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JuliaFEM.jl/test/test_mortar.jl
T
Jukka Aho ca7e2904cf Fix tests 
* Fix deprecation warnings from tests
* Refactor tests so that ´@testset` is usually called in master file
  `runtests.jl`, not inside test file. Later on we can convert tests
  to examples.
* Syntax of tests now follow more closely syntax used currently in
  JuliaFEM. We have had earlier studies with different kind of syntaxes,
  now we have kind of explicit way to do things.
2018-09-06 13:34:26 +03:00

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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
using JuliaFEM
using SparseArrays, Test
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
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
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
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
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: $C")
@test isapprox(C, [1.0397440690338993, 0.8047003412233396])
end
function test_assemble_3d_problem_tri3()
nodes = Vector{Float64}[
[0.0, 0.0, 0.0],
[1.0, 0.0, 0.0],
[0.0, 1.0, 0.0],
[0.0, 0.0, 0.1],
[1.0, 0.0, 0.1],
[0.0, 1.0, 0.1]]
mel = Tri3([4, 5, 6])
mel["geometry"] = Vector{Float64}[nodes[4], nodes[5], nodes[6]]
sel = Tri3([1, 2, 3])
sel["geometry"] = Vector{Float64}[nodes[1], nodes[2], nodes[3]]
# Rv = [0.0 1.0 0.0
# 0.0 0.0 1.0
# 1.0 0.0 0.0]
# sel["normal-tangential coordinates"] = Matrix{Float64}[Rv, Rv, Rv]
calculate_normal_tangential_coordinates!(sel, 0.0)
sel["master elements"] = Element[mel]
prob = MortarProblem("temperature", 1)
push!(prob, sel)
stiffness_matrix = full(assemble(prob, 0.0).stiffness_matrix)
@info("stiffness matrix for this problem:\n$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
function test_assemble_3d_problem_quad4()
@info("assemble 3d problem in quad4-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],
[2.0, 0.0, 0.1],
[2.0, 2.0, 0.1],
[0.0, 2.0, 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)*144
D = [16 8 4 8; 8 16 8 4; 4 8 16 8; 8 4 8 16]
M = [25 5 1 5; 20 10 2 4; 16 8 4 8; 20 4 2 10]
B = [D -M] # slave dofs are first in this.
@info("expected matrix for this problem:")
dump(round(B, 3))
@info("stiffness matrix for this problem:")
dump(round(stiffness_matrix, 3))
@test isapprox(stiffness_matrix, B)
end
function test_assemble_3d_problem_quad4_2()
@info("assemble 3d problem in quad4-quad4")
nodes = Vector{Float64}[
[0.0, 0.0, 0.0],
[1/4, 0.0, 0.0],
[1/4, 1/4, 0.0],
[0.0, 1/4, 0.0],
[0.0, 0.0, 0.0],
[1/3, 0.0, 0.0],
[1/3, 1/3, 0.0],
[0.0, 1/3, 0.0]]
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)*589824
D = [
4096 2048 1024 2048
2048 4096 2048 1024
1024 2048 4096 2048
2048 1024 2048 4096
]
M = [
5184 1728 576 1728
3456 3456 1152 1152
2304 2304 2304 2304
3456 1152 1152 3456
]
B = [D -M] # slave dofs are first in this.
@info("expected matrix for this problem:")
dump(round(B, 3))
@info("stiffness matrix for this problem:")
dump(round(stiffness_matrix, 3))
@test isapprox(stiffness_matrix, B)
end
function test_assemble_3d_problem_quad4_3()
@info("assemble 3d problem in quad4-quad4")
a = 1/4
b = 1/3
nodes = Vector{Float64}[
[2*a, a, 0],
[3*a, a, 0],
[3*a, 2*a, 0],
[2*a, 2*a, 0],
[ b, 0, 0],
[2*b, 0, 0],
[2*b, b, 0],
[ b, b, 0]]
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)*186624*9
D = [
7904 3040 560 1456
3040 2432 448 560
560 448 128 160
1456 560 160 416
]
M = [
504 1224 7956 3276
144 720 4680 936
18 90 990 198
63 153 1683 693
]
B = [D -M] # slave dofs are first in this.
@info("expected matrix for this problem:")
dump(round(B, 3))
@info("stiffness matrix for this problem:")
dump(round(stiffness_matrix, 3))
@test isapprox(stiffness_matrix, B)
end
function test_3d_problem()
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, 0.5],
[1.0, 0.0, 0.5],
[1.0, 1.0, 0.5],
[0.0, 1.0, 0.5],
[0.0, 0.0, 0.5],
[1.0, 0.0, 0.5],
[1.0, 1.0, 0.5],
[0.0, 1.0, 0.5],
[0.0, 0.0, 1.0],
[1.0, 0.0, 1.0],
[1.0, 1.0, 1.0],
[0.0, 1.0, 1.0],
]
el1 = Hex8([1, 2, 3, 4, 5, 6, 7, 8])
el2 = Hex8([9, 10, 11, 12, 13, 14, 15, 16])
sym121 = Quad4([1, 2, 3, 4])
sym131 = Quad4([1, 2, 6, 5])
sym132 = Quad4([9, 10, 14, 13])
sym231 = Quad4([4, 1, 5, 8])
sym232 = Quad4([12, 9, 13, 16])
force = Quad4([14, 15, 16, 13])
l2u = Quad4([5, 6, 7, 8])
u2l = Quad4([9, 10, 11, 12])
elements = Element[el1, el2, sym121, sym131, sym132, sym231, sym232, force, l2u, u2l]
update!(elements, "geometry", nodes)
el1["youngs modulus"] = el2["youngs modulus"] = 900.0
el1["poissons ratio"] = el2["poissons ratio"] = 0.25
sym121["displacement 3"] = 0.0
sym131["displacement 2"] = sym132["displacement 2"] = 0.0
sym231["displacement 1"] = sym232["displacement 1"] = 0.0
force["displacement traction force 3"] = -100.0
l2u["master elements"] = Element[u2l]
calculate_normal_tangential_coordinates!(l2u, 0.0)
fb = LinearElasticityProblem("two elastic blocks")
push!(fb, el1, el2, force)
bc = DirichletProblem("symmetry boundaries", "displacement", 3)
push!(bc, sym121, sym131, sym132, sym231, sym232)
tie = MortarProblem("tie contact between bodies", "displacement", 3)
push!(tie, l2u)
solver = DirectSolver("solution of elasticity problem")
push!(solver, fb)
push!(solver, bc)
push!(solver, tie)
solver.nonlinear_problem = false
solver.method = :UMFPACK
solver()
X = el2("geometry", [1.0, 1.0, 1.0], 0.0)
u = el2("displacement", [1.0, 1.0, 1.0], 0.0)
@info("displacement at $X = $u")
@test isapprox(u, 1/36*[1, 1, -4])
end
#=
@testset "plane quad4 projector tests" begin
a = 1/2
b = 1/3
nodes = Dict{Int64, Vector{Float64}}(
1 => [0.0, 0.0, 0.0],
2 => [1/2, 0.0, 0.0],
3 => [1.0, 0.0, 0.0],
4 => [0.0, 1.0, 0.0],
5 => [1/2, 1.0, 0.0],
6 => [1.0, 1.0, 0.0],
7 => [0.0, 0.0, 0.0],
8 => [1/3, 0.0, 0.0],
9 => [2/3, 0.0, 0.0],
10 => [1.0, 0.0, 0.0],
11 => [0.0, 1/2, 0.0],
12 => [1/3, 1/2, 0.0],
13 => [2/3, 1/2, 0.0],
14 => [1.0, 1/2, 0.0],
15 => [0.0, 1.0, 0.0],
16 => [1/3, 1.0, 0.0],
17 => [2/3, 1.0, 0.0],
18 => [1.0, 1.0, 0.0],
)
sel1 = Quad4([1, 2, 5, 4])
sel2 = Quad4([2, 3, 6, 5])
mel1 = Quad4([7, 8, 12, 11])
mel2 = Quad4([8, 9, 13, 12])
mel3 = Quad4([9, 10, 14, 13])
mel4 = Quad4([11, 12, 16, 15])
mel5 = Quad4([12, 13, 17, 16])
mel6 = Quad4([13, 14, 18, 17])
update(Element[sel1, sel2, mel1, mel2, mel3, mel4, mel5, mel6], "geometry", nodes)
calculate_normal_tangential_coordinates!(sel1, 0.0)
calculate_normal_tangential_coordinates!(sel2, 0.0)
prob = MortarProblem("temperature", 1)
push!(prob, sel1)
push!(prob, sel2)
sel1["master elements"] = [mel1, mel2, mel4, mel5]
sel2["master elements"] = [mel2, mel3, mel5, mel6]
stiffness_matrix = full(assemble(prob, 0.0).stiffness_matrix)*2592*6
@info("interface matrix:")
dump(round(stiffness_matrix, 3))
B = [
864 432 0 432 216 0 -420 -375 -15 0 -504 -450 -18 0 -84 -75 -3 0
432 1728 432 216 864 216 -120 -690 -690 -120 -144 -828 -828 -144 -24 -138 -138 -24
0 432 864 0 216 432 0 -15 -375 -420 0 -18 -450 -504 0 -3 -75 -84
432 216 0 864 432 0 -84 -75 -3 0 -504 -450 -18 0 -420 -375 -15 0
216 864 216 432 1728 432 -24 -138 -138 -24 -144 -828 -828 -144 -120 -690 -690 -120
0 216 432 0 432 864 0 -3 -75 -84 0 -18 -450 -504 0 -15 -375 -420
]
@info("expected interface matrix:")
dump(round(B, 3))
@test isapprox(stiffness_matrix, B)
end
=#
#= TODO: Fix test.
@testset "plane quad4 projector master 3x3 slave 2x2" begin
a = 1/2
b = 1/3
nodes = Dict{Int64, Vector{Float64}}(
1 => [0*a, 0*a, 0.0],
2 => [1*a, 0*a, 0.0],
3 => [2*a, 0*a, 0.0],
4 => [0*a, 1*a, 0.0],
5 => [1*a, 1*a, 0.0],
6 => [2*a, 1*a, 0.0],
7 => [0*a, 2*a, 0.0],
8 => [1*a, 2*a, 0.0],
9 => [2*a, 2*a, 0.0],
10 => [0*b, 0*b, 0.0],
11 => [1*b, 0*b, 0.0],
12 => [2*b, 0*b, 0.0],
13 => [3*b, 0*b, 0.0],
14 => [0*b, 1*b, 0.0],
15 => [1*b, 1*b, 0.0],
16 => [2*b, 1*b, 0.0],
17 => [3*b, 1*b, 0.0],
18 => [0*b, 2*b, 0.0],
19 => [1*b, 2*b, 0.0],
20 => [2*b, 2*b, 0.0],
21 => [3*b, 2*b, 0.0],
22 => [0*b, 3*b, 0.0],
23 => [1*b, 3*b, 0.0],
24 => [2*b, 3*b, 0.0],
25 => [3*b, 3*b, 0.0],
)
sel1 = Quad4([1, 2, 5, 4])
sel2 = Quad4([2, 3, 6, 5])
sel3 = Quad4([4, 5, 8, 7])
sel4 = Quad4([5, 6, 9, 8])
mel1 = Quad4([10, 11, 15, 14])
mel2 = Quad4([11, 12, 16, 15])
mel3 = Quad4([12, 13, 17, 16])
mel4 = Quad4([14, 15, 19, 18])
mel5 = Quad4([15, 16, 20, 19])
mel6 = Quad4([16, 17, 21, 20])
mel7 = Quad4([18, 19, 23, 22])
mel8 = Quad4([19, 20, 24, 23])
mel9 = Quad4([20, 21, 25, 24])
update!(Element[sel1, sel2, sel3, sel4, mel1, mel2, mel3,
mel4, mel5, mel6, mel7, mel8, mel9], "geometry", nodes)
calculate_normal_tangential_coordinates!(sel1, 0.0)
calculate_normal_tangential_coordinates!(sel2, 0.0)
calculate_normal_tangential_coordinates!(sel3, 0.0)
calculate_normal_tangential_coordinates!(sel4, 0.0)
prob = MortarProblem("temperature", 1)
push!(prob, sel1)
push!(prob, sel2)
push!(prob, sel3)
push!(prob, sel4)
master_elements = [mel1, mel2, mel3, mel4, mel5, mel6, mel7, mel8, mel9]
sel1["master elements"] = master_elements
sel2["master elements"] = master_elements
sel3["master elements"] = master_elements
sel4["master elements"] = master_elements
B = sparse(assemble(prob, 0.0).stiffness_matrix, 25, 25)*46656
B = full(B)
D = B[1:9,1:9]
M = B[1:9,10:end]
@info("interface matrix D:")
dump(round(D, 3))
@info("interface matrix M:")
dump(round(M, 3))
D_expected = [
1296 648 0 648 324 0 0 0 0
648 2592 648 324 1296 324 0 0 0
0 648 1296 0 324 648 0 0 0
648 324 0 2592 1296 0 648 324 0
324 1296 324 1296 5184 1296 324 1296 324
0 324 648 0 1296 2592 0 324 648
0 0 0 648 324 0 1296 648 0
0 0 0 324 1296 324 648 2592 648
0 0 0 0 324 648 0 648 1296]
M_expected = [
-784 -700 -28 0 -700 -625 -25 0 -28 -25 -1 0 0 0 0 0
-224 -1288 -1288 -224 -200 -1150 -1150 -200 -8 -46 -46 -8 0 0 0 0
0 -28 -700 -784 0 -25 -625 -700 0 -1 -25 -28 0 0 0 0
-224 -200 -8 0 -1288 -1150 -46 0 -1288 -1150 -46 0 -224 -200 -8 0
-64 -368 -368 -64 -368 -2116 -2116 -368 -368 -2116 -2116 -368 -64 -368 -368 -64
0 -8 -200 -224 0 -46 -1150 -1288 0 -46 -1150 -1288 0 -8 -200 -224
0 0 0 0 -28 -25 -1 0 -700 -625 -25 0 -784 -700 -28 0
0 0 0 0 -8 -46 -46 -8 -200 -1150 -1150 -200 -224 -1288 -1288 -224
0 0 0 0 0 -1 -25 -28 0 -25 -625 -700 0 -28 -700 -784]
@info("D - D_expected")
dump(D - D_expected)
@info("M - M_expected")
dump(M - M_expected)
@test isapprox(D, D_expected)
@test isapprox(M, M_expected)
#=
B = [
864 432 0 432 216 0 -420 -375 -15 0 -504 -450 -18 0 -84 -75 -3 0
432 1728 432 216 864 216 -120 -690 -690 -120 -144 -828 -828 -144 -24 -138 -138 -24
0 432 864 0 216 432 0 -15 -375 -420 0 -18 -450 -504 0 -3 -75 -84
432 216 0 864 432 0 -84 -75 -3 0 -504 -450 -18 0 -420 -375 -15 0
216 864 216 432 1728 432 -24 -138 -138 -24 -144 -828 -828 -144 -120 -690 -690 -120
0 216 432 0 432 864 0 -3 -75 -84 0 -18 -450 -504 0 -15 -375 -420
]
@info("expected interface matrix:")
dump(round(B, 3))
@test isapprox(stiffness_matrix, B)
=#
end
=#
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