mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-09-10 04:50:49 +00:00
Jukka Aho
82 lines
2.5 KiB
Julia
82 lines
2.5 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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module TestAutoDiffWeakForm
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using JuliaFEM.Test
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using JuliaFEM
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using JuliaFEM: Quad4, Equation, IntegrationPoint,
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solve!, get_field, get_element, get_basis,
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grad
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""" Plane stress formulation for 4-node bilinear element. """
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type CPS4 <: Equation
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element :: Quad4
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integration_points :: Array{IntegrationPoint, 1}
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end
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function CPS4(element::Quad4)
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integration_points = [
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IntegrationPoint(1.0/sqrt(3.0)*[-1, -1], 1.0),
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IntegrationPoint(1.0/sqrt(3.0)*[ 1, -1], 1.0),
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IntegrationPoint(1.0/sqrt(3.0)*[ 1, 1], 1.0),
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IntegrationPoint(1.0/sqrt(3.0)*[-1, 1], 1.0)]
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if !haskey(element, "displacement")
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# initial field must be defined if using autodiff
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element["displacement"] = zeros(2, 4)
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end
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CPS4(element, integration_points)
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end
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JuliaFEM.size(eq::CPS4) = (2, 4)
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function JuliaFEM.get_residual_vector(equation::CPS4, ip, time; variation=nothing)
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element = get_element(equation)
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basis = get_basis(element)
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dbasis = grad(basis)
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# material parameters
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E = basis("youngs modulus", ip, time)
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nu = basis("poissons ratio", ip, time)
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mu = E/(2*(1+nu))
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la = E*nu/((1+nu)*(1-2*nu))
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la = 2*la*mu/(la + 2*mu) # <- correction for 2d
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# elasticity formulation
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u = basis("displacement", ip, time, variation)
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gradu = dbasis("displacement", ip, time, variation)
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F = I + gradu
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b = basis("displacement volume load", ip, time)
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E = 1/2*(F'*F - I)
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S = la*trace(E)*I + 2*mu*E
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P = F*S
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# residual vector
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r_int = P*dbasis(ip,time)
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r_ext = b*basis(ip,time)
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r = r_int - r_ext
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return vec(r)
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end
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JuliaFEM.has_residual_vector(equation::CPS4) = true
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function test_residual_form()
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# create model -- start
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element = Quad4([1, 2, 3, 4])
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element["geometry"] = Vector[[0.0,0.0], [10.0,0.0], [10.0,1.0], [0.0,1.0]]
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element["youngs modulus"] = 500.0
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element["poissons ratio"] = 0.3
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element["displacement volume load"] = Vector[[0.0,-10.0], [0.0,-10.0], [0.0,-10.0], [0.0,-10.0]]
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equation = CPS4(element)
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# create model -- end
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free_dofs = [3, 4, 5, 6]
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solve!(equation, "displacement", free_dofs) # launch a newton solver for single element
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disp = get_basis(element)("displacement", [1.0, 1.0])[2]
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println("displacement at tip: $disp")
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# verified using Code Aster.
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@test isapprox(disp, -8.77303119819776E+00)
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end
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end
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