# This file is a part of JuliaFEM. # License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md module MortarTests using JuliaFEM.Test using JuliaFEM.Core: Element, Seg2, Quad4, Tri3, MortarProblem, Assembly, assemble! using JuliaFEM.Core: PlaneStressElasticityProblem, DirichletProblem, DirectSolver # 2d stuff using JuliaFEM.Core: project_from_slave_to_master, project_from_master_to_slave # 3d stuff using JuliaFEM.Core: create_auxiliary_plane, project_point_to_auxiliary_plane, get_edge_intersections, get_points_inside_triangle, clip_polygon, calculate_polygon_centerpoint, project_point_from_plane_to_surface, assemble, calculate_normal_tangential_coordinates!, is_point_inside_convex_polygon function get_test_2d_model() # this is hand calculated and given as an example in my thesis N = Vector[ [0.0, 2.0], [1.0, 2.0], [2.0, 2.0], [0.0, 0.0], [1.0, 0.0], [2.0, 0.0], [0.0, 1.0], [5/4, 1.0], [2.0, 1.0], [0.0, 1.0], [3/4, 1.0], [2.0, 1.0]] rotation_matrix(phi) = [cos(phi) -sin(phi); sin(phi) cos(phi)] master1 = Seg2([7, 8]) master1["geometry"] = Vector[N[7], N[8]] master2 = Seg2([8, 9]) master2["geometry"] = Vector[N[8], N[9]] #= master1 = Seg2([9, 8]) master1["geometry"] = Vector[N[9], N[8]] master2 = Seg2([8, 7]) master2["geometry"] = Vector[N[8], N[7]] =# slave1 = Seg2([10, 11]) slave1["geometry"] = Vector[N[10], N[11]] # should be n = [0 -1]' and t = [1 0]' slave1["normal-tangential coordinates"] = Matrix[rotation_matrix(-pi/2), rotation_matrix(-pi/2)] slave1["master elements"] = Element[master1, master2] slave2 = Seg2([11, 12]) 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 function test_calc_flat_2d_projection_slave_to_master() 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 function test_calc_flat_2d_projection_master_to_slave() 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 #test_calc_flat_2d_projection_master_to_slave() function test_calc_flat_2d_projection_rotated() 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 function test_create_flat_2d_assembly() 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 = Assembly() assemble!(assembly, problem, slave1, 0.0) B = round(full(assembly.stiffness_matrix, 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) empty!(assembly) 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] assemble!(assembly, problem, slave2, 0.0) B = full(assembly.stiffness_matrix) 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 #test_create_flat_2d_assembly() function test_2d_mortar_multiple_bodies_multiple_dirichlet_bc() 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 #test_2d_mortar_multiple_bodies_multiple_dirichlet_bc() function test_2d_mortar_three_bodies_shared_nodes() 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 #test_2d_mortar_three_bodies_shared_nodes() function test_auxiliary_plane_transforms() nodes = Vector{Float64}[ [0.0, 0.0, 0.0], [1.0, 0.0, 0.0], [0.0, 1.0, 0.0]] e1 = Tri3([1, 2, 3]) # local coordinate system N, T1, T2 in node R = [0.0 1.0 0.0 0.0 0.0 1.0 1.0 0.0 0.0] e1["geometry"] = Vector{Float64}[nodes[1], nodes[2], nodes[3]] e1["normal-tangential coordinates"] = Matrix{Float64}[R, R, R] time::Real = 0.0 x0, Q = create_auxiliary_plane(e1, time) info("x0 = $x0") info("Q = $Q") @test isapprox(x0, [1.0/3.0, 1.0/3.0, 0.0]) @test isapprox(Q, R) p1 = Float64[1.0/3.0+0.1, 1.0/3.0+0.1, 1.0] p2 = project_point_to_auxiliary_plane(p1, x0, Q) info("point in auxiliary plane p2 = $p2") @test isapprox(p2, [0.1, 0.1]) theta = project_point_from_plane_to_surface(p2, x0, Q, e1, time) info("theta = $theta") @test isapprox(theta[1], 0.0) X = e1("geometry", theta[2:3], time) info("projected point = $X") @test isapprox(X, Float64[1.0/3.0+0.1, 1.0/3.0+0.1, 0.0]) end #test_auxiliary_plane_transforms() function test_get_edge_intersections() # first case, two triangles S = [ 0.0 0.0; 3.0 0.0; 0.0 3.0]' M = [-1.0 1.0; 2.0 -0.5; 1.0 1.5]' P, n = get_edge_intersections(S, M) P_expected = [ 1.00 1.75 0.00 0.00 0.00 0.00 0.50 1.25] n_expected = [ 1 1 0 0 0 0 1 0 1] @test isapprox(P, P_expected) @test isapprox(n, n_expected) # slave 4 vertices non-convex, master triangle S = [ 0.0 0.0; 2.5 0.0; 1.0 1.0; 0.0 2.0]' M = [-1.0 1.0; 2.0 -0.5; 1.0 1.5]' P, n = get_edge_intersections(S, M) P_expected = [ 1.0 1.75 1.375 0.60 0.00 0.00 0.0 0.00 0.750 1.40 0.50 1.25] n_expected = [ 1 1 0 0 1 0 0 0 1 1 0 1] @test isapprox(P, P_expected) @test isapprox(n, n_expected) # slave 3 triangle, master 4 vertices S = [ 0.0 0.0; 3.0 0.0; 0.0 3.0]' M = [-1.0 1.0; 2.0 -0.5; 1.0 1.5; -1.0 2.0]' P, n = get_edge_intersections(S, M) P_expected = [ 1.00 1.75 0.00 0.00 0.00 0.00 0.50 1.75] n_expected = [ 1 1 0 0 0 0 0 0 1 0 1 0] @test isapprox(P, P_expected) @test isapprox(n, n_expected) end #test_get_edge_intersections() function test_get_points_inside_triangle() S = [0.0 0.0; 3.0 0.0; 0.0 3.0]' pts = [-1.0 1.0; 2.0 -0.5; 1.0 1.5; 0.5 1.5]' P = get_points_inside_triangle(S, pts) @test isapprox(P, [1.0 1.5; 0.5 1.5]') end #test_get_points_inside_triangle() function test_is_point_inside_convex_polygon() X = Vector{Float64}[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 1.0]] @test is_point_inside_convex_polygon([0.5, 0.5], X) == true @test is_point_inside_convex_polygon([1.0, 0.5], X) == true @test is_point_inside_convex_polygon([1.1, 0.5], X) == false @test is_point_inside_convex_polygon([1.0, 1.0], X) == true @test is_point_inside_convex_polygon([0.0, 0.3], X) == true @test is_point_inside_convex_polygon([0.0, -0.000001], X) == false end function test_polygon_clipping_easy() S = [0 0; 3 0; 0 3]' M = [-1 1; 2 -1/2; 2 2]' P, n = clip_polygon(S, M) @test isapprox(P, [0.0 0.5; 1.0 0.0; 2.0 0.0; 2.0 1.0; 1.25 1.75; 0.0 4/3]') @test isapprox(n, [1 0 1; 1 1 0; 0 1 1]) end function test_polygon_clipping_no_clip() # no clipping at all S = [-0.125 0.125 0.125 -0.125 -0.125 -0.125 0.125 0.125] M = [-0.291667 -0.625 -0.625 -0.291667 -0.208333 -0.208333 0.125 0.125 ] P, n = clip_polygon(S, M) # FIXME: check better. @test isa(P, Void) @test isa(n, Void) end #test_polygon_clipping_no_clip() function test_calculate_polygon_centerpoint() P = [ 0.0 1.0 2.0 2.0 1.25 0.0 0.5 0.0 0.0 1.0 1.75 1.33333] C = calculate_polygon_centerpoint(P) info("Polygon centerpoint: $C") @test isapprox(C, [1.0397440690338993, 0.8047003412233396]) end #test_calculate_polygon_centerpoint() function test_assemble_3d_problem_tri3() nodes = Vector{Float64}[ [0.0, 0.0, 0.0], [1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 0.1], [1.0, 0.0, 0.1], [0.0, 1.0, 0.1]] mel = Tri3([4, 5, 6]) mel["geometry"] = Vector{Float64}[nodes[4], nodes[5], nodes[6]] sel = Tri3([1, 2, 3]) sel["geometry"] = Vector{Float64}[nodes[1], nodes[2], nodes[3]] # Rv = [0.0 1.0 0.0 # 0.0 0.0 1.0 # 1.0 0.0 0.0] # sel["normal-tangential coordinates"] = Matrix{Float64}[Rv, Rv, Rv] calculate_normal_tangential_coordinates!(sel, 0.0) sel["master elements"] = Element[mel] prob = MortarProblem("temperature", 1) push!(prob, sel) stiffness_matrix = full(assemble(prob, 0.0).stiffness_matrix) info("stiffness matrix for this problem:\n$stiffness_matrix") M = D = 1/24*[2 1 1; 1 2 1; 1 1 2] B = [D -M] # slave dofs are first in this. info("expected matrix for this problem:\n$B") @test isapprox(stiffness_matrix, B) # rotate and translate surface and check that we are still having same results Rx(t) = [ 1.0 0.0 0.0 0.0 cos(t) -sin(t) 0.0 sin(t) cos(t)] Ry(t) = [ cos(t) 0.0 sin(t) 0.0 1.0 0.0 -sin(t) 0.0 cos(t) ] Rz(t) = [ cos(t) -sin(t) 0.0 sin(t) cos(t) 0.0 0.0 0.0 1.0] T = [1.0, 1.0, 1.0] tx = pi/3.0 ty = pi/4.0 tz = pi/5.0 for node in nodes node[:] = Rz(tz)*Ry(ty)*Rx(tx)*node + T end calculate_normal_tangential_coordinates!(sel, 0.0) stiffness_matrix = full(assemble(prob, 0.0).stiffness_matrix) info("sel midpnt: ", sel("geometry", [1/3, 1/3], 0.0)) info("nt basis: ", sel("normal-tangential coordinates", [1/3, 1/3], 0.0)) @test isapprox(stiffness_matrix, B) end #test_assemble_3d_problem_tri3() function test_assemble_3d_problem_quad4() nodes = Vector{Float64}[ [0.0, 0.0, 0.0], [1.0, 0.0, 0.0], [1.0, 1.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 0.1], [1.0, 0.0, 0.1], [1.0, 1.0, 0.1], [0.0, 1.0, 0.1]] #= nodes = Vector{Float64}[ [-1.0, -1.0, 0.0], [+1.0, -1.0, 0.0], [+1.0, +1.0, 0.0], [-1.0, +1.0, 0.0], [-1.0, -1.0, 0.1], [+1.0, -1.0, 0.1], [+1.0, +1.0, 0.1], [-1.0, +1.0, 0.1]] =# mel = Quad4([5, 6, 7, 8]) mel["geometry"] = Vector{Float64}[nodes[5], nodes[6], nodes[7], nodes[8]] sel = Quad4([1, 2, 3, 4]) sel["geometry"] = Vector{Float64}[nodes[1], nodes[2], nodes[3], nodes[4]] calculate_normal_tangential_coordinates!(sel, 0.0) sel["master elements"] = Element[mel] prob = MortarProblem("temperature", 1) push!(prob, sel) stiffness_matrix = full(assemble(prob, 0.0).stiffness_matrix) info("stiffness matrix for this problem:\n$stiffness_matrix") M = D = 1/36*[4 2 1 2; 2 4 2 1; 1 2 4 2; 2 1 2 4] B = [D -M] # slave dofs are first in this. info("expected matrix for this problem:\n$B") @test isapprox(stiffness_matrix, B) end #test_assemble_3d_problem_quad4() end