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JuliaFEM.jl/test/test_mortar.jl
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Jukka Aho 69bd7ce58c code aster .med reader, notebook of 3d mortar.
2015-12-14 02:09:33 +02:00

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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
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
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