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Improve documentation (#199)
Let's use Literate.jl to automatically generate usage examples. * Automatically generate documentation from other packages (first try to include each package's docs/src/index.md, but if that fails, then use README.md to introduce the package). * Add example how to calculate local element matrices. * Add example how to perform 2d contact analysis.
This commit is contained in:
Jukka Aho
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# 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
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using JuliaFEM.Preprocess
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using JuliaFEM.Postprocess
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using JuliaFEM.Testing
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testdir = joinpath(Pkg.dir("JuliaFEM"), "test")
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datadir = first(splitext(basename(@__FILE__)))
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@testset "hertz contact, full 2d model, linear elements, flat slave surface" begin
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meshfile = joinpath(testdir, datadir, "hertz_2d_full.med")
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mesh = aster_read_mesh(meshfile)
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upper = Problem(Elasticity, "CYLINDER", 2)
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upper.properties.formulation = :plane_strain
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upper.elements = create_elements(mesh, "CYLINDER")
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update!(upper, "youngs modulus", 70.0e3)
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update!(upper, "poissons ratio", 0.3)
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lower = Problem(Elasticity, "BLOCK", 2)
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lower.properties.formulation = :plane_strain
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lower.elements = create_elements(mesh, "BLOCK")
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update!(lower, "youngs modulus", 210.0e3)
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update!(lower, "poissons ratio", 0.3)
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# support block to ground
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bc_fixed = Problem(Dirichlet, "fixed", 2, "displacement")
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bc_fixed.elements = create_elements(mesh, "FIXED")
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update!(bc_fixed, "displacement 2", 0.0)
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# symmetry line
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bc_sym_23 = Problem(Dirichlet, "symmetry line 23", 2, "displacement")
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bc_sym_23.elements = create_elements(mesh, "SYM23")
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update!(bc_sym_23, "displacement 1", 0.0)
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nid = find_nearest_node(mesh, [0.0, 100.0])
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#load = Problem(Dirichlet, "load", 2, "displacement")
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load = Problem(Elasticity, "point load", 2)
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load.properties.formulation = :plane_strain
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load.elements = [Element(Poi1, [nid])]
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#update!(load.elements, "displacement 2", -10.0)
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update!(load, "displacement traction force 2", -35.0e3)
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contact = Problem(Contact2D, "contact between block and cylinder", 2, "displacement")
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contact.properties.rotate_normals = true
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contact_slave_elements = create_elements(mesh, "BLOCK_TO_CYLINDER")
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contact_master_elements = create_elements(mesh, "CYLINDER_TO_BLOCK")
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add_master_elements!(contact, contact_master_elements)
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add_slave_elements!(contact, contact_slave_elements)
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solver = Solver(Nonlinear)
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push!(solver, upper, lower, bc_fixed, bc_sym_23, load, contact)
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solver()
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node_ids, la = get_nodal_vector(contact_slave_elements, "lambda", 0.0)
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node_ids, n = get_nodal_vector(contact_slave_elements, "normal", 0.0)
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pres = [dot(ni, lai) for (ni, lai) in zip(n, la)]
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#@test isapprox(maximum(pres), 4060.010799583303)
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# 12 % error in maximum pressure
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# integrate pressure in normal and tangential direction
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Rn = 0.0
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Rt = 0.0
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Q = [0.0 -1.0; 1.0 0.0]
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time = 0.0
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for sel in contact_slave_elements
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for ip in get_integration_points(sel)
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w = ip.weight*sel(ip, time, Val{:detJ})
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n = sel("normal", ip, time)
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t = Q'*n
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la = sel("lambda", ip, time)
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Rn += w*dot(n, la)
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Rt += w*dot(t, la)
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end
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end
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info("2d hertz: Rn = $Rn, Rt = $Rt")
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info("2d hertz: maximum pressure pmax = ", maximum(pres))
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@test isapprox(maximum(pres), 3585.0; rtol = 0.13)
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# under 0.15 % error in resultant force
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@test isapprox(Rn, 35.0e3; rtol=0.020)
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@test isapprox(Rt, 0.0; atol=200.0)
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end
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function get_model()
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meshfile = joinpath(testdir, datadir, "block_2d.med")
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mesh = aster_read_mesh(meshfile)
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println(mesh.nodes[1])
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upper = Problem(mesh, Elasticity, "UPPER", 2)
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lower = Problem(mesh, Elasticity, "LOWER", 2)
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for body in [upper, lower]
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body.properties.formulation = :plane_stress
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update!(body, "youngs modulus", 288.0)
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update!(body, "poissons ratio", 1/3)
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end
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load = Problem(mesh, Elasticity, "UPPER_TOP", 2)
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load.properties.formulation = :plane_stress
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update!(load, "displacement traction force 2", -28.8)
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bc1 = Problem(mesh, Dirichlet, "LOWER_BOTTOM", 2, "displacement")
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update!(bc1, "displacement 2", 0.0)
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bc2 = Problem(mesh, Dirichlet, "LOWER_LEFT", 2, "displacement")
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update!(bc2, "displacement 1", 0.0)
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bc3 = Problem(mesh, Dirichlet, "UPPER_LEFT", 2, "displacement")
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update!(bc3, "displacement 1", 0.0)
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interface = Problem(Contact2D, "interface", 2, "displacement")
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interface.properties.rotate_normals = true
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interface_slave_elements = create_elements(mesh, "LOWER_TOP")
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interface_master_elements = create_elements(mesh, "UPPER_BOTTOM")
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add_master_elements!(interface, interface_master_elements)
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add_slave_elements!(interface, interface_slave_elements)
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# in LOWER_LEFT we have node belonging also to contact interface
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# let's remove it from dirichlet bc
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create_node_set_from_element_set!(mesh, "LOWER_LEFT")
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nid = find_nearest_node(mesh, [0.0, 0.5]; node_set="LOWER_LEFT")
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coords = mesh.nodes[nid]
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info("nearest node to (0.0, 0.5) = $nid, coordinates = $coords")
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dofs = [2*(nid-1)+1, 2*(nid-1)+2]
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info("removing nid $nid, dofs $dofs from LOWER_LEFT")
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push!(bc2.assembly.removed_dofs, dofs...)
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solver = Solver(Nonlinear)
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#push!(solver, upper, lower, load, bc1, interface)
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push!(solver, upper, lower, load, bc1, bc2, bc3, interface)
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return solver
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end
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@testset "small sliding 2d patch test, linear Seg2 elements, standard basis" begin
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solver = get_model()
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interface = solver["interface"]
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solver()
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node_ids, displacement = get_nodal_vector(interface.elements, "displacement", 0.0)
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node_ids, geometry = get_nodal_vector(interface.elements, "geometry", 0.0)
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node_ids, lambda = get_nodal_vector(interface.elements, "lambda", 0.0)
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u2 = [u[2] for u in displacement]
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f2 = [f[2] for f in lambda]
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maxabsu2 = maximum(abs.(u2))
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stdabsu2 = std(abs.(u2))
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info("max(abs(u2)) = $maxabsu2, std(abs(u2)) = $stdabsu2")
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@test isapprox(stdabsu2, 0.0; atol=1.0e-12)
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maxabsf2 = maximum(abs.(f2))
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stdabsf2 = std(abs.(f2))
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info("max(abs(f2)) = $maxabsf2, std(abs(f2)) = $stdabsf2")
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@test isapprox(stdabsf2, 0.0; atol=1.0e-12)
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@test isapprox(mean(abs.(f2)), 28.8; atol=1.0e-12)
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end
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@testset "small sliding 2d patch test, linear Seg2 elements, dual basis" begin
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solver = get_model()
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interface = solver["interface"]
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interface.properties.dual_basis = true
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solver()
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node_ids, displacement = get_nodal_vector(interface.elements, "displacement", 0.0)
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node_ids, geometry = get_nodal_vector(interface.elements, "geometry", 0.0)
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node_ids, lambda = get_nodal_vector(interface.elements, "lambda", 0.0)
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u2 = [u[2] for u in displacement]
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f2 = [f[2] for f in lambda]
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maxabsu2 = maximum(abs.(u2))
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stdabsu2 = std(abs.(u2))
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info("max(abs(u2)) = $maxabsu2, std(abs(u2)) = $stdabsu2")
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@test isapprox(stdabsu2, 0.0; atol=1.0e-12)
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maxabsf2 = maximum(abs.(f2))
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stdabsf2 = std(abs.(f2))
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info("max(abs(f2)) = $maxabsf2, std(abs(f2)) = $stdabsf2")
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@test isapprox(stdabsf2, 0.0; atol=1.0e-12)
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@test isapprox(mean(abs.(f2)), 28.8; atol=1.0e-12)
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end
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@@ -1,86 +0,0 @@
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# 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
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using JuliaFEM.Preprocess
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using JuliaFEM.Postprocess
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using JuliaFEM.Testing
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pkgdir = Pkg.dir("JuliaFEM")
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datadir = joinpath(pkgdir, "test", first(splitext(basename(@__FILE__))))
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# from fenet d3613 advanced finite element contact benchmarks
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# a = 6.21 mm, pmax = 3585 MPa
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# this is a very sparse mesh and for that reason pmax is not very accurate
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# (only 6 elements in -20 .. 20 mm contact zone, 3 elements in contact
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meshfile = joinpath(datadir, "hertz_2d_full.med")
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mesh = aster_read_mesh(meshfile)
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upper = Problem(Elasticity, "CYLINDER", 2)
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upper.properties.formulation = :plane_strain
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upper.elements = create_elements(mesh, "CYLINDER")
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update!(upper, "youngs modulus", 70.0e3)
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update!(upper, "poissons ratio", 0.3)
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lower = Problem(Elasticity, "BLOCK", 2)
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lower.properties.formulation = :plane_strain
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lower.elements = create_elements(mesh, "BLOCK")
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update!(lower, "youngs modulus", 210.0e3)
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update!(lower, "poissons ratio", 0.3)
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# support block to ground
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bc_fixed = Problem(Dirichlet, "fixed", 2, "displacement")
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bc_fixed.elements = create_elements(mesh, "FIXED")
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update!(bc_fixed, "displacement 2", 0.0)
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# symmetry line
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bc_sym_23 = Problem(Dirichlet, "symmetry line 23", 2, "displacement")
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bc_sym_23.elements = create_elements(mesh, "SYM23")
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update!(bc_sym_23, "displacement 1", 0.0)
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nid = find_nearest_node(mesh, [0.0, 100.0])
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#load = Problem(Dirichlet, "load", 2, "displacement")
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load = Problem(Elasticity, "point load", 2)
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load.properties.formulation = :plane_strain
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load.elements = [Element(Poi1, [nid])]
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#update!(load.elements, "displacement 2", -10.0)
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update!(load, "displacement traction force 2", -35.0e3)
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contact = Problem(Contact2D, "contact between block and cylinder", 2, "displacement")
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contact.properties.rotate_normals = true
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contact_slave_elements = create_elements(mesh, "CYLINDER_TO_BLOCK")
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contact_master_elements = create_elements(mesh, "BLOCK_TO_CYLINDER")
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add_master_elements!(contact, contact_master_elements)
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add_slave_elements!(contact, contact_slave_elements)
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solver = Solver(Nonlinear)
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push!(solver, upper, lower, bc_fixed, bc_sym_23, load, contact)
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solver()
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node_ids, la = get_nodal_vector(contact_slave_elements, "lambda", 0.0)
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node_ids, n = get_nodal_vector(contact_slave_elements, "normal", 0.0)
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pres = [dot(ni, lai) for (ni, lai) in zip(n, la)]
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#@test isapprox(maximum(pres), 4060.010799583303)
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# 12 % error in maximum pressure
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# integrate pressure in normal and tangential direction
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Rn = 0.0
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Rt = 0.0
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Q = [0.0 -1.0; 1.0 0.0]
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time = 0.0
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for sel in contact_slave_elements
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for ip in get_integration_points(sel)
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w = ip.weight*sel(ip, time, Val{:detJ})
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n = sel("normal", ip, time)
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t = Q'*n
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la = sel("lambda", ip, time)
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Rn += w*dot(n, la)
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Rt += w*dot(t, la)
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end
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end
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info("2d hertz: Rn = $Rn, Rt = $Rt")
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info("2d hertz: maximum pressure pmax = ", maximum(pres))
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@test isapprox(maximum(pres), 3585.0; rtol = 0.13)
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# under 0.15 % error in resultant force
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@test isapprox(Rn, 35.0e3; rtol=0.020)
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@test isapprox(Rt, 0.0; atol=200.0)
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