mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-09-19 01:48:47 +00:00
Jukka Aho
571 lines
14 KiB
Julia
571 lines
14 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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### 0d element
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type Poi1 <: AbstractElement
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end
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function description(::Type{Poi1})
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"1 node point"
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end
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function size(element::Element{Poi1})
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return (0, 1)
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end
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function length(element::Element{Poi1})
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return 1
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end
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function get_basis(element::Element{Poi1}, ip, time)
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return [1]
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end
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function call(element::Element{Poi1}, ip, time, ::Type{Val{:detJ}})
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return 1.0
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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 description(::Type{Seg2})
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"2 node segment"
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end
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function size(element::Element{Seg2})
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return (1, 2)
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end
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function length(element::Element{Seg2})
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return 2
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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 description(::Type{Seg3})
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"3 node segment"
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end
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function size(element::Element{Seg3})
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return (1, 3)
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end
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function length(element::Element{Seg3})
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return 3
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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 description(::Type{Tri3})
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"3 node triangle"
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end
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function size(element::Element{Tri3})
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return (2, 3)
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end
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function length(element::Element{Tri3})
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return 3
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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 description(::Type{Tri6})
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"6 node triangle"
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end
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function size(element::Element{Tri6})
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return (2, 6)
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end
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function length(element::Element{Tri6})
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return 6
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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 Quad4 <: AbstractElement
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end
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function description(::Type{Quad4})
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"4 node quadrangle"
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end
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function size(element::Element{Quad4})
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return (2, 4)
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end
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function length(element::Element{Quad4})
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return 4
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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 description(::Type{Quad8})
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"8 node Serendip quadrangle"
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end
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function size(element::Element{Quad8})
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return (2, 8)
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end
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function length(element::Element{Quad8})
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return 8
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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 description(::Type{Quad9})
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"9 node quadrangle"
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end
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function size(element::Element{Quad9})
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return (2, 9)
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end
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function length(element::Element{Quad9})
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return 9
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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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end
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function description(::Type{Tet4})
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"4 node tetrahedral element"
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end
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function size(element::Element{Tet4})
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return (3, 4)
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end
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function length(element::Element{Tet4})
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return 4
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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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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 description(::Type{Tet10})
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"10 node tetrahedral element"
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end
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function size(element::Element{Tet10})
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return (3, 10)
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end
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function length(element::Element{Tet10})
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return 10
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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 Hex8 <: AbstractElement
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end
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function description(::Type{Hex8})
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"8 node hexahedral element"
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end
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function size(element::Element{Hex8})
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return (3, 8)
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end
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function length(element::Element{Hex8})
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return 8
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end
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function get_reference_coordinates(::Type{Hex8})
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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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[-1.0, -1.0, 1.0], # N5
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[ 1.0, -1.0, 1.0], # N6
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[ 1.0, 1.0, 1.0], # N7
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[-1.0, 1.0, 1.0]] # N8
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end
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function get_interpolation_polynomial(::Type{Hex8}, xi)
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[
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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]
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]
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end
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function get_interpolation_polynomial(::Type{Hex8}, xi, ::Type{Val{:partial_derivatives}})
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[
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0 0 0 1 0 xi[3] xi[2] xi[2]*xi[3]
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0 0 1 0 xi[3] 0 xi[1] xi[1]*xi[3]
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0 1 0 0 xi[2] xi[1] 0 xi[1]*xi[2]
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]
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end
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#
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type Hex20 <: AbstractElement
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end
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function description(::Type{Hex20})
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"20 node hexahedral element"
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end
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function size(element::Element{Hex20})
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return (3, 20)
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end
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function length(element::Element{Hex20})
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return 20
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end
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function get_reference_coordinates(::Type{Hex20})
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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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[-1.0, -1.0, 1.0], # N5
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[ 1.0, -1.0, 1.0], # N6
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[ 1.0, 1.0, 1.0], # N7
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[-1.0, 1.0, 1.0], # N8
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[ 0.0, -1.0, -1.0], # N9
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[ 1.0, 0.0, -1.0], # N10
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[ 0.0, 1.0, -1.0], # N11
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[-1.0, 0.0, -1.0], # N12
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[-1.0, -1.0, 0.0], # N13
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[ 1.0, -1.0, 0.0], # N14
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[ 1.0, 1.0, 0.0], # N15
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[-1.0, 1.0, 0.0], # N16
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[ 0.0, -1.0, 1.0], # N17
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[ 1.0, 0.0, 1.0], # N18
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[ 0.0, 1.0, 1.0], # N19
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[-1.0, 0.0, 1.0]] # N20
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end
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function get_interpolation_polynomial(::Type{Hex20}, xi)
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[
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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]
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]
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end
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function get_interpolation_polynomial(::Type{Hex20}, xi, ::Type{Val{:partial_derivatives}})
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[
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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]
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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]
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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]
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]
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end
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###
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type Hex27 <: AbstractElement
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end
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function description(::Type{Hex27})
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"27 node hexahedral element"
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end
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function size(element::Element{Hex27})
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return (3, 27)
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end
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function length(element::Element{Hex27})
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return 27
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end
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function get_reference_coordinates(::Type{Hex27})
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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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[-1.0, -1.0, 1.0], # N5
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[ 1.0, -1.0, 1.0], # N6
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[ 1.0, 1.0, 1.0], # N7
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[-1.0, 1.0, 1.0], # N8
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[ 0.0, -1.0, -1.0], # N9
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[ 1.0, 0.0, -1.0], # N10
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[ 0.0, 1.0, -1.0], # N11
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[-1.0, 0.0, -1.0], # N12
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[-1.0, -1.0, 0.0], # N13
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[ 1.0, -1.0, 0.0], # N14
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[ 1.0, 1.0, 0.0], # N15
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[-1.0, 1.0, 0.0], # N16
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[ 0.0, -1.0, 1.0], # N17
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[ 1.0, 0.0, 1.0], # N18
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[ 0.0, 1.0, 1.0], # N19
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[-1.0, 0.0, 1.0], # N20
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[ 0.0, 0.0, -1.0], # N21
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[ 0.0, -1.0, 0.0], # N22
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[ 1.0, 0.0, 0.0], # N23
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[ 0.0, 1.0, 0.0], # N24
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[-1.0, 0.0, 0.0], # N25
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[ 0.0, 0.0, 1.0], # N26
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[ 0.0, 0.0, 0.0]] # N27
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|
end
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|
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function get_interpolation_polynomial(::Type{Hex27}, xi)
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|
[
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|
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
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|
]
|
|
end
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|
|
|
function get_interpolation_polynomial(::Type{Hex27}, xi, ::Type{Val{:partial_derivatives}})
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|
[
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|
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 Quad4
|
|
@create_basis Quad8
|
|
@create_basis Quad9
|
|
@create_basis Tet4
|
|
@create_basis Tet10
|
|
@create_basis Hex8
|
|
@create_basis Hex20
|
|
@create_basis Hex27
|
|
|