mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-09-22 10:48:32 +00:00
Jukka Aho
016e3cd8bf
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.
|
|
# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
|
|
|
|
using JuliaFEM: get_basis, grad, FieldSet, Field, Quad4
|
|
using FactCheck
|
|
|
|
element = Quad4([1, 2, 3, 4])
|
|
|
|
geometry_field = Field(0.0, Vector[]) # Create empty field at time t=0.0
|
|
push!(geometry_field, [ 0.0, 0.0]) # push some values for field
|
|
push!(geometry_field, [ 1.0, 0.0])
|
|
push!(geometry_field, [ 1.0, 1.0])
|
|
push!(geometry_field, [ 0.0, 1.0])
|
|
geometry_fieldset = FieldSet("geometry") # create fieldset "geometry"
|
|
push!(geometry_fieldset, geometry_field) # add field to fieldset
|
|
push!(element, geometry_fieldset) # add fieldset to element
|
|
|
|
temperature_fieldset = FieldSet("temperature")
|
|
push!(temperature_fieldset, Field(0.0, [0.0, 0.0, 0.0, 0.0]))
|
|
push!(temperature_fieldset, Field(1.0, [1.0, 2.0, 3.0, 4.0]))
|
|
push!(element, temperature_fieldset)
|
|
|
|
displacement_fieldset = FieldSet("displacement")
|
|
push!(displacement_fieldset, Field(0.0, Vector[[0.0, 0.0], [0.0, 0.0], [0.0, 0.0], [0.0, 0.0]]))
|
|
push!(displacement_fieldset, Field(1.0, Vector[[0.0, 0.0], [0.0, 0.0], [0.25, 0.0], [0.0, 0.0]]))
|
|
push!(element, displacement_fieldset)
|
|
|
|
facts("basic continuum interpolations") do
|
|
# from my old home works
|
|
basis = get_basis(element)
|
|
dbasis = grad(basis)
|
|
@fact basis("geometry", [0.0, 0.0], 1.0) + basis("displacement", [0.0, 0.0], 1.0) --> [9/16, 1/2]
|
|
gradu = dbasis("displacement", [0.0, 0.0], 1.0)
|
|
epsilon = 1/2*(gradu + gradu')
|
|
rotation = 1/2*(gradu - gradu')
|
|
X = basis("geometry", [0.0, 0.0], 1.0)
|
|
k = 0.25
|
|
epsilon_wanted = [X[2]*k 1/2*X[1]*k; 1/2*X[1]*k 0]
|
|
rotation_wanted = [0 k/2*X[1]; -k/2*X[1] 0]
|
|
@fact epsilon --> roughly(epsilon_wanted)
|
|
@fact rotation --> roughly(rotation_wanted)
|
|
F = I + gradu
|
|
@fact F --> [X[2]*k+1 X[1]*k; 0 1]
|
|
C = F'*F
|
|
@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]
|
|
E = 1/2*(F'*F - I)
|
|
@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]
|
|
U = 1/sqrt(trace(C) + 2*sqrt(det(C)))*(C + sqrt(det(C))*I)
|
|
#@fact U --> roughly([1.24235 0.13804; 0.13804 1.02149])
|
|
end
|