calculate stress, interpolate stress to nodes using lsq fitting

test/test_common_failures.jl

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+# This file is a part of JuliaFEM.
+# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
+
+using JuliaFEM
+using JuliaFEM.Test
+
+@testset "geometry missing" begin
+    el = Element(Quad4, [1, 2, 3, 4])
+    pr = Problem(Elasticity, "problem", 2)
+    # this throws KeyError: geometry not found.
+    # it's descriptive enough to give hint to user
+    # what went wrong
+    @test_throws KeyError assemble!(pr, el)
+end
+
+@testset "connectivity information missing" begin
+    el = Element(Quad4)
+    nodes = Vector{Float64}[[0,0],[1,0],[1,1],[0,1]]
+    update!(el, "geometry", nodes)
+    pr = Problem(Elasticity, "problem", 2)
+    @test_throws Exception assemble!(pr, el)
+end

test/test_elasticity_2d_nonhomogeneous_boundary_conditions.jl

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+# This file is a part of JuliaFEM.
+# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
+
+using JuliaFEM
+using JuliaFEM.Preprocess
+using JuliaFEM.Test
+
+@testset "2d nonlinear elasticity: test nonhomogeneous boundary conditions and stress calculation" begin
+
+    # field problem
+    block = Problem(Elasticity, "BLOCK", 2)
+    block.properties.formulation = :plane_stress
+
+    nodes = Dict{Int, Vector{Float64}}(
+        1 => [0.0, 0.0],
+        2 => [1.0, 0.0],
+        3 => [1.0, 1.0],
+        4 => [0.0, 1.0])
+
+    element = Element(Quad4, [1, 2, 3, 4])
+    update!(element, "geometry", nodes)
+    update!(element, "youngs modulus", 288.0)
+    update!(element, "poissons ratio", 1/3)
+    push!(block, element)
+
+    # boundary conditions
+    bc = Problem(Dirichlet, "bc", 2, "displacement")
+    bel1 = Element(Seg2, [1, 2])
+    bel2 = Element(Seg2, [3, 4])
+    bel3 = Element(Seg2, [4, 1])
+    update!([bel1, bel2, bel3], "geometry", nodes)
+    update!(bel1, "displacement 2", 0.0)
+    update!(bel2, "displacement 2", 0.5)
+    update!(bel3, "displacement 1", 0.0)
+    push!(bc, bel1, bel2, bel3)
+
+    solver = Solver("solve block problem")
+    push!(solver, block, bc)
+    call(solver)
+
+    # from code aster
+    eps_expected = [-2.08333312468287E-01, 6.25000000000000E-01, 0.0]
+    sig_expected = [ 4.50685020821470E-06, 4.62857140373777E+02, 0.0]
+    u3_expected =  [-2.36237356855269E-01, 5.00000000000000E-01]
+
+    u3 = reshape(block.assembly.u, 2, 4)[:, 3]
+    info("u3 = $u3")
+    @test isapprox(u3, u3_expected, atol=1.0e-5)
+
+    info("strain")
+    for ip in get_integration_points(element)
+        eps = ip("strain")
+        @printf "%i | %8.3f %8.3f | %8.3f %8.3f %8.3f\n" ip.id ip.coords[1] ip.coords[2] eps[1] eps[2] eps[3]
+        @test isapprox(eps, eps_expected)
+    end
+
+    info("cauchy stress")
+    for ip in get_integration_points(element)
+        sig = ip("cauchy stress")
+        @printf "%i | %8.3f %8.3f | %8.3f %8.3f %8.3f\n" ip.id ip.coords[1] ip.coords[2] sig[1] sig[2] sig[3]
+        @test isapprox(sig, sig_expected)
+    end
+
+    info("pk2 stress")
+    for ip in get_integration_points(element)
+        sig = ip("pk2 stress")
+        @printf "%i | %8.3f %8.3f | %8.3f %8.3f %8.3f\n" ip.id ip.coords[1] ip.coords[2] sig[1] sig[2] sig[3]
+        @test isapprox(sig, sig_expected)
+    end
+end
+

test/test_extrapolate_to_nodes.jl

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+# This file is a part of JuliaFEM.
+# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
+
+using JuliaFEM
+using JuliaFEM.Postprocess
+using JuliaFEM.Test
+
+@testset "extrapolate stress from gauss points to nodes" begin
+    X = Dict{Int, Vector{Float64}}(
+        1 => [0.0, 0.0],
+        2 => [6.0, 0.0],
+        3 => [6.0, 6.0],
+        4 => [0.0, 6.0],
+        5 => [12.0, 0.0],
+        6 => [12.0, 6.0])
+    el1 = Element(Quad4, [1, 2, 3, 4])
+    el2 = Element(Quad4, [2, 5, 6, 3])
+    el1.id = 1
+    el2.id = 2
+    elements = [el1, el2]
+    time = 0.0
+    update!(elements, "geometry", X)
+    update!(get_integration_points(el1), "stress", time => [1.0, 2.0, 3.0])
+    update!(get_integration_points(el2), "stress", time => [2.0, 3.0, 4.0])
+    field_name = "stress"
+    field_dim = 3
+    calc_nodal_values!(elements, field_name, field_dim, time)
+    s1 = el1("stress", [0.0, 0.0], time)
+    s2 = el2("stress", [0.0, 0.0], time)
+    # visually checked, see blog post "Postprocessing stress"
+    @test isapprox(s1, [1.125, 2.125, 3.125])
+    @test isapprox(s2, [1.875, 2.875, 3.875])
+end
+