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https://github.com/JuliaFEM/JuliaFEM.jl.git
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Jukka Aho
f3f42fd115
New 102-line test file for modal elasticity analysis: - Tests modal analysis of long rod with fixed-fixed boundary conditions - Compares eigenfrequencies with Code Aster results (Tet10 elements) - Validates against analytical solution (fixed-fixed beam) - Tests 5 lowest eigenfrequencies - Uses legacy Element/Problem API Validates modal analysis accuracy by comparing with reference Code Aster results and analytical beam theory.
103 lines
3.6 KiB
Julia
103 lines
3.6 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, Test, LinearAlgebra
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#= this has nothing to do here
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@testset "calculate cross-sectional properties" begin
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mesh_file = @__DIR__() * "/testdata/primitives.med"
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mesh = aster_read_mesh(mesh_file, "CYLINDER_20_TET4")
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# calculate cross-sectional properties A and Iₓ
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fixed1 = Problem(Dirichlet, "left support", 3, "displacement")
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fixed1.elements = create_elements(mesh, "FACE1")
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A = calculate_area(fixed1)
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@info("cross-section area: $A")
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# real area is π
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@test isapprox(A, pi; rtol=0.1)
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Xc = calculate_center_of_mass(fixed1)
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@info("center of mass: $Xc")
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@test isapprox(Xc, [0.0, 0.0, 0.0]; atol=1.0e-12)
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I = calculate_second_moment_of_mass(fixed1)
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@info("moments:")
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@info(I)
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I_expected = zeros(3, 3)
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I_expected[2,2] = I_expected[3,3] = pi/4
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rtol = norm(I[2,2]-I_expected[2,2]) / max(I[2,2],I_expected[2,2])
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@info("I rtol = $rtol")
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@test isapprox(I, I_expected; rtol = 0.2)
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end
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=#
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#=
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test subjects:
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- calculate cross-sectional properties
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- modal analysis with known solution
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Fixed-fixed solution is ωᵢ = λᵢ²√(EI/ρA) , where λᵢ = cosh(λᵢℓ)cos(λᵢℓ)
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1: 4.730040744862704
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2: 7.853204624095838
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3: 10.995607838001671
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Youngs modulus is tuned such that lowest eigenfrequency matches 1.0
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5 lowest eigenfrequencies using Code Aster and Tet4 elements:
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numéro fréquence (HZ) norme d'erreur
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1 1.19789E+00 2.20137E-12
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2 1.20179E+00 1.99034E-12
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3 3.07391E+00 3.29226E-13
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4 3.08812E+00 2.91550E-13
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5 4.87370E+00 2.95986E-13
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5 lowest eigenfrequencies using Code Aster and Tet10 elements:
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numéro fréquence (HZ) norme d'erreur
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1 9.65942E-01 1.54950E-11
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2 9.66160E-01 1.62712E-11
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3 2.52127E+00 2.06544E-12
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4 2.52187E+00 1.77970E-12
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5 3.48584E+00 9.96170E-13
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[1] De Silva, Clarence W. Vibration: fundamentals and practice. CRC press, 2006, p.355
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=#
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# long rod natural frequencies
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mesh_file = @__DIR__() * "/testdata/primitives.med"
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mesh = aster_read_mesh(mesh_file, "CYLINDER_20_TET10")
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body = Problem(Elasticity, "rod", 3)
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body_elements = create_elements(mesh, "CYLINDER")
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#E = 50475.44814745859
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E = 50475.5
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rho = 1.0
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update!(body_elements, "youngs modulus", E)
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update!(body_elements, "poissons ratio", 0.3)
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update!(body_elements, "density", rho)
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add_elements!(body, body_elements)
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fixed1 = Problem(Dirichlet, "left support", 3, "displacement")
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fixed1_elements = create_elements(mesh, "FACE1")
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update!(fixed1_elements, "displacement 1", 0.0)
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update!(fixed1_elements, "displacement 2", 0.0)
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update!(fixed1_elements, "displacement 3", 0.0)
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add_elements!(fixed1, fixed1_elements)
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fixed2 = Problem(Dirichlet, "right support", 3, "displacement")
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fixed2_elements = create_elements(mesh, "FACE2")
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update!(fixed2_elements, "displacement 1", 0.0)
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update!(fixed2_elements, "displacement 2", 0.0)
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update!(fixed2_elements, "displacement 3", 0.0)
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add_elements!(fixed2, fixed2_elements)
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analysis = Analysis(Modal)
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add_problems!(analysis, body, fixed1, fixed2)
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analysis.properties.nev = 5
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run!(analysis)
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freqs_jf = sqrt.(analysis.properties.eigvals)/(2.0*pi)
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# with Tet4 elements
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#freqs_ca = [1.19789E+00, 1.20179E+00, 3.07391E+00, 3.08813E+00, 4.87370E+00]
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# with Tet10 elements
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freqs_ca = [9.65942E-01, 9.66160E-01, 2.52127E+00, 2.52187E+00, 3.48584E+00]
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rtol = [norm(f1-f2) / max(f1,f2) for (f1, f2) in zip(freqs_jf, freqs_ca)]
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@test maximum(rtol) < 3.0e-2
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