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JuliaFEM.jl/test/test_mortar.jl
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Jukka Aho 757ba2b3d9 all tests pass now
2016-07-03 21:16:03 +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 JuliaFEM.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
call(solver, 0.0)
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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