mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-09-12 22:33:19 +00:00
Calculate shape functions using FEMBasis.jl
A lot of code is moved to FEMBasis.jl regarding calculating basis / shape functions of finite elements. * add FEMBasis to REQUIRE * remove obsolete files * remove obsolete test files * make integration point iterable * loosen type definitions * get length of element rather from basis than connectivity * calculate midpoint of reference element * wrong input argument to eval_basis! fixed
This commit is contained in:
Jukka Aho
+7
-6
@@ -19,6 +19,12 @@ import Base: getindex, setindex!, convert, length, size, isapprox, similar,
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start, first, next, done, last, endof, vec, ==, +, -, *, /, haskey, copy,
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push!, isempty, empty!, append!, sparse, full, read
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using FEMBasis
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using FEMBasis: AbstractBasis
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using FEMQuad
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using AbaqusReader
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using AsterReader
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using Logging
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Logging.configure(level=INFO)
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@@ -45,7 +51,7 @@ export AbstractPoint, Point, IntegrationPoint, IP, Node
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### ELEMENTS ###
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include("elements.jl") # common element routines
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export Node, AbstractElement, Element, update!, get_connectivity, get_basis,
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export Node, Element, update!, get_connectivity, get_basis,
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get_dbasis, inside, get_local_coordinates, get_element_type,
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filter_by_element_type, get_element_id
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@@ -62,11 +68,6 @@ export Poi1,
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Wedge6,
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Hex8, Hex20, Hex27
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include("elements_nurbs.jl")
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export NSeg, NSurf, NSolid, is_nurbs
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#include("hierarchical.jl") # P-elements
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include("integrate.jl") # default integration points for elements
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export get_integration_points
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+15
-4
@@ -1,9 +1,7 @@
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# 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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abstract type AbstractElement end
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type Element{E<:AbstractElement}
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type Element{E<:AbstractBasis}
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id :: Int
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connectivity :: Vector{Int}
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integration_points :: Vector{IP}
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@@ -17,10 +15,23 @@ Examples
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--------
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julia> element = Element(Tri3, [1, 2, 3])
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"""
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function Element{E<:AbstractElement}(::Type{E}, connectivity::Vector{Int})
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function Element{E<:AbstractBasis}(::Type{E}, connectivity::Vector{Int})
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return Element{E}(-1, connectivity, [], Dict(), E())
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end
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"""
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length(element::Element)
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Return the number of nodes in element.
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"""
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function length{B}(element::Element{B})
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return length(B)
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end
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function size{B}(element::Element{B})
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return size(B)
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end
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function getindex(element::Element, field_name::AbstractString)
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return element.fields[field_name]
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end
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+25
-589
@@ -1,66 +1,11 @@
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# 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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global const ELEMENT_DESCRIPTIONS = Dict(
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"Poi1" => "1 node discrete point element",
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"Seg2" => "2 node linear segment/line element",
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"Seg3" => "3 node quadratic segment/line element",
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"Tri3" => "3 node linear triangle element",
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"Tri6" => "6 node quadratic triangle element",
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"Tri7" => "7 node quadratic triangle element (has middle node)",
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"Quad4" => "4 node linear quadrangle element",
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"Quad8" => "8 node quadratic quadrangle element (Serendip)",
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"Quad9" => "9 node quadratic quadrangle element",
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"Tet4" => "4 node linear tetrahedral element",
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"Tet10" => "10 node quadratic tetrahedral element",
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"Pyr5" => "5 node linear pyramid element",
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"Wedge6" => "6 node linear prismatic element (wedge)",
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"Wedge15" => "15 node quadratic prismatic element (wedge)",
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"Hex8" => "8 node linear hexahedral element",
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"Hex20" => "20 node biquadratic hexahedral element",
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"Hex27" => "27 node quadratic hexahedral element")
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using FEMBasis
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global const ELEMENT_SIZES = Dict(
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"Poi1" => (0, 1),
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"Seg2" => (1, 2),
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"Seg3" => (1, 3),
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"Tri3" => (2, 3),
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"Tri6" => (2, 6),
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"Tri7" => (2, 7),
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"Quad4" => (2, 4),
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"Quad8" => (2, 8),
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"Quad9" => (2, 9),
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"Tet4" => (3, 4),
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"Tet10" => (3, 10),
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"Pyr5" => (3,5),
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"Wedge6" => (3, 6),
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"Wedge15" => (3, 15),
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"Hex8" => (3, 8),
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"Hex20" => (3, 20),
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"Hex27" => (3, 27))
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""" Return description line of element. """
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function description{T}(element::Element{T})
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element_type = last(split("$T", '.'))
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return get(ELEMENT_DESCRIPTIONS, element_type, "Unknown element description")
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end
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""" Return size of element, i.e. tuple (n, m) where n is dimension of element
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(0, 1, 2, 3) and m is number of nodes. """
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function size{T}(element::Element{T})
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element_type = last(split("$T", '.'))
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return ELEMENT_SIZES[element_type]
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end
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""" Return length of element, i.e. number of nodes. """
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function length{T}(element::Element{T})
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return size(element)[end]
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end
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### 0d element
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type Poi1 <: AbstractElement
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# "Poi1" => (0, 1),
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"1 node discrete point element",
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type Poi1 <: AbstractBasis
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end
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function get_basis(element::Element{Poi1}, ip, time)
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@@ -83,541 +28,32 @@ function get_integration_points(element::Poi1, order::Int64)
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return [ (1.0, [] ) ]
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end
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function get_reference_coordinates(::Type{Poi1})
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function size(::Type{Poi1})
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return (0, 1)
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end
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function length(::Type{Poi1})
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return 1
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end
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function FEMBasis.get_reference_element_coordinates(::Type{Poi1})
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Vector{Float64}[[0.0]]
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end
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### 1d elements
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type Seg2 <: AbstractElement
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end
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function get_reference_coordinates(::Type{Seg2})
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Vector{Float64}[
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[-1.0], # N1
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[ 1.0]] # N2
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end
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function get_interpolation_polynomial(::Type{Seg2}, xi)
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[1.0 xi[1]]
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end
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function get_interpolation_polynomial(::Type{Seg2}, xi, ::Type{Val{:partial_derivatives}})
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[0.0 1.0]
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end
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#
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type Seg3 <: AbstractElement
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end
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function get_reference_coordinates(::Type{Seg3})
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Vector{Float64}[
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[-1.0], # N1
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[ 1.0], # N2
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[ 0.0]] # N3
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end
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function get_interpolation_polynomial(::Type{Seg3}, xi)
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[1.0 xi[1] xi[1]^2]
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end
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function get_interpolation_polynomial(::Type{Seg3}, xi, ::Type{Val{:partial_derivatives}})
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[0.0 1.0 2.0*xi[1]]
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end
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### 2d elements
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type Tri3 <: AbstractElement
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end
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function get_reference_coordinates(::Type{Tri3})
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Vector{Float64}[
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[0.0, 0.0], # N1
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[1.0, 0.0], # N2
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[0.0, 1.0]] # N3
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end
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function get_interpolation_polynomial(::Type{Tri3}, xi)
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[
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1 xi[1] xi[2]
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]
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end
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function get_interpolation_polynomial(::Type{Tri3}, xi, ::Type{Val{:partial_derivatives}})
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[
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0.0 1.0 0.0
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0.0 0.0 1.0
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]
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end
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#
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type Tri6 <: AbstractElement
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end
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function get_reference_coordinates(::Type{Tri6})
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Vector{Float64}[
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[0.0, 0.0], # N1
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[1.0, 0.0], # N2
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[0.0, 1.0], # N3
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[0.5, 0.0], # N4
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[0.5, 0.5], # N5
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[0.0, 0.5]] # N6
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end
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function get_interpolation_polynomial(::Type{Tri6}, xi)
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[
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1 xi[1] xi[2] xi[1]^2 xi[1]*xi[2] xi[2]^2
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]
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end
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function get_interpolation_polynomial(::Type{Tri6}, xi, ::Type{Val{:partial_derivatives}})
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[
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0 1 0 2*xi[1] xi[2] 0
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0 0 1 0 xi[1] 2*xi[2]
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]
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end
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#
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type Tri7 <: AbstractElement
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end
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function get_reference_coordinates(::Type{Tri7})
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Vector{Float64}[
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[0.0, 0.0], # N1
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[1.0, 0.0], # N2
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[0.0, 1.0], # N3
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[0.5, 0.0], # N4
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[0.5, 0.5], # N5
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[0.0, 0.5], # N6
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[1/3, 1/3]] # N7
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end
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function get_interpolation_polynomial(::Type{Tri7}, xi)
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[
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1 xi[1] xi[2] xi[1]^2 xi[1]*xi[2] xi[2]^2 xi[1]^2*xi[2]^2
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]
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end
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function get_interpolation_polynomial(::Type{Tri7}, xi, ::Type{Val{:partial_derivatives}})
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[
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0 1 0 2*xi[1] xi[2] 0 2*xi[1]*xi[2]^2
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0 0 1 0 xi[1] 2*xi[2] 2*xi[1]^2*xi[2]
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]
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end
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#
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type Quad4 <: AbstractElement
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end
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function get_reference_coordinates(::Type{Quad4})
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Vector{Float64}[
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[-1.0, -1.0], # N1
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[ 1.0, -1.0], # N2
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[ 1.0, 1.0], # N3
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[-1.0, 1.0]] # N4
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end
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function get_interpolation_polynomial(::Type{Quad4}, xi)
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[
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1.0 xi[1] xi[2] xi[1]*xi[2]
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]
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end
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function get_interpolation_polynomial(::Type{Quad4}, xi, ::Type{Val{:partial_derivatives}})
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[
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0 1 0 xi[2]
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0 0 1 xi[1]
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]
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end
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#
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type Quad8 <: AbstractElement
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end
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function get_reference_coordinates(::Type{Quad8})
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Vector{Float64}[
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[-1.0, -1.0], # N1
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[ 1.0, -1.0], # N2
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[ 1.0, 1.0], # N3
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[-1.0, 1.0], # N4
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[ 0.0, -1.0], # N5
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[ 1.0, 0.0], # N6
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[ 0.0, 1.0], # N7
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[-1.0, 0.0]] # N8
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end
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function get_interpolation_polynomial(::Type{Quad8}, xi)
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[
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1 xi[2] xi[1] xi[2]^2 xi[1]*xi[2] xi[1]^2 xi[1]*xi[2]^2 xi[1]^2*xi[2]
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]
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end
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function get_interpolation_polynomial(::Type{Quad8}, xi, ::Type{Val{:partial_derivatives}})
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[
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0 0 1 0 xi[2] 2*xi[1] xi[2]^2 2*xi[1]*xi[2]
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0 1 0 2*xi[2] xi[1] 0 2*xi[1]*xi[2] xi[1]^2
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]
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end
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#
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type Quad9 <: AbstractElement
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end
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function get_reference_coordinates(::Type{Quad9})
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Vector{Float64}[
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[-1.0, -1.0], # N1
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[ 1.0, -1.0], # N2
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[ 1.0, 1.0], # N3
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[-1.0, 1.0], # N4
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[ 0.0, -1.0], # N5
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[ 1.0, 0.0], # N6
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[ 0.0, 1.0], # N7
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[-1.0, 0.0], # N8
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[ 0.0, 0.0]] # N9
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end
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function get_interpolation_polynomial(::Type{Quad9}, xi)
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[
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1 xi[2] xi[1] xi[2]^2 xi[1]*xi[2] xi[1]^2 xi[1]*xi[2]^2 xi[1]^2*xi[2] xi[1]^2*xi[2]^2
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]
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end
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function get_interpolation_polynomial(::Type{Quad9}, xi, ::Type{Val{:partial_derivatives}})
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[
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0 0 1 0 xi[2] 2*xi[1] xi[2]^2 2*xi[1]*xi[2] 2*xi[1]*xi[2]^2
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0 1 0 2*xi[2] xi[1] 0 2*xi[1]*xi[2] xi[1]^2 2*xi[1]^2*xi[2]
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]
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end
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### 3d elements
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type Tet4 <: AbstractElement
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function get_basis{B}(element::Element{B}, ip, time)
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T = typeof(first(ip))
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N = zeros(T, 1, length(B))
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eval_basis!(B, N, tuple(ip...))
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return N
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end
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function get_reference_coordinates(::Type{Tet4})
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Vector{Float64}[
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[0.0, 0.0, 0.0], # N1
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[1.0, 0.0, 0.0], # N2
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[0.0, 1.0, 0.0], # N3
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[0.0, 0.0, 1.0]] # N4
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function get_dbasis{B}(element::Element{B}, ip, time)
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T = typeof(first(ip))
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dN = zeros(T, size(B)...)
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eval_dbasis!(B, dN, tuple(ip...))
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return dN
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end
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function get_interpolation_polynomial(::Type{Tet4}, xi)
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[
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1.0 xi[1] xi[2] xi[3]
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]
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end
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function get_interpolation_polynomial(::Type{Tet4}, xi, ::Type{Val{:partial_derivatives}})
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[
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0.0 1.0 0.0 0.0
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0.0 0.0 1.0 0.0
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0.0 0.0 0.0 1.0
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]
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end
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#
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type Tet10 <: AbstractElement
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end
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function get_reference_coordinates(::Type{Tet10})
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Vector{Float64}[
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[0.0, 0.0, 0.0], # N1
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[1.0, 0.0, 0.0], # N2
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[0.0, 1.0, 0.0], # N3
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[0.0, 0.0, 1.0], # N4
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[0.5, 0.0, 0.0], # N5
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[0.5, 0.5, 0.0], # N6
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[0.0, 0.5, 0.0], # N7
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[0.0, 0.0, 0.5], # N8
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[0.5, 0.0, 0.5], # N9
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[0.0, 0.5, 0.5]] # N10
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end
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function get_interpolation_polynomial(::Type{Tet10}, xi)
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[
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1.0 xi[3] xi[2] xi[1] xi[3]^2 xi[2]*xi[3] xi[2]^2 xi[1]*xi[3] xi[1]*xi[2] xi[1]^2
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]
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end
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function get_interpolation_polynomial(::Type{Tet10}, xi, ::Type{Val{:partial_derivatives}})
|
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[
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0 0 0 1 0 0 0 xi[3] xi[2] 2*xi[1]
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0 0 1 0 0 xi[3] 2*xi[2] 0 xi[1] 0
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0 1 0 0 2*xi[3] xi[2] 0 xi[1] 0 0
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]
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end
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#
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type Pyr5 <: AbstractElement
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end
|
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|
||||
|
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function get_reference_coordinates(::Type{Pyr5})
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Vector{Float64}[
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[-1.0,-1.0,-1.0], # N1
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[ 1.0,-1.0,-1.0], # N2
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[ 1.0, 1.0,-1.0], # N3
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[-1.0, 1.0,-1.0], # N4
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[ 0.0, 0.0, 1.0]] # N5
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end
|
||||
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||||
function get_interpolation_polynomial(::Type{Pyr5}, xi)
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||||
[
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1.0/8.0*(1.0-1.0*xi[1])*(1.0-1.0*xi[2])*(1.0-1.0*xi[3])
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||||
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
|
||||
|
||||
function get_reference_coordinates(::Type{Wedge6})
|
||||
Vector{Float64}[
|
||||
[0.0, 0.0, -1.0], # N1
|
||||
[1.0, 0.0, -1.0], # N2
|
||||
[0.0, 1.0, -1.0], # N3
|
||||
[0.0, 0.0, 1.0], # N4
|
||||
[1.0, 0.0, 1.0], # N5
|
||||
[0.0, 1.0, 1.0]] # N6
|
||||
end
|
||||
|
||||
function get_interpolation_polynomial(::Type{Wedge6}, x)
|
||||
[
|
||||
1 x[1] x[2] x[3] x[1]*x[3] x[2]*x[3]
|
||||
]
|
||||
end
|
||||
|
||||
function get_interpolation_polynomial(::Type{Wedge6}, x, ::Type{Val{:partial_derivatives}})
|
||||
[
|
||||
0 1 0 0 x[3] 0
|
||||
0 0 1 0 0 x[3]
|
||||
0 0 0 1 x[1] x[2]
|
||||
]
|
||||
end
|
||||
|
||||
#
|
||||
|
||||
type Wedge15 <: AbstractElement
|
||||
end
|
||||
|
||||
function get_reference_coordinates(::Type{Wedge15})
|
||||
Vector{Float64}[
|
||||
[0.0, 0.0, -1.0], # N1
|
||||
[1.0, 0.0, -1.0], # N2
|
||||
[0.0, 1.0, -1.0], # N3
|
||||
[0.0, 0.0, 1.0], # N4
|
||||
[1.0, 0.0, 1.0], # N5
|
||||
[0.0, 1.0, 1.0], # N6
|
||||
[0.5, 0.0, -1.0], # N7
|
||||
[0.5, 0.5, -1.0], # N8
|
||||
[0.0, 0.5, -1.0], # N9
|
||||
[0.5, 0.0, 1.0], # N10
|
||||
[0.5, 0.5, 1.0], # N11
|
||||
[0.0, 0.5, 1.0], # N12
|
||||
[0.0, 0.0, 0.0], # N13
|
||||
[1.0, 0.0, 0.0], # N14
|
||||
[0.0, 1.0, 0.0]] # N15
|
||||
end
|
||||
|
||||
function get_interpolation_polynomial(::Type{Wedge15}, x)
|
||||
[
|
||||
1 x[1] x[1]^2 x[2] x[1]*x[2] x[2]^2 x[3] x[1]*x[3] x[1]^2*x[3] x[2]*x[3] x[1]*x[2]*x[3] x[2]^2*x[3] x[3]^2 x[1]*x[3]^2 x[2]*x[3]^2
|
||||
]
|
||||
end
|
||||
|
||||
function get_interpolation_polynomial(::Type{Wedge15}, x, ::Type{Val{:partial_derivatives}})
|
||||
[
|
||||
0 1 2*x[1] 0 x[2] 0 0 x[3] 2*x[1]*x[3] 0 x[2]*x[3] 0 0 x[3]^2 0
|
||||
0 0 0 1 x[1] 2*x[2] 0 0 0 x[3] x[1]*x[3] 2*x[2]*x[3] 0 0 x[3]^2
|
||||
0 0 0 0 0 0 1 x[1] x[1]^2 x[2] x[1]*x[2] x[2]^2 2*x[3] 2*x[1]*x[3] 2*x[2]*x[3]
|
||||
]
|
||||
end
|
||||
|
||||
#
|
||||
|
||||
type Hex8 <: AbstractElement
|
||||
end
|
||||
|
||||
function get_reference_coordinates(::Type{Hex8})
|
||||
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
|
||||
[-1.0, -1.0, 1.0], # N5
|
||||
[ 1.0, -1.0, 1.0], # N6
|
||||
[ 1.0, 1.0, 1.0], # N7
|
||||
[-1.0, 1.0, 1.0]] # N8
|
||||
end
|
||||
|
||||
function get_interpolation_polynomial(::Type{Hex8}, xi)
|
||||
[
|
||||
1 xi[3] xi[2] xi[1] xi[2]*xi[3] xi[1]*xi[3] xi[1]*xi[2] xi[1]*xi[2]*xi[3]
|
||||
]
|
||||
end
|
||||
|
||||
function get_interpolation_polynomial(::Type{Hex8}, xi, ::Type{Val{:partial_derivatives}})
|
||||
[
|
||||
0 0 0 1 0 xi[3] xi[2] xi[2]*xi[3]
|
||||
0 0 1 0 xi[3] 0 xi[1] xi[1]*xi[3]
|
||||
0 1 0 0 xi[2] xi[1] 0 xi[1]*xi[2]
|
||||
]
|
||||
end
|
||||
|
||||
#
|
||||
|
||||
type Hex20 <: AbstractElement
|
||||
end
|
||||
|
||||
function get_reference_coordinates(::Type{Hex20})
|
||||
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
|
||||
[-1.0, -1.0, 1.0], # N5
|
||||
[ 1.0, -1.0, 1.0], # N6
|
||||
[ 1.0, 1.0, 1.0], # N7
|
||||
[-1.0, 1.0, 1.0], # N8
|
||||
[ 0.0, -1.0, -1.0], # N9
|
||||
[ 1.0, 0.0, -1.0], # N10
|
||||
[ 0.0, 1.0, -1.0], # N11
|
||||
[-1.0, 0.0, -1.0], # N12
|
||||
[-1.0, -1.0, 0.0], # N13
|
||||
[ 1.0, -1.0, 0.0], # N14
|
||||
[ 1.0, 1.0, 0.0], # N15
|
||||
[-1.0, 1.0, 0.0], # N16
|
||||
[ 0.0, -1.0, 1.0], # N17
|
||||
[ 1.0, 0.0, 1.0], # N18
|
||||
[ 0.0, 1.0, 1.0], # N19
|
||||
[-1.0, 0.0, 1.0]] # N20
|
||||
end
|
||||
|
||||
function get_interpolation_polynomial(::Type{Hex20}, xi)
|
||||
[
|
||||
1 xi[3] xi[2] xi[1] xi[2]*xi[3] xi[1]*xi[3] xi[1]*xi[2] xi[1]*xi[2]*xi[3] xi[3]^2 xi[2]^2 xi[1]^2 xi[2]*xi[3]^2 xi[2]^2*xi[3] xi[1]*xi[3]^2 xi[1]*xi[2]^2 xi[1]^2*xi[3] xi[1]^2*xi[2] xi[1]*xi[2]*xi[3]^2 xi[1]*xi[2]^2*xi[3] xi[1]^2*xi[2]*xi[3]
|
||||
]
|
||||
end
|
||||
|
||||
function get_interpolation_polynomial(::Type{Hex20}, xi, ::Type{Val{:partial_derivatives}})
|
||||
[
|
||||
0 0 0 1 0 xi[3] xi[2] xi[2]*xi[3] 0 0 2*xi[1] 0 0 xi[3]^2 xi[2]^2 2*xi[1]*xi[3] 2*xi[1]*xi[2] xi[2]*xi[3]^2 xi[2]^2*xi[3] 2*xi[1]*xi[2]*xi[3]
|
||||
0 0 1 0 xi[3] 0 xi[1] xi[1]*xi[3] 0 2*xi[2] 0 xi[3]^2 2*xi[2]*xi[3] 0 2*xi[1]*xi[2] 0 xi[1]^2 xi[1]*xi[3]^2 2*xi[1]*xi[2]*xi[3] xi[1]^2*xi[3]
|
||||
0 1 0 0 xi[2] xi[1] 0 xi[1]*xi[2] 2*xi[3] 0 0 2*xi[2]*xi[3] xi[2]^2 2*xi[1]*xi[3] 0 xi[1]^2 0 2*xi[1]*xi[2]*xi[3] xi[1]*xi[2]^2 xi[1]^2*xi[2]
|
||||
]
|
||||
end
|
||||
|
||||
###
|
||||
|
||||
type Hex27 <: AbstractElement
|
||||
end
|
||||
|
||||
function get_reference_coordinates(::Type{Hex27})
|
||||
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
|
||||
[-1.0, -1.0, 1.0], # N5
|
||||
[ 1.0, -1.0, 1.0], # N6
|
||||
[ 1.0, 1.0, 1.0], # N7
|
||||
[-1.0, 1.0, 1.0], # N8
|
||||
[ 0.0, -1.0, -1.0], # N9
|
||||
[ 1.0, 0.0, -1.0], # N10
|
||||
[ 0.0, 1.0, -1.0], # N11
|
||||
[-1.0, 0.0, -1.0], # N12
|
||||
[-1.0, -1.0, 0.0], # N13
|
||||
[ 1.0, -1.0, 0.0], # N14
|
||||
[ 1.0, 1.0, 0.0], # N15
|
||||
[-1.0, 1.0, 0.0], # N16
|
||||
[ 0.0, -1.0, 1.0], # N17
|
||||
[ 1.0, 0.0, 1.0], # N18
|
||||
[ 0.0, 1.0, 1.0], # N19
|
||||
[-1.0, 0.0, 1.0], # N20
|
||||
[ 0.0, 0.0, -1.0], # N21
|
||||
[ 0.0, -1.0, 0.0], # N22
|
||||
[ 1.0, 0.0, 0.0], # N23
|
||||
[ 0.0, 1.0, 0.0], # N24
|
||||
[-1.0, 0.0, 0.0], # N25
|
||||
[ 0.0, 0.0, 1.0], # N26
|
||||
[ 0.0, 0.0, 0.0]] # N27
|
||||
end
|
||||
|
||||
function get_interpolation_polynomial(::Type{Hex27}, xi)
|
||||
[
|
||||
1 xi[3] xi[2] xi[1] xi[2]*xi[3] xi[1]*xi[3] xi[1]*xi[2] xi[1]*xi[2]*xi[3] xi[3]^2 xi[2]^2 xi[1]^2 xi[2]*xi[3]^2 xi[2]^2*xi[3] xi[1]*xi[3]^2 xi[1]*xi[2]^2 xi[1]^2*xi[3] xi[1]^2*xi[2] xi[2]^2*xi[3]^2 xi[1]*xi[2]*xi[3]^2 xi[1]*xi[2]^2*xi[3] xi[1]^2*xi[3]^2 xi[1]^2*xi[2]*xi[3] xi[1]^2*xi[2]^2 xi[1]*xi[2]^2*xi[3]^2 xi[1]^2*xi[2]*xi[3]^2 xi[1]^2*xi[2]^2*xi[3] xi[1]^2*xi[2]^2*xi[3]^2
|
||||
]
|
||||
end
|
||||
|
||||
function get_interpolation_polynomial(::Type{Hex27}, xi, ::Type{Val{:partial_derivatives}})
|
||||
[
|
||||
0 0 0 1 0 xi[3] xi[2] xi[2]*xi[3] 0 0 2*xi[1] 0 0 xi[3]^2 xi[2]^2 2*xi[1]*xi[3] 2*xi[1]*xi[2] 0 xi[2]*xi[3]^2 xi[2]^2*xi[3] 2*xi[1]*xi[3]^2 2*xi[1]*xi[2]*xi[3] 2*xi[1]*xi[2]^2 xi[2]^2*xi[3]^2 2*xi[1]*xi[2]*xi[3]^2 2*xi[1]*xi[2]^2*xi[3] 2*xi[1]*xi[2]^2*xi[3]^2
|
||||
0 0 1 0 xi[3] 0 xi[1] xi[1]*xi[3] 0 2*xi[2] 0 xi[3]^2 2*xi[2]*xi[3] 0 2*xi[1]*xi[2] 0 xi[1]^2 2*xi[2]*xi[3]^2 xi[1]*xi[3]^2 2*xi[1]*xi[2]*xi[3] 0 xi[1]^2*xi[3] 2*xi[1]^2*xi[2] 2*xi[1]*xi[2]*xi[3]^2 xi[1]^2*xi[3]^2 2*xi[1]^2*xi[2]*xi[3] 2*xi[1]^2*xi[2]*xi[3]^2
|
||||
0 1 0 0 xi[2] xi[1] 0 xi[1]*xi[2] 2*xi[3] 0 0 2*xi[2]*xi[3] xi[2]^2 2*xi[1]*xi[3] 0 xi[1]^2 0 2*xi[2]^2*xi[3] 2*xi[1]*xi[2]*xi[3] xi[1]*xi[2]^2 2*xi[1]^2*xi[3] xi[1]^2*xi[2] 0 2*xi[1]*xi[2]^2*xi[3] 2*xi[1]^2*xi[2]*xi[3] xi[1]^2*xi[2]^2 2*xi[1]^2*xi[2]^2*xi[3]
|
||||
]
|
||||
end
|
||||
|
||||
###
|
||||
|
||||
macro create_basis(T)
|
||||
quote
|
||||
T = $T
|
||||
global get_basis, get_dbasis, length, size
|
||||
X = get_reference_coordinates(T)
|
||||
nbasis = length(X)
|
||||
A = zeros(nbasis, nbasis)
|
||||
for i=1:nbasis
|
||||
A[i,:] = get_interpolation_polynomial(T, X[i])
|
||||
end
|
||||
invA = inv(A)
|
||||
function get_basis(element::Element{$T}, ip, time)
|
||||
return get_interpolation_polynomial($T, ip)*invA
|
||||
end
|
||||
function get_dbasis(element::Element{$T}, ip, time)
|
||||
return get_interpolation_polynomial($T, ip, Val{:partial_derivatives})*invA
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
@create_basis Seg2
|
||||
@create_basis Seg3
|
||||
@create_basis Tri3
|
||||
@create_basis Tri6
|
||||
@create_basis Tri7
|
||||
@create_basis Quad4
|
||||
@create_basis Quad8
|
||||
@create_basis Quad9
|
||||
@create_basis Tet4
|
||||
@create_basis Tet10
|
||||
@create_basis Pyr5
|
||||
@create_basis Wedge6
|
||||
@create_basis Wedge15
|
||||
@create_basis Hex8
|
||||
@create_basis Hex20
|
||||
@create_basis Hex27
|
||||
|
||||
function inside(::Union{Type{Seg2}, Type{Seg3}, Type{Quad4}, Type{Quad8},
|
||||
Type{Quad9}, Type{Pyr5}, Type{Hex8}, Type{Hex20},
|
||||
Type{Hex27}}, xi)
|
||||
@@ -628,7 +64,7 @@ function inside(::Union{Type{Tri3}, Type{Tri6}, Type{Tri7}, Type{Tet4}, Type{Tet
|
||||
return all(xi .>= 0.0) && (sum(xi) <= 1.0)
|
||||
end
|
||||
|
||||
function get_reference_coordinates{E}(element::Element{E})
|
||||
get_reference_coordinates(E)
|
||||
function get_reference_coordinates{B}(element::Element{B})
|
||||
return get_reference_element_coordinates(B)
|
||||
end
|
||||
|
||||
|
||||
@@ -1,149 +0,0 @@
|
||||
# This file is a part of JuliaFEM.
|
||||
# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
|
||||
|
||||
using ForwardDiff
|
||||
# TODO: evaluate partial derivatives of basis functions without forwarddiff
|
||||
|
||||
""" NURBS segment. """
|
||||
type NSeg <: AbstractElement
|
||||
order :: Int
|
||||
knots :: Vector{Float64}
|
||||
weights :: Vector{Float64}
|
||||
end
|
||||
|
||||
function NSeg()
|
||||
NSeg(1,
|
||||
[-1.0, -1.0, 1.0, 1.0],
|
||||
ones(4))
|
||||
end
|
||||
|
||||
type NSurf <: AbstractElement
|
||||
order_u :: Int
|
||||
order_v :: Int
|
||||
knots_u :: Vector{Float64}
|
||||
knots_v :: Vector{Float64}
|
||||
weights :: Matrix{Float64}
|
||||
end
|
||||
|
||||
function NSurf()
|
||||
NSurf(1, 1,
|
||||
[-1.0, -1.0, 1.0, 1.0],
|
||||
[-1.0, -1.0, 1.0, 1.0],
|
||||
ones(2, 2))
|
||||
end
|
||||
|
||||
type NSolid <: AbstractElement
|
||||
order_u :: Int
|
||||
order_v :: Int
|
||||
order_w :: Int
|
||||
knots_u :: Vector{Float64}
|
||||
knots_v :: Vector{Float64}
|
||||
knots_w :: Vector{Float64}
|
||||
weights :: Array{Float64, 3}
|
||||
end
|
||||
|
||||
function NSolid()
|
||||
NSolid(1, 1, 1,
|
||||
[-1.0, -1.0, 1.0, 1.0],
|
||||
[-1.0, -1.0, 1.0, 1.0],
|
||||
[-1.0, -1.0, 1.0, 1.0],
|
||||
ones(2, 2, 2))
|
||||
end
|
||||
|
||||
function NURBS(i, p, u, t)
|
||||
p == 0 && return t[i] <= u <= t[i+1] ? 1.0 : 0.0
|
||||
anom = u-t[i]
|
||||
adenom = t[i+p]-t[i]
|
||||
a = isapprox(adenom, 0.0) ? 0.0 : anom/adenom
|
||||
bnom = t[i+p+1]-u
|
||||
bdenom = t[i+p+1]-t[i+1]
|
||||
b = isapprox(bdenom, 0.0) ? 0.0 : bnom/bdenom
|
||||
result = a*NURBS(i,p-1,u,t) + b*NURBS(i+1,p-1,u,t)
|
||||
return result
|
||||
end
|
||||
|
||||
function get_basis(element::Element{NSeg}, xi::Vector, time)
|
||||
pu = element.properties.order
|
||||
tu = element.properties.knots
|
||||
w = element.properties.weights
|
||||
nu = length(tu)-pu-1
|
||||
u = xi[1]
|
||||
N = vec([w[j]*NURBS(j,pu,u,tu) for j=1:nu])'
|
||||
return N/sum(N)
|
||||
end
|
||||
|
||||
function get_basis(element::Element{NSurf}, xi::Vector, time)
|
||||
pu = element.properties.order_u
|
||||
pv = element.properties.order_v
|
||||
tu = element.properties.knots_u
|
||||
tv = element.properties.knots_v
|
||||
w = element.properties.weights
|
||||
nu = length(tu)-pu-1
|
||||
nv = length(tv)-pv-1
|
||||
u, v = xi
|
||||
N = vec([w[i,j]*NURBS(i,pu,u,tu)*NURBS(j,pv,v,tv) for i=1:nu, j=1:nv])'
|
||||
return N / sum(N)
|
||||
end
|
||||
|
||||
function get_basis(element::Element{NSolid}, xi::Vector, time)
|
||||
pu = element.properties.order_u
|
||||
pv = element.properties.order_v
|
||||
pw = element.properties.order_w
|
||||
tu = element.properties.knots_u
|
||||
tv = element.properties.knots_v
|
||||
tw = element.properties.knots_w
|
||||
weights = element.properties.weights
|
||||
nu = length(tu)-pu-1
|
||||
nv = length(tv)-pv-1
|
||||
nw = length(tw)-pw-1
|
||||
u, v, w = xi
|
||||
N = vec([weights[i,j,k]*NURBS(i,pu,u,tu)*NURBS(j,pv,v,tv)*NURBS(k,pw,w,tw) for i=1:nu, j=1:nv, k=1:nw])'
|
||||
return N / sum(N)
|
||||
end
|
||||
|
||||
# TODO: evaluate partial derivatives of basis functions without forwarddiff
|
||||
""" Evaluate partial derivatives of basis functions using ForwardDiff. """
|
||||
function get_dbasis{E<:Union{NSeg, NSurf, NSolid}}(element::Element{E}, ip, time)
|
||||
xi = isa(ip, IP) ? ip.coords : ip
|
||||
basis(xi) = vec(get_basis(element, xi, time))
|
||||
return ForwardDiff.jacobian(basis, xi)'
|
||||
end
|
||||
|
||||
function length(element::Element{NSeg})
|
||||
nu = length(element.properties.knots) - element.properties.order - 1
|
||||
return nu
|
||||
end
|
||||
|
||||
function size(element::Element{NSeg})
|
||||
return (1, length(element))
|
||||
end
|
||||
|
||||
function length(element::Element{NSurf})
|
||||
nu = length(element.properties.knots_u) - element.properties.order_u - 1
|
||||
nv = length(element.properties.knots_v) - element.properties.order_v - 1
|
||||
return nu*nv
|
||||
end
|
||||
|
||||
function size(element::Element{NSurf})
|
||||
return (2, length(element))
|
||||
end
|
||||
|
||||
function length(element::Element{NSolid})
|
||||
nu = length(element.properties.knots_u) - element.properties.order_u - 1
|
||||
nv = length(element.properties.knots_v) - element.properties.order_v - 1
|
||||
nw = length(element.properties.knots_w) - element.properties.order_w - 1
|
||||
return nu*nv*nw
|
||||
end
|
||||
|
||||
function size(element::Element{NSolid})
|
||||
return (3, length(element))
|
||||
end
|
||||
|
||||
function is_nurbs(element::Element)
|
||||
return false
|
||||
end
|
||||
|
||||
function is_nurbs{E<:Union{NSeg, NSurf, NSolid}}(element::Element{E})
|
||||
return true
|
||||
end
|
||||
|
||||
+1
-1
@@ -416,7 +416,7 @@ function (field::CCTV)(xi::Vector, time::Number)
|
||||
return field.data(time)
|
||||
end
|
||||
|
||||
function (field::CVTV)(xi::Vector, time::Number)
|
||||
function (field::CVTV)(xi, time)
|
||||
return field.data(xi, time)
|
||||
end
|
||||
|
||||
|
||||
@@ -122,7 +122,7 @@ function assemble!(problem::Problem{Contact}, slave_element::Element{Tri3}, time
|
||||
Q3 = create_rotation_matrix(slave_element, time)
|
||||
|
||||
# project slave nodes to auxiliary plane (x0, Q)
|
||||
xi = mean(get_reference_coordinates(slave_element))
|
||||
xi = get_mean_xi(slave_element)
|
||||
N = vec(get_basis(slave_element, xi, time))
|
||||
x0 = N*X1
|
||||
n0 = N*n1
|
||||
@@ -280,7 +280,7 @@ function assemble!(problem::Problem{Contact}, slave_element::Element{Tri6}, time
|
||||
#la = sub_slave_element("lambda", time)
|
||||
|
||||
# create auxiliary plane
|
||||
xi = mean(get_reference_coordinates(sub_slave_element))
|
||||
xi = get_mean_xi(sub_slave_element)
|
||||
N = vec(get_basis(sub_slave_element, xi, time))
|
||||
x0 = N*X1
|
||||
n0 = N*n1
|
||||
@@ -356,7 +356,7 @@ function assemble!(problem::Problem{Contact}, slave_element::Element{Tri6}, time
|
||||
n1 = sub_slave_element("normal", time)
|
||||
|
||||
# create auxiliary plane
|
||||
xi = mean(get_reference_coordinates(sub_slave_element))
|
||||
xi = get_mean_xi(sub_slave_element)
|
||||
N = vec(get_basis(sub_slave_element, xi, time))
|
||||
x0 = N*X1
|
||||
n0 = N*n1
|
||||
|
||||
@@ -56,7 +56,7 @@ function assemble!(problem::Problem{Dirichlet}, time::Float64=0.0;
|
||||
for i=1:field_dim
|
||||
haskey(element, field_name*" $i") || continue
|
||||
ldofs = gdofs[i:field_dim:end]
|
||||
xis = get_reference_coordinates(typeof(element.properties))
|
||||
xis = get_reference_coordinates(element)
|
||||
vals = Float64[]
|
||||
for xi in xis
|
||||
g = element(field_name*" $i", xi, time)
|
||||
|
||||
@@ -146,7 +146,7 @@ function diagnose_interface(problem::Problem{Mortar}, time::Float64)
|
||||
n1 = Field([normals[j] for j in slave_element_nodes])
|
||||
|
||||
# project slave nodes to auxiliary plane (x0, Q)
|
||||
xi = mean(get_reference_coordinates(slave_element))
|
||||
xi = get_mean_xi(slave_element)
|
||||
N = vec(get_basis(slave_element, xi, time))
|
||||
x0 = N*X1
|
||||
n0 = N*n1
|
||||
|
||||
@@ -103,11 +103,11 @@ function approx_in{T}(q::T, P::Vector{T}; rtol=1.0e-4, atol=0.0)
|
||||
return false
|
||||
end
|
||||
|
||||
function get_polygon_clip(xs, xm, n)
|
||||
function get_polygon_clip{T}(xs::Vector{T}, xm::Vector{T}, n::T)
|
||||
# objective: search does line xm1 - xm2 clip xs
|
||||
nm = length(xm)
|
||||
ns = length(xs)
|
||||
P = Vector[]
|
||||
P = T[]
|
||||
|
||||
# 1. test is master point inside slave, if yes, add to clip
|
||||
for i=1:nm
|
||||
@@ -330,6 +330,17 @@ function split_quadratic_elements(elements::Vector, time::Float64)
|
||||
return new_elements
|
||||
end
|
||||
|
||||
function get_mean_xi(element::Element)
|
||||
xi = zeros(2)
|
||||
coords = get_reference_coordinates(element)
|
||||
for (xi1,xi2) in coords
|
||||
xi[1] += xi1
|
||||
xi[2] += xi2
|
||||
end
|
||||
xi /= length(coords)
|
||||
return xi
|
||||
end
|
||||
|
||||
""" Assemble linear surface element to problem.
|
||||
|
||||
Dual basis is constructed such that partially integrated slave segments are taken into account in a proper way.
|
||||
@@ -357,7 +368,7 @@ function assemble!{E<:Union{Tri3, Quad4}}(problem::Problem{Mortar}, slave_elemen
|
||||
n1 = slave_element("normal", time)
|
||||
|
||||
# project slave nodes to auxiliary plane (x0, Q)
|
||||
xi = mean(get_reference_coordinates(slave_element))
|
||||
xi = get_mean_xi(slave_element)
|
||||
first_slave_element && debug("midpoint xi = $xi")
|
||||
N = vec(get_basis(slave_element, xi, time))
|
||||
x0 = N*X1
|
||||
@@ -465,7 +476,7 @@ function assemble!{E<:Union{Tri3, Quad4}}(problem::Problem{Mortar}, slave_elemen
|
||||
all_cells = get_cells(P, C0)
|
||||
for cell in all_cells
|
||||
virtual_element = Element(Tri3, Int[])
|
||||
update!(virtual_element, "geometry", cell)
|
||||
virtual_element.fields["geometry"] = DVTI(cell)
|
||||
|
||||
# 5. loop integration point of integration cell
|
||||
for ip in get_integration_points(virtual_element, 3)
|
||||
@@ -579,7 +590,7 @@ function assemble!{E<:Union{Tri6}}(problem::Problem{Mortar}, slave_element::Elem
|
||||
n1 = sub_slave_element("normal", time)
|
||||
|
||||
# create auxiliary plane
|
||||
xi = mean(get_reference_coordinates(sub_slave_element))
|
||||
xi = get_mean_xi(sub_slave_element)
|
||||
first_slave_element && debug("midpoint xi = $xi")
|
||||
N = vec(get_basis(sub_slave_element, xi, time))
|
||||
x0 = N*X1
|
||||
@@ -662,7 +673,7 @@ function assemble!{E<:Union{Tri6}}(problem::Problem{Mortar}, slave_element::Elem
|
||||
n1 = sub_slave_element("normal", time)
|
||||
|
||||
# create auxiliary plane
|
||||
xi = mean(get_reference_coordinates(sub_slave_element))
|
||||
xi = get_mean_xi(sub_slave_element)
|
||||
first_slave_element && debug("midpoint xi = $xi")
|
||||
N = vec(get_basis(sub_slave_element, xi, time))
|
||||
x0 = N*X1
|
||||
|
||||
@@ -33,6 +33,18 @@ function (point::Point)(field_name, time=0.0)
|
||||
point.fields[field_name](time).data
|
||||
end
|
||||
|
||||
function start(point::Point)
|
||||
return start(point.coords)
|
||||
end
|
||||
|
||||
function done(point::Point, i)
|
||||
return done(point.coords, i)
|
||||
end
|
||||
|
||||
function next(point::Point, i)
|
||||
return next(point.coords, i)
|
||||
end
|
||||
|
||||
function update!{T}(point::Point, field_name, val::Pair{Float64, T})
|
||||
if haskey(point, field_name)
|
||||
update!(point[field_name], val)
|
||||
|
||||
Reference in New Issue
Block a user