mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-08-06 04:21:33 +00:00
Jukka Aho
91 lines
3.3 KiB
Julia
91 lines
3.3 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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# # Natural frequency analysis of 3d frame structure
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# For general information about Euler-Bernoulli beam theory, see
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# [this](https://en.wikipedia.org/wiki/Euler%E2%80%93Bernoulli_beam_theory)
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# wikipedia page.
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# The model is a 3d frame, shown in picture.
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# 
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using JuliaFEM, LinearAlgebra
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# Reading mesh
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datadir = Pkg.dir("JuliaFEM", "examples", "3d_frame")
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mesh = aster_read_mesh(joinpath(datadir, "model.med"))
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println("Number of nodes in a model: ", length(mesh.nodes))
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# Create beam elements. For 3d model, we need to define at least
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# [Young's modulus](https://en.wikipedia.org/wiki/Young%27s_modulus),
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# [shear modulus](https://en.wikipedia.org/wiki/Shear_modulus),
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# [density](https://en.wikipedia.org/wiki/Density)
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# cross-section area, moment of inertia in local coordinate
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# system and polar moment of inertia.
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beam_elements = create_elements(mesh, "FRAME")
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@info("Number of elements: ", length(beam_elements))
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update!(beam_elements, "youngs modulus", 210.0e6)
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update!(beam_elements, "shear modulus", 84.0e6)
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update!(beam_elements, "density", 7850.0e-3)
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update!(beam_elements, "cross-section area", 20.0e-2)
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update!(beam_elements, "torsional moment of inertia 1", 10.0e-5)
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update!(beam_elements, "torsional moment of inertia 2", 10.0e-5)
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update!(beam_elements, "polar moment of inertia", 30.0e-5)
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# The direction of beam is defined in same way than in ABAQUS.
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# That is, we have a tangent direction and one normal direction.
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# The third direction is then cross product of tangent and normal.
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# Because the second area moment is same in both directions, we can
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# choose normal direction freely.
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for element in beam_elements
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X1, X2 = element("geometry", 0.0)
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t = (X2-X1)/norm(X2-X1)
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I = [1.0 0.0 0.0; 0.0 1.0 0.0; 0.0 0.0 1.0]
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k = indmax([norm(cross(t, I[:,k])) for k in 1:3])
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n = cross(t, I[:,k])/norm(cross(t, I[:,k]))
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update!(element, "normal", n)
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end
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# Create boundary conditions: fix all degrees of freedom for nodes in
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# a set FIXED. Here we first create elements of type `Poi1` for each
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# node j in set FIXED, update geometry field and then create new fields
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# `fixed displacmeent 1`, `fixed displacement 2`, and so on, where the
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# displacement / rotation is prescribed.
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bc_elements = [Element(Poi1, [j]) for j in mesh.node_sets[:FIXED]]
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update!(bc_elements, "geometry", mesh.nodes)
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for i=1:3
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update!(bc_elements, "fixed displacement $i", 0.0)
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update!(bc_elements, "fixed rotation $i", 0.0)
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end
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# Create a problem, containing beam elements and boundary conditions:
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frame = Problem(Beam, "3d frame", 6)
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add_elements!(frame, beam_elements)
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add_elements!(frame, bc_elements)
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# Perform modal analysis
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analysis = Analysis(Modal)
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xdmf = Xdmf(joinpath(datadir, "3d_frame_results"); overwrite=true)
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add_results_writer!(analysis, xdmf)
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add_problems!(analysis, frame)
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run!(analysis)
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close(xdmf)
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# Each `Analysis` can have properties, e.g. time, maximum number of iterations,
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# convergence tolerance and so on. Eigenvalues of calculation are stored as a
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# properties of analysis:
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freqs = sqrt.(step.properties.eigvals) / (2*pi)
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println("Natural frequencies [Hz]: $(round.(freqs, 2))")
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# [](https://www.youtube.com/watch?v=GzktCqeASmo)
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