mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-09-09 20:43:33 +00:00
Jukka Aho
304 lines
8.5 KiB
Julia
304 lines
8.5 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 SolverTests
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using JuliaFEM.Test
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using JuliaFEM
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using JuliaFEM: DirichletProblem, Seg2, PlaneHeatProblem, Quad4, SimpleSolver, get_element, get_basis, MortarElement, MortarProblem, PlaneStressElasticityProblem, solve!, DirectSolver
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""" Define Problem 1:
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- Field function: Laplace equation Δu=0 in Ω={u∈R²|(x,y)∈[0,1]×[0,1]}
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- Neumann boundary on Γ₁={0<=x<=1, y=0}, ∂u/∂n=600 on Γ₁
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"""
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function get_heatproblem()
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el1 = Quad4([1, 2, 3, 4])
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el1["geometry"] = Vector[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 1.0]]
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el1["temperature thermal conductivity"] = 6.0
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el1["density"] = 36.0
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el2 = Seg2([1, 2])
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el2["geometry"] = Vector[[0.0, 0.0], [1.0, 0.0]]
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el2["temperature flux"] = (
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(0.0 => 0.0),
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(1.0 => 600.0)
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)
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problem1 = PlaneHeatProblem()
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push!(problem1, el1)
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push!(problem1, el2)
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return problem1
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end
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""" Define Problem 2:
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- Dirichlet boundary Γ₂={0<=x<=1, y=1}, u=0 on Γ₂
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"""
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function get_boundaryproblem()
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el3 = Seg2([3, 4])
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el3["geometry"] = Vector[[1.0, 1.0], [0.0, 1.0]]
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el3["temperature"] = 0.0
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problem2 = DirichletProblem("temperature", 1)
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push!(problem2, el3)
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return problem2
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end
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function test_simplesolver()
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info("construct heat problem")
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problem1 = get_heatproblem()
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info("construct boundary problem")
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problem2 = get_boundaryproblem()
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# Create a solver for a set of problems
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info("create SimpleSolver with problems.")
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solver = SimpleSolver()
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push!(solver, problem1)
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push!(solver, problem2)
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info("solve!")
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# Solve problem at time t=1.0 and update fields
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call(solver, 1.0)
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# Postprocess.
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# Interpolate temperature field along boundary of Γ₁ at time t=1.0
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xi = [0.0, -1.0]
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el2 = get_element(problem1.equations[2])
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basis = get_basis(el2)
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X = basis("geometry", xi, 1.0)
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T = basis("temperature", xi, 1.0)
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info("Temperature at point X = $X is T = $T")
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@test isapprox(T, 100.0)
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end
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#test_simplesolver()
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function atest_direct_solver()
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N = Dict{Int, Vector}(
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1 => [0.0, 0.0],
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2 => [2.0, 0.0],
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3 => [4.0, 0.0],
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4 => [0.0, 1.0],
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5 => [2.0, 1.0],
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6 => [4.0, 1.0],
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7 => [0.0, 1.0],
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8 => [1.0, 1.0],
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9 => [3.0, 1.0],
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10 => [4.0, 1.0],
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11 => [0.0, 2.0],
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12 => [1.0, 2.0],
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13 => [3.0, 2.0],
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13 => [4.0, 1.0])
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# volume elements
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e1 = Quad4([1, 2, 5, 4])
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e1["geometry"] = Vector[N[1], N[2], N[5], N[4]]
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e2 = Quad4([2, 3, 6, 5])
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e2["geometry"] = Vector[N[2], N[3], N[6], N[5]]
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e3 = Quad4([7, 8, 12, 11])
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e3["geometry"] = Vector[N[7], N[8], N[12], N[11]]
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e4 = Quad4([8, 9, 13, 12])
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e4["geometry"] = Vector[N[8], N[9], N[13], N[12]]
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e5 = Quad4([9, 10, 14, 13])
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e5["geometry"] = Vector[N[9], N[10], N[14], N[13]]
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# boundary elements for boundary load
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b1 = Seg2([11, 12])
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b1["geometry"] = Vector[N[11], N[12]]
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b1["displacement traction force"] = Vector[[0.0, -10.0], [0.0, -10.0]]
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b2 = Seg2([12, 13])
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b2["geometry"] = Vector[N[12], N[13]]
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b2["displacement traction force"] = Vector[[0.0, -10.0], [0.0, -10.0]]
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b3 = Seg3([13, 14])
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b3["geometry"] = Vector[N[13], N[14]]
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b3["displacement traction force"] = Vector[[0.0, -10.0], [0.0, -10.0]]
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# boundary elements for dirichlet dy=0
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d1 = Seg2([1, 2])
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d1["geometry"] = Vector[N[1], N[2]]
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d1["displacement 2"] = 0.0
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d2 = Seg2([2, 3])
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d2["geometry"] = Vector[N[2], N[3]]
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d2["displacement 2"] = 0.0
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# boundary elements for dirichlet dx=0
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d3 = Seg2([1, 4])
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d3["geometry"] = Vector[N[1], N[4]]
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d3["displacement 1"] = 0.0
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d4 = Seg2([4, 11])
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d4["geometry"] = Vector[N[4], N[11]]
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d4["displacmeent 1"] = 0.0
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# mortar elements to tie meshes -- masters
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m1 = MSeg2([4, 5])
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m1["geometry"] = Vector[N[4], N[5]]
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m2 = MSeg2([5, 6])
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m2["geometry"] = Vector[N[5], N[6]]
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# mortar elements to tie meshes -- slaves
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rotation_matrix(phi) = [cos(phi) -sin(phi); sin(phi) cos(phi)]
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phi = rotation_matrix(-pi/2)
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m3 = MSeg2([7, 8])
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m3["geometry"] = Vector[N[7], N[8]]
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m3["nodal ntsys"] = Matrix[phi, phi]
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m3["master elements"] = MortarElement[m1, m2]
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m4 = MSeg2([8, 9])
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m4["geometry"] = Vector[N[8], N[9]]
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m4["nodal ntsys"] = Matrix[phi, phi]
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m4["master elements"] = MortarElement[m1, m2]
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m5 = MSeg2([9, 10])
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m5["geometry"] = Vector[N[9], N[10]]
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m5["nodal ntsys"] = Matrix[phi, phi]
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m5["master elements"] = MortarElement[m1, m2]
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problem1 = PlaneStressElasticityProblem()
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push!(problem1, e1)
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push!(problem1, e2)
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push!(problem1, e3)
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push!(problem1, e4)
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push!(problem1, e5)
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push!(problem1, b1)
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push!(problem1, b2)
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push!(problem1, b3)
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problem2 = DirichletProblem()
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push!(problem2, d1)
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push!(problem2, d2)
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push!(problem2, d3)
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push!(problem2, d4)
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problem3 = MortarProblem()
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push!(problem3, m1)
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push!(problem3, m2)
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push!(problem3, m3)
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push!(problem3, m4)
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push!(problem3, m5)
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solver = DirectSolver()
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push!(solver, problem1)
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push!(solver, problem2)
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push!(solver, problem3)
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call(solver)
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end
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function test_solver_multiple_dirichlet_bc()
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N = Vector[[0.0, 0.0], [1.0, 0.0], [0.0, 1.0], [1.0, 1.0]]
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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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e1["youngs modulus"] = 900.0
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e1["poissons ratio"] = 0.25
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b1 = Seg2([3, 4])
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b1["geometry"] = Vector[N[3], N[4]]
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b1["displacement traction force"] = Vector[[0.0, -100.0], [0.0, -100.0]]
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problem = PlaneStressElasticityProblem()
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push!(problem, e1)
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push!(problem, b1)
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# manually solve problem 1
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# free_dofs = [3, 5, 6, 8]
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# free_dofs = [3, 6, 7, 8]
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#solve!(problem, free_dofs, 0.0; max_iterations=10)
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#disp = e1("displacement", [1.0, 1.0], 0.0)
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#info("displacement at tip: $disp")
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#@test isapprox(disp, [3.17431158889468E-02, -1.38591518927826E-01])
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# boundary elements for dirichlet dx=0
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dx = Seg2([1, 3])
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dx["geometry"] = Vector[N[1], N[3]]
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dx["displacement 1"] = 0.0
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# boundary elements for dirichlet dy=0
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dy = Seg2([1, 2])
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dy["geometry"] = Vector[N[1], N[2]]
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dy["displacement 2"] = 0.0
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problem2 = DirichletProblem("displacement", 2)
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push!(problem2, dx)
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problem3 = DirichletProblem("displacement", 2)
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push!(problem3, dy)
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solver = DirectSolver()
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push!(solver, problem)
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push!(solver, problem2)
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push!(solver, problem3)
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# launch solver
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norm = solver(0.0)
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# info(e1("displacement"))
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# info(last(e1["displacement"]))
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disp = e1("displacement", [1.0, 1.0], 0.0)
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info("displacement at tip: $disp")
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@test isapprox(disp, [3.17431158889468E-02, -1.38591518927826E-01])
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end
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function test_solver_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, 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([3, 4, 6, 5])
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e2["geometry"] = Vector[N[3], N[4], N[6], N[5]]
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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([5, 6])
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b1["geometry"] = Vector[N[5], N[6]]
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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([3, 5])
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dx2["geometry"] = Vector[N[3], N[5]]
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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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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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# 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_solver_multiple_bodies_multiple_dirichlet_bc()
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end
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