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FEMPlates.jl

FEMPlates.jl contains mathematical formulations for plate bending problems.

Supported formulations:

  • Mindlin plate
using JuliaFEM

field_elements, boundary_elements = get_unit_square()

using FEMPlates

update!(field_elements, "youngs modulus", 4880.0)
update!(field_elements, "poissons ratio", 1/3)
update!(field_elements, "thickness", 0.5)
update!(field_elements, "distributed load", 10.0)
plate = Problem(MindlinPlate, "test problem", 3)
add_elements!(plate, field_elements)
bc = Problem(Dirichlet, "fixed", 3, "displacement")
add_elements!(bc, boundary_elements)
update!(bc, "displacement 1", 0.0)
analysis = Analysis(Linear)
add_problems!(analysis, [plate, bc])
run!(analysis)

u = plate.assembly.u
X = plate("geometry", 0.0)
N = length(X)
x = [X[i][1] for i=1:N]
y = [X[i][2] for i=1:N]

using Plots
surface(x, y, u[1:3:end])

result

Discrete Kirchhoff plate

using JuliaFEM
using JuliaFEM.Preprocess
add_elements! = JuliaFEM.add_elements!
meshfile = Pkg.dir("FEMPlates", "examples", "dkt", "mesh.med")
mesh = aster_read_mesh(meshfile)
field_elements = create_elements(mesh, "PLATE")
update!(field_elements, "youngs modulus", 210.0e9)
update!(field_elements, "poissons ratio", 0.3)
update!(field_elements, "thickness", 50.0e-3)
update!(field_elements, "distributed load", 1.0)
plate = Problem(DKT, "test problem", 3)
add_elements!(plate, field_elements)
boundary_elements = create_elements(mesh, "BORDER")
update!(boundary_elements, "displacement 1", 0.0)
bc = Problem(Dirichlet, "fixed", 3, "displacement")
add_elements!(bc, boundary_elements)
analysis = Analysis(Linear)
add_problems!(analysis, [plate, bc])
run!(analysis)

dkt

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femplates.jl's Issues

Typos in DKT Element; function dHxdeta(ip) and B-Matrix

Needs to be the following:
d9 = -2.0 + 6.0eta + r5(1.0-2.0eta)+xi(r4-r5)
(Apologies, I am a noob at Github, but I saw the error when comparing the results to the exact stiffness matrix formulation paper. With this small change both formulations give the same results for the stiffness matrix.)

Implement Morley element for plate bending problems

Let's implement Morley element for plate bending problems. I'm not sure if this has any practical usage in daily calculations but it's basis functions seems to be quite interesting and giving us some ideas what kind of cumbersome basis functions we should be able to automatically generate using FEMBasis.jl.

Implement DKQ element

DKQ - Discrete Kirchhof Quadrilateral
The DKT element is already implemented and the DKQ element does not really need a lot of adjustments.

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