, [ 0.0, 1.0])
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geometry_fieldset = FieldSet("geometry") # create fieldset "geometry"
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push!(geometry_fieldset, geometry_field) # add field to fieldset
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push!(element, geometry_fieldset) # add fieldset to element
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temperature_fieldset = FieldSet("temperature")
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push!(temperature_fieldset, Field(0.0, [0.0, 0.0, 0.0, 0.0]))
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push!(temperature_fieldset, Field(1.0, [1.0, 2.0, 3.0, 4.0]))
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push!(element, temperature_fieldset)
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displacement_fieldset = FieldSet("displacement")
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push!(displacement_fieldset, Field(0.0, Vector[[0.0, 0.0], [0.0, 0.0], [0.0, 0.0], [0.0, 0.0]]))
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push!(displacement_fieldset, Field(1.0, Vector[[0.0, 0.0], [0.0, 0.0], [0.25, 0.0], [0.0, 0.0]]))
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push!(element, displacement_fieldset)
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facts("basic continuum interpolations") do
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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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