mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-09-11 22:21:52 +00:00
Jukka Aho
335 lines
10 KiB
Julia
335 lines
10 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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module MortarTests
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using JuliaFEM.Test
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using JuliaFEM.Core: Element, Seg2, Quad4, MortarProblem, Assembly, assemble!
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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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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["nodal ntsys"] = 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["nodal ntsys"] = 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["nodal ntsys"] = 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["nodal ntsys"] = 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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# launch solver
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norm = 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 = Vector[
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[0.0, 0.0], [2.0, 0.0],
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[0.0, 1.0], [2.0, 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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[1.0, 1.0], [2.0, 1.0],
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[1.0, 2.0], [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["nodal ntsys"] = 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["nodal ntsys"] = 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["nodal ntsys"] = Matrix[rotation_matrix(-pi/2), rotation_matrix(-pi/2)]
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slave3["nodal ntsys"] = 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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norm = 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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end
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