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Merge pull request #110 from AndiMD/Pyr5

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Pyr5 element implemented.
This commit is contained in:
Jukka Aho
2017-05-29 12:03:39 +07:00
committed by GitHub
parent 2e5f68d2f6 d50f5fadf0
commit 4a857f4f62
8 changed files with 160 additions and 7 deletions
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src/JuliaFEM.jl
+1
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@@ -58,6 +58,7 @@ export Poi1,
Tri3, Tri6, Tri7,
Quad4, Quad8, Quad9,
Tet4, Tet10,
Pyr5,
Wedge6,
Hex8, Hex20, Hex27
src/elements_lagrange.jl
+38 -1
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@@ -13,6 +13,7 @@ global const ELEMENT_DESCRIPTIONS = Dict(
"Quad9" => "9 node quadratic quadrangle element",
"Tet4" => "4 node linear tetrahedral element",
"Tet10" => "10 node quadratic tetrahedral element",
"Pyr5" => "5 node linear pyramid element",
"Wedge6" => "6 node linear prismatic element (wedge)",
"Wedge15" => "15 node quadratic prismatic element (wedge)",
"Hex8" => "8 node linear hexahedral element",
@@ -31,6 +32,7 @@ global const ELEMENT_SIZES = Dict(
"Quad9" => (2, 9),
"Tet4" => (3, 4),
"Tet10" => (3, 10),
"Pyr5" => (3,5),
"Wedge6" => (3, 6),
"Wedge15" => (3, 15),
"Hex8" => (3, 8),
@@ -355,6 +357,39 @@ end
#
type Pyr5 <: AbstractElement
end
function get_reference_coordinates(::Type{Pyr5})
Vector{Float64}[
[-1.0,-1.0,-1.0], # N1
[ 1.0,-1.0,-1.0], # N2
[ 1.0, 1.0,-1.0], # N3
[-1.0, 1.0,-1.0], # N4
[ 0.0, 0.0, 1.0]] # N5
end
function get_interpolation_polynomial(::Type{Pyr5}, xi)
[
1.0/8.0*(1.0-1.0*xi[1])*(1.0-1.0*xi[2])*(1.0-1.0*xi[3])
1.0/8.0*(1.0+1.0*xi[1])*(1.0-1.0*xi[2])*(1.0-1.0*xi[3])
1.0/8.0*(1.0+1.0*xi[1])*(1.0+1.0*xi[2])*(1.0-1.0*xi[3])
1.0/8.0*(1.0-1.0*xi[1])*(1.0+1.0*xi[2])*(1.0-1.0*xi[3])
1.0/2.0*(1.0+xi[3])
]'
end
function get_interpolation_polynomial(::Type{Pyr5}, xi, ::Type{Val{:partial_derivatives}})
[
-0.125*(1.0-xi[2])*(1.0-xi[3]) 0.125*(1.0-xi[2])*(1.0-xi[3]) 0.125*(1.0+xi[2])*(1.0-xi[3]) -0.125*(1.0+xi[2])*(1.0-xi[3]) 0.0
-0.125*(1.0-xi[1])*(1.0-xi[3]) -0.125*(1.0+xi[1])*(1.0-xi[3]) 0.125*(1.0+xi[1])*(1.0-xi[3]) 0.125*(1.0-xi[1])*(1.0-xi[3]) 0.0
-0.125*(1.0-xi[1])*(1.0-xi[2]) -0.125*(1.0+xi[1])*(1.0-xi[2]) -0.125*(1.0+xi[1])*(1.0+xi[2]) -0.125*(1.0-xi[1])*(1.0+xi[2]) 0.5
]
end
#
type Wedge6 <: AbstractElement
end
@@ -576,6 +611,7 @@ end
@create_basis Quad9
@create_basis Tet4
@create_basis Tet10
@create_basis Pyr5
@create_basis Wedge6
@create_basis Wedge15
@create_basis Hex8
@@ -583,7 +619,8 @@ end
@create_basis Hex27
function inside(::Union{Type{Seg2}, Type{Seg3}, Type{Quad4}, Type{Quad8},
Type{Quad9}, Type{Hex8}, Type{Hex20}, Type{Hex27}}, xi)
Type{Quad9}, Type{Pyr5}, Type{Hex8}, Type{Hex20},
Type{Hex27}}, xi)
return all(-1.0 .<= xi .<= 1.0)
end
src/integrate.jl
+23 -2
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@@ -271,6 +271,27 @@ function get_integration_points(element::TetrahedralElement, ::Type{Val{4}})
return zip(weights, points)
end
# http://www.colorado.edu/engineering/CAS/courses.d/AFEM.d/AFEM.Ch12.d/AFEM.Ch12.pdf
typealias PyramidalElement Union{Pyr5,}
function get_integration_points(element::PyramidalElement, ::Type{Val{2}})
g1 = 0.5842373946721771876874344
g2 = -2.0/3.0
g3 = 2.0/5.0
w1 = 81.0/100.0
w2 = 125.0/27.0
weights = [w1, w1, w1, w1, w2]
points = Vector{Float64}[
[-g1, -g1, g2],
[ g1, -g1, g2],
[ g1, g1, g2],
[-g1, g1, g2],
[0.0, 0.0, g3],
]
return zip(weights, points)
end
typealias PrismaticElement Union{Wedge6, Wedge15}
function get_integration_points(element::PrismaticElement, ::Type{Val{2}})
@@ -408,14 +429,14 @@ function get_integration_points(element::PrismaticElement, ::Type{Val{3}})
end
function get_integration_points(element::Union{TriangularElement,
TetrahedralElement, PrismaticElement}, order::Int64)
TetrahedralElement, PyramidalElement, PrismaticElement}, order::Int64)
return get_integration_points(element, Val{order})
end
### default number of integration points for each element
### 2 for linear elements, 3 for quadratic
typealias LinearElement Union{Seg2, Tri3, Quad4, Tet4, Wedge6, Hex8}
typealias LinearElement Union{Seg2, Tri3, Quad4, Tet4, Pyr5, Wedge6, Hex8}
typealias QuadraticElement Union{Seg3, Tri6, Tri7, Tet10, Quad8, Quad9, Wedge15, Hex20, Hex27}
src/preprocess_aster_reader.jl
+3 -2
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@@ -176,6 +176,7 @@ end
global const med_connectivity = Dict{Symbol, Vector{Int}}(
:Tet4 => [4,3,1,2],
:Tet10 => [4,3,1,2,10,7,8,9,6,5],
:Pyr5 => [1,4,3,2,5],
:Wedge6 => [4,5,6,1,2,3],
:Hex8 => [4,8,7,3,1,5,6,2],
:Hex20 => [4,8,7,3,1,5,6,2,20,15,19,11,12,16,14,10,17,13,18,9],
@@ -209,8 +210,8 @@ global const mapping = Dict(
:H20 => :Hex20,
:H27 => :Hex27,
:PY5 => :Pyramid5,
:P13 => :Pyramid13,
:PY5 => :Pyr5,
:P13 => :Pyr13,
)
src/problems_elasticity.jl
+1 -1
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@@ -69,7 +69,7 @@ end
typealias Elasticity2DSurfaceElements Union{Poi1, Seg2, Seg3}
typealias Elasticity2DVolumeElements Union{Tri3, Tri6, Quad4, Quad8, Quad9}
typealias Elasticity3DSurfaceElements Union{Poi1, Tri3, Tri6, Quad4, Quad8, Quad9}
typealias Elasticity3DVolumeElements Union{Tet4, Wedge6, Wedge15, Hex8, Tet10, Hex20, Hex27}
typealias Elasticity3DVolumeElements Union{Tet4, Pyr5, Wedge6, Wedge15, Hex8, Tet10, Hex20, Hex27}
function initialize_internal_params!(params, ip, type_) #::Type{Val{:type_2d}})
param_keys = keys(params)
src/problems_heat.jl
+1 -1
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@@ -67,7 +67,7 @@ function assemble!{E}(assembly::Assembly, problem::Problem{Heat}, element::Eleme
info("Unknown element type $E for 3d heat problem!")
end
typealias Heat3DVolumeElements Union{Tet4, Tet10, Hex8, Hex20, Hex27}
typealias Heat3DVolumeElements Union{Tet4, Tet10, Pyr5, Hex8, Hex20, Hex27}
typealias Heat3DSurfaceElements Union{Tri3, Tri6, Quad4, Quad8, Quad9}
function assemble!{E<:Heat3DVolumeElements}(assembly::Assembly, problem::Problem{Heat}, element::Element{E}, time, ::Type{Val{Symbol("3D")}})
test/test_elasticity_med_pyr5_point_load.jl
+46
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@@ -0,0 +1,46 @@
# 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.Preprocess
using JuliaFEM.Testing
@testset "test Pyr5 elasticity with point load" begin
fn = Pkg.dir("JuliaFEM") * "/geometry/3d_pyr/Pyr5.med"
mesh = aster_read_mesh(fn)
element_sets = join(keys(mesh.element_sets), ", ")
info("element sets: $element_sets")
element1 = create_elements(mesh,"Pyr5")
baseQuad = create_elements(mesh,"baseQuad")
tipPoint = Element(Poi1, collect(mesh.node_sets[:tipPoint]))
update!([element1,baseQuad,tipPoint], "geometry", mesh.nodes)
update!([element1], "youngs modulus", 288.0)
update!([element1], "poissons ratio", 1/3)
update!([tipPoint], "displacement traction force 1", 5.0)
update!([tipPoint], "displacement traction force 2", -7.0)
update!([tipPoint], "displacement traction force 3", 3.0)
elasticity_problem = Problem(Elasticity, "solve continuum block", 3)
elasticity_problem.properties.finite_strain = false
push!(elasticity_problem, element1)
push!(elasticity_problem, tipPoint)
baseQuad[1]["displacement 1"] = 0.0
baseQuad[1]["displacement 2"] = 0.0
baseQuad[1]["displacement 3"] = 0.0
boundary_problem = Problem(Dirichlet, "Boundary conditions", 3, "displacement")
push!(boundary_problem, baseQuad)
solver = LinearSolver(elasticity_problem, boundary_problem)
solver()
disp = element1[1]("displacement", [0.0, 0.0, 1.0], 0.0)
info("########################################################")
info("displacement at tip: $disp")
# Code_Aster Result in verification/2017-05-27-pyramids/Pyr5_displacement.txt
u_expected = [6.9444444444427100E-02,-9.7222222222197952E-02,1.0416666666679683E-02]
@test isapprox(disp, u_expected)
end
test/test_elasticity_pyr5_point_load.jl
+47
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@@ -0,0 +1,47 @@
# 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.Preprocess
using JuliaFEM.Testing
@testset "test Pyr5 elasticity with point load" begin
nodes = Dict{Int64, Node}(
1 => [-1.0,-1.0,-1.0],
2 => [ 1.0,-1.0,-1.0],
3 => [ 1.0, 1.0,-1.0],
4 => [-1.0, 1.0,-1.0],
5 => [ 0.0, 0.0, 1.0])
element1 = Element(Pyr5, [1, 2, 3, 4, 5])
baseQuad = Element(Quad4, [1, 2, 3, 4])
tipPoint = Element(Poi1, [5,])
update!([element1,baseQuad,tipPoint], "geometry", nodes)
update!([element1], "youngs modulus", 288.0)
update!([element1], "poissons ratio", 1/3)
update!([tipPoint], "displacement traction force 1", 5.0)
update!([tipPoint], "displacement traction force 2", -7.0)
update!([tipPoint], "displacement traction force 3", 3.0)
elasticity_problem = Problem(Elasticity, "solve continuum block", 3)
elasticity_problem.properties.finite_strain = false
push!(elasticity_problem, element1, baseQuad, tipPoint)
baseQuad["displacement 1"] = 0.0
baseQuad["displacement 2"] = 0.0
baseQuad["displacement 3"] = 0.0
boundary_problem = Problem(Dirichlet, "Boundary conditions", 3, "displacement")
push!(boundary_problem, baseQuad)
solver = LinearSolver(elasticity_problem, boundary_problem)
solver()
disp = element1("displacement", [0.0, 0.0, 1.0], 0.0)
info("########################################################")
info("displacement at tip: $disp")
# Code_Aster Result in verification/2017-05-27-pyramids/Pyr5_displacement.txt
u_expected = [6.9444444444427100E-02,-9.7222222222197952E-02,1.0416666666679683E-02]
@test isapprox(disp, u_expected)
end