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https://github.com/JuliaFEM/JuliaFEM.jl.git
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more general way to define saddle point problem.
This commit is contained in:
Jukka Aho
+1
-350
@@ -1,7 +1,7 @@
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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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module MortarTests
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module MortarTests3D
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using JuliaFEM.Test
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@@ -9,9 +9,6 @@ using JuliaFEM.Core: Element, Seg2, Quad4, Tri3, Hex8, MortarProblem, Assembly,
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get_connectivity, update!
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using JuliaFEM.Core: PlaneStressElasticityProblem, DirichletProblem, DirectSolver
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# 2d stuff
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using JuliaFEM.Core: project_from_slave_to_master, project_from_master_to_slave
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# 3d stuff
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using JuliaFEM.Core: create_auxiliary_plane, project_point_to_auxiliary_plane,
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get_edge_intersections, get_points_inside_triangle,
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@@ -22,352 +19,6 @@ using JuliaFEM.Core: create_auxiliary_plane, project_point_to_auxiliary_plane,
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using JuliaFEM.Core: LinearElasticityProblem
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function get_test_2d_model()
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# this is hand calculated and given as an example in my thesis
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N = Vector[
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[0.0, 2.0], [1.0, 2.0], [2.0, 2.0],
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[0.0, 0.0], [1.0, 0.0], [2.0, 0.0],
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[0.0, 1.0], [5/4, 1.0], [2.0, 1.0],
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[0.0, 1.0], [3/4, 1.0], [2.0, 1.0]]
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rotation_matrix(phi) = [cos(phi) -sin(phi); sin(phi) cos(phi)]
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master1 = Seg2([7, 8])
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master1["geometry"] = Vector[N[7], N[8]]
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master2 = Seg2([8, 9])
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master2["geometry"] = Vector[N[8], N[9]]
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#=
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master1 = Seg2([9, 8])
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master1["geometry"] = Vector[N[9], N[8]]
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master2 = Seg2([8, 7])
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master2["geometry"] = Vector[N[8], N[7]]
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=#
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slave1 = Seg2([10, 11])
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slave1["geometry"] = Vector[N[10], N[11]]
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# should be n = [0 -1]' and t = [1 0]'
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slave1["normal-tangential coordinates"] = Matrix[rotation_matrix(-pi/2), rotation_matrix(-pi/2)]
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slave1["master elements"] = Element[master1, master2]
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slave2 = Seg2([11, 12])
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slave2["geometry"] = Vector[N[11], N[12]]
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# should be n = [0 -1]' and t = [1 0]'
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slave2["normal-tangential coordinates"] = Matrix[rotation_matrix(-pi/2), rotation_matrix(-pi/2)]
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slave2["master elements"] = Element[master1, master2]
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return [slave1, slave2], [master1, master2]
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end
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function test_calc_flat_2d_projection_slave_to_master()
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slaves, masters = get_test_2d_model()
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slave1, slave2 = slaves
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master1, master2 = masters
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xi2a = project_from_slave_to_master(slave1, master1, [-1.0])
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@test xi2a == [-1.0]
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xi2b = project_from_slave_to_master(slave1, master1, [1.0])
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@test xi2b == [ 0.2]
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X2 = master1("geometry", xi2b, 0.0)
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@test X2 == [3/4, 1.0]
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end
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function test_calc_flat_2d_projection_master_to_slave()
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slaves, masters = get_test_2d_model()
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slave1, slave2 = slaves
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master1, master2 = masters
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xi1a = project_from_master_to_slave(slave1, master1, [-1.0])
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@test xi1a == [-1.0]
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xi1b = project_from_master_to_slave(slave1, master1, [1.0])
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X1 = slave1("geometry", xi1b, 0.0)
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@test X1 == [5/4, 1.0]
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end
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#test_calc_flat_2d_projection_master_to_slave()
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function test_calc_flat_2d_projection_rotated()
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master1 = Seg2([3, 4])
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master1["geometry"] = Vector{Float64}[[0.0, 1.0], [0.0, 0.0]]
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slave1 = Seg2([1, 2])
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slave1["geometry"] = Vector{Float64}[[0.0, 0.0], [0.0, 1.0]]
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slave1["normal-tangential coordinates"] = Matrix{Float64}[[1.0 0.0; 0.0 1.0], [1.0 0.0; 0.0 1.0]]
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xi = project_from_master_to_slave(slave1, master1, [-1.0])
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info("xi = $xi")
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@test xi == [ 1.0]
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xi = project_from_master_to_slave(slave1, master1, [1.0])
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info("xi = $xi")
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@test xi == [-1.0]
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xi = project_from_slave_to_master(slave1, master1, [-1.0])
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info("xi = $xi")
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@test xi == [ 1.0]
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xi = project_from_slave_to_master(slave1, master1, [1.0])
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info("xi = $xi")
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@test xi == [-1.0]
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end
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function test_create_flat_2d_assembly()
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slaves, masters = get_test_2d_model()
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slave1, slave2 = slaves
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master1, master2 = masters
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info("creating problem")
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problem = MortarProblem("temperature", 1)
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info("pushing slave elements to problem")
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push!(problem, slave1)
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push!(problem, slave2)
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B_expected = zeros(12, 12)
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S1 = [10, 11]
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M1 = [7, 8]
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B_expected[S1,S1] += [1/4 1/8; 1/8 1/4]
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B_expected[S1,M1] -= [3/10 3/40; 9/40 3/20]
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info("creating assembly")
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assembly = Assembly()
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assemble!(assembly, problem, slave1, 0.0)
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B = round(full(assembly.stiffness_matrix, 12, 12), 6)
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info("size of B = $(size(B))")
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info("B matrix in first slave element = \n$(B[10:11,:])")
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info("B matrix expected = \n$(B_expected[10:11,:])")
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@test isapprox(B, B_expected)
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fill!(B_expected, 0.0)
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empty!(assembly)
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S2 = [11, 12]
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M2 = [7, 8]
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B_expected[S2,S2] += [49/150 11/150; 11/150 2/75]
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B_expected[S2,M2] -= [13/150 47/150; 1/75 13/150]
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S3 = [11, 12]
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M3 = [8, 9]
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B_expected[S3,S3] += [9/100 27/200; 27/200 39/100]
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B_expected[S3,M3] -= [3/20 3/40; 9/40 3/10]
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assemble!(assembly, problem, slave2, 0.0)
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B = full(assembly.stiffness_matrix)
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info("size of B = $(size(B))")
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info("B matrix in second slave element = \n$(B[11:12,:])")
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info("B matrix expected = \n$(B_expected[11:12,:])")
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@test isapprox(B, B_expected)
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end
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#test_create_flat_2d_assembly()
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function test_2d_mortar_multiple_bodies_multiple_dirichlet_bc()
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N = Vector[
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[0.0, 0.0], [1.0, 0.0],
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[0.0, 1.0], [1.0, 1.0],
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[0.0, 1.0], [1.0, 1.0],
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[0.0, 2.0], [1.0, 2.0]]
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e1 = Quad4([1, 2, 4, 3])
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e1["geometry"] = Vector[N[1], N[2], N[4], N[3]]
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e2 = Quad4([5, 6, 8, 7])
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e2["geometry"] = Vector[N[5], N[6], N[8], N[7]]
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for el in [e1, e2]
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el["youngs modulus"] = 900.0
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el["poissons ratio"] = 0.25
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end
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b1 = Seg2([7, 8])
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b1["geometry"] = Vector[N[7], N[8]]
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b1["displacement traction force"] = Vector[[0.0, -100.0], [0.0, -100.0]]
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body1 = PlaneStressElasticityProblem()
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push!(body1, e1)
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body2 = PlaneStressElasticityProblem()
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push!(body2, e2)
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push!(body2, b1)
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# boundary elements for dirichlet dx=0
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dx1 = Seg2([1, 3])
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dx1["geometry"] = Vector[N[1], N[3]]
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dx2 = Seg2([5, 7])
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dx2["geometry"] = Vector[N[5], N[7]]
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for dx in [dx1, dx2]
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dx["displacement 1"] = 0.0
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end
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boundary1 = DirichletProblem("displacement", 2)
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push!(boundary1, dx1)
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push!(boundary1, dx2)
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# boundary elements for dirichlet dy=0
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dy1 = Seg2([1, 2])
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dy1["geometry"] = Vector[N[1], N[2]]
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dy1["displacement 2"] = 0.0
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boundary2 = DirichletProblem("displacement", 2)
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push!(boundary2, dy1)
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# mortar boundary between two bodies
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rotation_matrix(phi) = [cos(phi) -sin(phi); sin(phi) cos(phi)]
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master1 = Seg2([3, 4])
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master1["geometry"] = Vector[N[3], N[4]]
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slave1 = Seg2([5, 6])
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slave1["geometry"] = Vector[N[5], N[6]]
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slave1["normal-tangential coordinates"] = Matrix[rotation_matrix(-pi/2), rotation_matrix(-pi/2)]
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slave1["master elements"] = Element[master1]
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boundary3 = MortarProblem("displacement", 2)
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push!(boundary3, slave1)
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solver = DirectSolver()
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push!(solver, body1)
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push!(solver, body2)
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push!(solver, boundary1)
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push!(solver, boundary2)
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push!(solver, boundary3)
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solver.name = "test_2d_mortar_multiple_bodies_multiple_dirichlet_bcs"
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solver.dump_matrices = true
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solver.method = :UMFPACK
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# launch solver
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solver(0.0)
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disp = e2("displacement", [1.0, 1.0], 0.0)
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info("displacement at tip: $disp")
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# code aster verification, two_elements.comm
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@test isapprox(disp, [3.17431158889468E-02, -2.77183037855653E-01])
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end
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#test_2d_mortar_multiple_bodies_multiple_dirichlet_bc()
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function test_2d_mortar_three_bodies_shared_nodes()
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N = Dict{Int, Vector{Float64}}(
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1 => [0.0, 0.0],
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2 => [2.0, 0.0],
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3 => [0.0, 1.0],
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4 => [2.0, 1.0],
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5 => [0.0, 1.0],
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6 => [1.3, 1.0],
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7 => [0.0, 2.0],
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8 => [1.3, 2.0],
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9 => [1.3, 1.0],
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10 => [2.0, 1.0],
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11 => [1.3, 2.0],
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12 => [2.0, 2.0])
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e1 = Quad4([1, 2, 4, 3])
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e1["geometry"] = Vector[N[1], N[2], N[4], N[3]]
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e2 = Quad4([5, 6, 8, 7])
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e2["geometry"] = Vector[N[5], N[6], N[8], N[7]]
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e3 = Quad4([9, 10, 12, 11])
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e3["geometry"] = Vector[N[9], N[10], N[12], N[11]]
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for el in [e1, e2, e3]
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el["youngs modulus"] = 900.0
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el["poissons ratio"] = 0.25
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end
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b1 = Seg2([7, 8])
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b1["geometry"] = Vector[N[7], N[8]]
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b1["displacement traction force"] = Vector[[0.0, -100.0], [0.0, -100.0]]
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b2 = Seg2([11, 12])
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b2["geometry"] = Vector[N[11], N[12]]
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b2["displacement traction force"] = Vector[[0.0, -100.0], [0.0, -100.0]]
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body1 = PlaneStressElasticityProblem()
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push!(body1, e1)
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body2 = PlaneStressElasticityProblem()
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push!(body2, e2)
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push!(body2, b1)
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body3 = PlaneStressElasticityProblem()
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push!(body3, e3)
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push!(body3, b2)
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# boundary elements for dirichlet dx=0
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dx1 = Seg2([1, 3])
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dx1["geometry"] = Vector[N[1], N[3]]
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dx2 = Seg2([5, 7])
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dx2["geometry"] = Vector[N[5], N[7]]
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for dx in [dx1, dx2]
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dx["displacement 1"] = 0.0
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end
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bc1 = DirichletProblem("displacement", 2)
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push!(bc1, dx1)
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push!(bc1, dx2)
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# boundary elements for dirichlet dy=0
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dy1 = Seg2([1, 2])
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dy1["geometry"] = Vector[N[1], N[2]]
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dy1["displacement 2"] = 0.0
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bc2 = DirichletProblem("displacement", 2)
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push!(bc2, dy1)
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# mortar boundary between body 1 and body 2
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rotation_matrix(phi) = [cos(phi) -sin(phi); sin(phi) cos(phi)]
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master1 = Seg2([3, 4])
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master1["geometry"] = Vector[N[3], N[4]]
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slave1 = Seg2([5, 6])
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slave1["geometry"] = Vector[N[5], N[6]]
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slave1["normal-tangential coordinates"] = Matrix[rotation_matrix(-pi/2), rotation_matrix(-pi/2)]
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slave1["master elements"] = Element[master1]
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bc3 = MortarProblem("displacement", 2)
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push!(bc3, slave1)
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# mortar boundary between body 1 and body 3
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slave2 = Seg2([9, 10])
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slave2["geometry"] = Vector[N[9], N[10]]
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slave2["normal-tangential coordinates"] = Matrix[rotation_matrix(-pi/2), rotation_matrix(-pi/2)]
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slave2["master elements"] = Element[master1]
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bc4 = MortarProblem("displacement", 2)
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push!(bc4, slave2)
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# mortar boundary between body 2 and body 3
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master2 = Seg2([9, 11])
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master2["geometry"] = Vector[N[9], N[11]]
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slave3 = Seg2([6, 8])
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slave3["geometry"] = Vector[N[6], N[8]]
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#slave3["normal-tangential coordinates"] = Matrix[rotation_matrix(-pi/2), rotation_matrix(-pi/2)]
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slave3["normal-tangential coordinates"] = Matrix[rotation_matrix(0.0), rotation_matrix(0.0)]
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slave3["master elements"] = Element[master2]
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bc5 = MortarProblem("displacement", 2)
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push!(bc5, slave3)
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solver = DirectSolver()
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push!(solver, body1)
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push!(solver, body2)
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push!(solver, body3)
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push!(solver, bc1)
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push!(solver, bc2)
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push!(solver, bc3)
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push!(solver, bc4)
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push!(solver, bc5)
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# launch solver
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solver.method = :UMFPACK
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solver.name = "test_2d_mortar_three_bodies_shared_nodes"
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solver.dump_matrices = true
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call(solver, 0.0)
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X = e3("geometry", [1.0, 1.0], 0.0)
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u = e3("displacement", [1.0, 1.0], 0.0)
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info("displacement at $X: $u")
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# code aster verification, two_elements.comm
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@test isapprox(u, [2*3.17431158889468E-02, -2.77183037855653E-01])
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end
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#test_2d_mortar_three_bodies_shared_nodes()
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function test_auxiliary_plane_transforms()
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@@ -0,0 +1,355 @@
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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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module MortarTests2D
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using JuliaFEM.Test
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using JuliaFEM.Core: Element, Seg2, Quad4, Tri3, Hex8, MortarProblem, Assembly, assemble,
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get_connectivity, update!, assemble!, BoundaryAssembly
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using JuliaFEM.Core: PlaneStressElasticityProblem, DirichletProblem, DirectSolver
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using JuliaFEM.Core: project_from_slave_to_master, project_from_master_to_slave
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function get_test_2d_model()
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# this is hand calculated and given as an example in my thesis
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N = Vector[
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[0.0, 2.0], [1.0, 2.0], [2.0, 2.0],
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[0.0, 0.0], [1.0, 0.0], [2.0, 0.0],
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[0.0, 1.0], [5/4, 1.0], [2.0, 1.0],
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[0.0, 1.0], [3/4, 1.0], [2.0, 1.0]]
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rotation_matrix(phi) = [cos(phi) -sin(phi); sin(phi) cos(phi)]
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master1 = Seg2([7, 8])
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master1["geometry"] = Vector[N[7], N[8]]
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master2 = Seg2([8, 9])
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master2["geometry"] = Vector[N[8], N[9]]
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#=
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master1 = Seg2([9, 8])
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master1["geometry"] = Vector[N[9], N[8]]
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master2 = Seg2([8, 7])
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master2["geometry"] = Vector[N[8], N[7]]
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=#
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slave1 = Seg2([10, 11])
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slave1["geometry"] = Vector[N[10], N[11]]
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# should be n = [0 -1]' and t = [1 0]'
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slave1["normal-tangential coordinates"] = Matrix[rotation_matrix(-pi/2), rotation_matrix(-pi/2)]
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slave1["master elements"] = Element[master1, master2]
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slave2 = Seg2([11, 12])
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slave2["geometry"] = Vector[N[11], N[12]]
|
||||
# should be n = [0 -1]' and t = [1 0]'
|
||||
slave2["normal-tangential coordinates"] = Matrix[rotation_matrix(-pi/2), rotation_matrix(-pi/2)]
|
||||
slave2["master elements"] = Element[master1, master2]
|
||||
|
||||
return [slave1, slave2], [master1, master2]
|
||||
end
|
||||
|
||||
@testset "2d mortar projection tests" begin
|
||||
|
||||
@testset "calculate flat 2d projection from slave to master" begin
|
||||
slaves, masters = get_test_2d_model()
|
||||
slave1, slave2 = slaves
|
||||
master1, master2 = masters
|
||||
|
||||
xi2a = project_from_slave_to_master(slave1, master1, [-1.0])
|
||||
@test xi2a == [-1.0]
|
||||
|
||||
xi2b = project_from_slave_to_master(slave1, master1, [1.0])
|
||||
@test xi2b == [ 0.2]
|
||||
X2 = master1("geometry", xi2b, 0.0)
|
||||
@test X2 == [3/4, 1.0]
|
||||
end
|
||||
|
||||
@testset "calculate flat 2d projection from master to slave" begin
|
||||
slaves, masters = get_test_2d_model()
|
||||
slave1, slave2 = slaves
|
||||
master1, master2 = masters
|
||||
xi1a = project_from_master_to_slave(slave1, master1, [-1.0])
|
||||
@test xi1a == [-1.0]
|
||||
xi1b = project_from_master_to_slave(slave1, master1, [1.0])
|
||||
X1 = slave1("geometry", xi1b, 0.0)
|
||||
@test X1 == [5/4, 1.0]
|
||||
end
|
||||
|
||||
@testset "calculate flat 2d projection rotated 90 degrees" begin
|
||||
master1 = Seg2([3, 4])
|
||||
master1["geometry"] = Vector{Float64}[[0.0, 1.0], [0.0, 0.0]]
|
||||
slave1 = Seg2([1, 2])
|
||||
slave1["geometry"] = Vector{Float64}[[0.0, 0.0], [0.0, 1.0]]
|
||||
slave1["normal-tangential coordinates"] = Matrix{Float64}[[1.0 0.0; 0.0 1.0], [1.0 0.0; 0.0 1.0]]
|
||||
xi = project_from_master_to_slave(slave1, master1, [-1.0])
|
||||
info("xi = $xi")
|
||||
@test xi == [ 1.0]
|
||||
xi = project_from_master_to_slave(slave1, master1, [1.0])
|
||||
info("xi = $xi")
|
||||
@test xi == [-1.0]
|
||||
|
||||
xi = project_from_slave_to_master(slave1, master1, [-1.0])
|
||||
info("xi = $xi")
|
||||
@test xi == [ 1.0]
|
||||
xi = project_from_slave_to_master(slave1, master1, [1.0])
|
||||
info("xi = $xi")
|
||||
@test xi == [-1.0]
|
||||
|
||||
end
|
||||
|
||||
@testset "calculate flat 2d assembly" begin
|
||||
slaves, masters = get_test_2d_model()
|
||||
slave1, slave2 = slaves
|
||||
master1, master2 = masters
|
||||
|
||||
info("creating problem")
|
||||
problem = MortarProblem("temperature", 1)
|
||||
info("pushing slave elements to problem")
|
||||
push!(problem, slave1)
|
||||
push!(problem, slave2)
|
||||
|
||||
B_expected = zeros(12, 12)
|
||||
S1 = [10, 11]
|
||||
M1 = [7, 8]
|
||||
B_expected[S1,S1] += [1/4 1/8; 1/8 1/4]
|
||||
B_expected[S1,M1] -= [3/10 3/40; 9/40 3/20]
|
||||
|
||||
info("creating assembly")
|
||||
assembly = BoundaryAssembly()
|
||||
assemble!(assembly, problem, slave1, 0.0)
|
||||
B = round(full(assembly.C1, 12, 12), 6)
|
||||
info("size of B = $(size(B))")
|
||||
info("B matrix in first slave element = \n$(B[10:11,:])")
|
||||
info("B matrix expected = \n$(B_expected[10:11,:])")
|
||||
@test isapprox(B, B_expected)
|
||||
|
||||
fill!(B_expected, 0.0)
|
||||
|
||||
S2 = [11, 12]
|
||||
M2 = [7, 8]
|
||||
B_expected[S2,S2] += [49/150 11/150; 11/150 2/75]
|
||||
B_expected[S2,M2] -= [13/150 47/150; 1/75 13/150]
|
||||
S3 = [11, 12]
|
||||
M3 = [8, 9]
|
||||
B_expected[S3,S3] += [9/100 27/200; 27/200 39/100]
|
||||
B_expected[S3,M3] -= [3/20 3/40; 9/40 3/10]
|
||||
assembly = BoundaryAssembly()
|
||||
assemble!(assembly, problem, slave2, 0.0)
|
||||
B = full(assembly.C1)
|
||||
info("size of B = $(size(B))")
|
||||
info("B matrix in second slave element = \n$(B[11:12,:])")
|
||||
info("B matrix expected = \n$(B_expected[11:12,:])")
|
||||
|
||||
@test isapprox(B, B_expected)
|
||||
end
|
||||
|
||||
@testset "test mortar problem with multiple dirichlet boundary conditions and multiple bodies" begin
|
||||
N = Vector[
|
||||
[0.0, 0.0], [1.0, 0.0],
|
||||
[0.0, 1.0], [1.0, 1.0],
|
||||
[0.0, 1.0], [1.0, 1.0],
|
||||
[0.0, 2.0], [1.0, 2.0]]
|
||||
|
||||
e1 = Quad4([1, 2, 4, 3])
|
||||
e1["geometry"] = Vector[N[1], N[2], N[4], N[3]]
|
||||
e2 = Quad4([5, 6, 8, 7])
|
||||
e2["geometry"] = Vector[N[5], N[6], N[8], N[7]]
|
||||
for el in [e1, e2]
|
||||
el["youngs modulus"] = 900.0
|
||||
el["poissons ratio"] = 0.25
|
||||
end
|
||||
b1 = Seg2([7, 8])
|
||||
b1["geometry"] = Vector[N[7], N[8]]
|
||||
b1["displacement traction force"] = Vector[[0.0, -100.0], [0.0, -100.0]]
|
||||
|
||||
body1 = PlaneStressElasticityProblem()
|
||||
push!(body1, e1)
|
||||
|
||||
body2 = PlaneStressElasticityProblem()
|
||||
push!(body2, e2)
|
||||
push!(body2, b1)
|
||||
|
||||
# boundary elements for dirichlet dx=0
|
||||
dx1 = Seg2([1, 3])
|
||||
dx1["geometry"] = Vector[N[1], N[3]]
|
||||
dx2 = Seg2([5, 7])
|
||||
dx2["geometry"] = Vector[N[5], N[7]]
|
||||
for dx in [dx1, dx2]
|
||||
dx["displacement 1"] = 0.0
|
||||
end
|
||||
|
||||
boundary1 = DirichletProblem("displacement", 2)
|
||||
push!(boundary1, dx1)
|
||||
push!(boundary1, dx2)
|
||||
|
||||
# boundary elements for dirichlet dy=0
|
||||
dy1 = Seg2([1, 2])
|
||||
dy1["geometry"] = Vector[N[1], N[2]]
|
||||
dy1["displacement 2"] = 0.0
|
||||
|
||||
boundary2 = DirichletProblem("displacement", 2)
|
||||
push!(boundary2, dy1)
|
||||
|
||||
# mortar boundary between two bodies
|
||||
rotation_matrix(phi) = [cos(phi) -sin(phi); sin(phi) cos(phi)]
|
||||
|
||||
master1 = Seg2([3, 4])
|
||||
master1["geometry"] = Vector[N[3], N[4]]
|
||||
|
||||
slave1 = Seg2([5, 6])
|
||||
slave1["geometry"] = Vector[N[5], N[6]]
|
||||
slave1["normal-tangential coordinates"] = Matrix[rotation_matrix(-pi/2), rotation_matrix(-pi/2)]
|
||||
slave1["master elements"] = Element[master1]
|
||||
|
||||
boundary3 = MortarProblem("displacement", 2)
|
||||
push!(boundary3, slave1)
|
||||
|
||||
solver = DirectSolver()
|
||||
push!(solver, body1)
|
||||
push!(solver, body2)
|
||||
push!(solver, boundary1)
|
||||
push!(solver, boundary2)
|
||||
push!(solver, boundary3)
|
||||
|
||||
solver.name = "test_2d_mortar_multiple_bodies_multiple_dirichlet_bcs"
|
||||
solver.dump_matrices = true
|
||||
solver.method = :UMFPACK
|
||||
# launch solver
|
||||
solver(0.0)
|
||||
|
||||
disp = e2("displacement", [1.0, 1.0], 0.0)
|
||||
info("displacement at tip: $disp")
|
||||
# code aster verification, two_elements.comm
|
||||
@test isapprox(disp, [3.17431158889468E-02, -2.77183037855653E-01])
|
||||
end
|
||||
|
||||
@testset "test 2d mortar problem with three bodies and shared nodes" begin
|
||||
N = Dict{Int, Vector{Float64}}(
|
||||
1 => [0.0, 0.0],
|
||||
2 => [2.0, 0.0],
|
||||
3 => [0.0, 1.0],
|
||||
4 => [2.0, 1.0],
|
||||
5 => [0.0, 1.0],
|
||||
6 => [1.3, 1.0],
|
||||
7 => [0.0, 2.0],
|
||||
8 => [1.3, 2.0],
|
||||
9 => [1.3, 1.0],
|
||||
10 => [2.0, 1.0],
|
||||
11 => [1.3, 2.0],
|
||||
12 => [2.0, 2.0])
|
||||
|
||||
e1 = Quad4([1, 2, 4, 3])
|
||||
e1["geometry"] = Vector[N[1], N[2], N[4], N[3]]
|
||||
|
||||
e2 = Quad4([5, 6, 8, 7])
|
||||
e2["geometry"] = Vector[N[5], N[6], N[8], N[7]]
|
||||
|
||||
e3 = Quad4([9, 10, 12, 11])
|
||||
e3["geometry"] = Vector[N[9], N[10], N[12], N[11]]
|
||||
|
||||
for el in [e1, e2, e3]
|
||||
el["youngs modulus"] = 900.0
|
||||
el["poissons ratio"] = 0.25
|
||||
end
|
||||
|
||||
b1 = Seg2([7, 8])
|
||||
b1["geometry"] = Vector[N[7], N[8]]
|
||||
b1["displacement traction force"] = Vector[[0.0, -100.0], [0.0, -100.0]]
|
||||
|
||||
b2 = Seg2([11, 12])
|
||||
b2["geometry"] = Vector[N[11], N[12]]
|
||||
b2["displacement traction force"] = Vector[[0.0, -100.0], [0.0, -100.0]]
|
||||
|
||||
body1 = PlaneStressElasticityProblem()
|
||||
push!(body1, e1)
|
||||
|
||||
body2 = PlaneStressElasticityProblem()
|
||||
push!(body2, e2)
|
||||
push!(body2, b1)
|
||||
|
||||
body3 = PlaneStressElasticityProblem()
|
||||
push!(body3, e3)
|
||||
push!(body3, b2)
|
||||
|
||||
# boundary elements for dirichlet dx=0
|
||||
dx1 = Seg2([1, 3])
|
||||
dx1["geometry"] = Vector[N[1], N[3]]
|
||||
dx2 = Seg2([5, 7])
|
||||
dx2["geometry"] = Vector[N[5], N[7]]
|
||||
for dx in [dx1, dx2]
|
||||
dx["displacement 1"] = 0.0
|
||||
end
|
||||
|
||||
bc1 = DirichletProblem("displacement", 2)
|
||||
push!(bc1, dx1)
|
||||
push!(bc1, dx2)
|
||||
|
||||
# boundary elements for dirichlet dy=0
|
||||
dy1 = Seg2([1, 2])
|
||||
dy1["geometry"] = Vector[N[1], N[2]]
|
||||
dy1["displacement 2"] = 0.0
|
||||
|
||||
bc2 = DirichletProblem("displacement", 2)
|
||||
push!(bc2, dy1)
|
||||
|
||||
# mortar boundary between body 1 and body 2
|
||||
rotation_matrix(phi) = [cos(phi) -sin(phi); sin(phi) cos(phi)]
|
||||
|
||||
master1 = Seg2([3, 4])
|
||||
master1["geometry"] = Vector[N[3], N[4]]
|
||||
|
||||
slave1 = Seg2([5, 6])
|
||||
slave1["geometry"] = Vector[N[5], N[6]]
|
||||
slave1["normal-tangential coordinates"] = Matrix[rotation_matrix(-pi/2), rotation_matrix(-pi/2)]
|
||||
slave1["master elements"] = Element[master1]
|
||||
bc3 = MortarProblem("displacement", 2)
|
||||
push!(bc3, slave1)
|
||||
|
||||
# mortar boundary between body 1 and body 3
|
||||
slave2 = Seg2([9, 10])
|
||||
slave2["geometry"] = Vector[N[9], N[10]]
|
||||
slave2["normal-tangential coordinates"] = Matrix[rotation_matrix(-pi/2), rotation_matrix(-pi/2)]
|
||||
slave2["master elements"] = Element[master1]
|
||||
bc4 = MortarProblem("displacement", 2)
|
||||
push!(bc4, slave2)
|
||||
|
||||
# mortar boundary between body 2 and body 3
|
||||
master2 = Seg2([9, 11])
|
||||
master2["geometry"] = Vector[N[9], N[11]]
|
||||
|
||||
slave3 = Seg2([6, 8])
|
||||
slave3["geometry"] = Vector[N[6], N[8]]
|
||||
#slave3["normal-tangential coordinates"] = Matrix[rotation_matrix(-pi/2), rotation_matrix(-pi/2)]
|
||||
slave3["normal-tangential coordinates"] = Matrix[rotation_matrix(0.0), rotation_matrix(0.0)]
|
||||
slave3["master elements"] = Element[master2]
|
||||
bc5 = MortarProblem("displacement", 2)
|
||||
push!(bc5, slave3)
|
||||
|
||||
solver = DirectSolver()
|
||||
push!(solver, body1)
|
||||
push!(solver, body2)
|
||||
push!(solver, body3)
|
||||
|
||||
push!(solver, bc1)
|
||||
push!(solver, bc2)
|
||||
|
||||
push!(solver, bc3)
|
||||
push!(solver, bc4)
|
||||
push!(solver, bc5)
|
||||
|
||||
# launch solver
|
||||
solver.method = :UMFPACK
|
||||
solver.name = "test_2d_mortar_three_bodies_shared_nodes"
|
||||
solver.dump_matrices = true
|
||||
call(solver, 0.0)
|
||||
|
||||
X = e3("geometry", [1.0, 1.0], 0.0)
|
||||
u = e3("displacement", [1.0, 1.0], 0.0)
|
||||
info("displacement at $X: $u")
|
||||
# code aster verification, two_elements.comm
|
||||
@test isapprox(u, [2*3.17431158889468E-02, -2.77183037855653E-01])
|
||||
|
||||
end
|
||||
|
||||
end
|
||||
|
||||
end
|
||||
Reference in New Issue
Block a user