mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-08-20 20:22:03 +00:00
Jukka Aho
735 lines
18 KiB
Julia
735 lines
18 KiB
Julia
# This file is a part of JuliaFEM.
|
|
# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
|
|
|
|
### 0d element
|
|
|
|
type Poi1 <: AbstractElement
|
|
end
|
|
|
|
function description(::Type{Poi1})
|
|
"1 node point"
|
|
end
|
|
|
|
function size(element::Element{Poi1})
|
|
return (0, 1)
|
|
end
|
|
|
|
function length(element::Element{Poi1})
|
|
return 1
|
|
end
|
|
|
|
function get_basis(element::Element{Poi1}, ip, time)
|
|
return [1]
|
|
end
|
|
|
|
function get_dbasis(element::Element{Poi1}, ip, time)
|
|
return [0]
|
|
end
|
|
|
|
function (element::Element{Poi1})(ip, time::Float64, ::Type{Val{:detJ}})
|
|
return 1.0
|
|
end
|
|
|
|
function get_integration_order(element::Poi1)
|
|
return 1
|
|
end
|
|
|
|
function get_integration_points(element::Poi1, order::Int64)
|
|
return [ (1.0, [] ) ]
|
|
end
|
|
|
|
function get_reference_coordinates(::Type{Poi1})
|
|
Vector{Float64}[[0.0]]
|
|
end
|
|
|
|
### 1d elements
|
|
|
|
type Seg2 <: AbstractElement
|
|
end
|
|
|
|
function description(::Type{Seg2})
|
|
"2 node segment"
|
|
end
|
|
|
|
function size(element::Element{Seg2})
|
|
return (1, 2)
|
|
end
|
|
|
|
function length(element::Element{Seg2})
|
|
return 2
|
|
end
|
|
|
|
function get_reference_coordinates(::Type{Seg2})
|
|
Vector{Float64}[
|
|
[-1.0], # N1
|
|
[ 1.0]] # N2
|
|
end
|
|
|
|
function get_interpolation_polynomial(::Type{Seg2}, xi)
|
|
[1.0 xi[1]]
|
|
end
|
|
|
|
function get_interpolation_polynomial(::Type{Seg2}, xi, ::Type{Val{:partial_derivatives}})
|
|
[0.0 1.0]
|
|
end
|
|
|
|
#
|
|
|
|
type Seg3 <: AbstractElement
|
|
end
|
|
|
|
function description(::Type{Seg3})
|
|
"3 node segment"
|
|
end
|
|
|
|
function size(element::Element{Seg3})
|
|
return (1, 3)
|
|
end
|
|
|
|
function length(element::Element{Seg3})
|
|
return 3
|
|
end
|
|
|
|
function get_reference_coordinates(::Type{Seg3})
|
|
Vector{Float64}[
|
|
[-1.0], # N1
|
|
[ 1.0], # N2
|
|
[ 0.0]] # N3
|
|
end
|
|
|
|
function get_interpolation_polynomial(::Type{Seg3}, xi)
|
|
[1.0 xi[1] xi[1]^2]
|
|
end
|
|
|
|
function get_interpolation_polynomial(::Type{Seg3}, xi, ::Type{Val{:partial_derivatives}})
|
|
[0.0 1.0 2.0*xi[1]]
|
|
end
|
|
|
|
### 2d elements
|
|
|
|
type Tri3 <: AbstractElement
|
|
end
|
|
|
|
function description(::Type{Tri3})
|
|
"3 node triangle"
|
|
end
|
|
|
|
function size(element::Element{Tri3})
|
|
return (2, 3)
|
|
end
|
|
|
|
function length(element::Element{Tri3})
|
|
return 3
|
|
end
|
|
|
|
function get_reference_coordinates(::Type{Tri3})
|
|
Vector{Float64}[
|
|
[0.0, 0.0], # N1
|
|
[1.0, 0.0], # N2
|
|
[0.0, 1.0]] # N3
|
|
end
|
|
|
|
function get_interpolation_polynomial(::Type{Tri3}, xi)
|
|
[
|
|
1 xi[1] xi[2]
|
|
]
|
|
end
|
|
|
|
function get_interpolation_polynomial(::Type{Tri3}, xi, ::Type{Val{:partial_derivatives}})
|
|
[
|
|
0.0 1.0 0.0
|
|
0.0 0.0 1.0
|
|
]
|
|
end
|
|
|
|
#
|
|
|
|
type Tri6 <: AbstractElement
|
|
end
|
|
|
|
function description(::Type{Tri6})
|
|
"6 node triangle"
|
|
end
|
|
|
|
function size(element::Element{Tri6})
|
|
return (2, 6)
|
|
end
|
|
|
|
function length(element::Element{Tri6})
|
|
return 6
|
|
end
|
|
|
|
function get_reference_coordinates(::Type{Tri6})
|
|
Vector{Float64}[
|
|
[0.0, 0.0], # N1
|
|
[1.0, 0.0], # N2
|
|
[0.0, 1.0], # N3
|
|
[0.5, 0.0], # N4
|
|
[0.5, 0.5], # N5
|
|
[0.0, 0.5]] # N6
|
|
end
|
|
|
|
function get_interpolation_polynomial(::Type{Tri6}, xi)
|
|
[
|
|
1 xi[1] xi[2] xi[1]^2 xi[1]*xi[2] xi[2]^2
|
|
]
|
|
end
|
|
|
|
function get_interpolation_polynomial(::Type{Tri6}, xi, ::Type{Val{:partial_derivatives}})
|
|
[
|
|
0 1 0 2*xi[1] xi[2] 0
|
|
0 0 1 0 xi[1] 2*xi[2]
|
|
]
|
|
end
|
|
|
|
#
|
|
|
|
type Tri7 <: AbstractElement
|
|
end
|
|
|
|
function description(::Type{Tri7})
|
|
"7 node triangle"
|
|
end
|
|
|
|
function size(element::Element{Tri7})
|
|
return (2, 7)
|
|
end
|
|
|
|
function length(element::Element{Tri7})
|
|
return 7
|
|
end
|
|
|
|
function get_reference_coordinates(::Type{Tri7})
|
|
Vector{Float64}[
|
|
[0.0, 0.0], # N1
|
|
[1.0, 0.0], # N2
|
|
[0.0, 1.0], # N3
|
|
[0.5, 0.0], # N4
|
|
[0.5, 0.5], # N5
|
|
[0.0, 0.5], # N6
|
|
[1/3, 1/3]] # N7
|
|
end
|
|
|
|
function get_interpolation_polynomial(::Type{Tri7}, xi)
|
|
[
|
|
1 xi[1] xi[2] xi[1]^2 xi[1]*xi[2] xi[2]^2 xi[1]^2*xi[2]^2
|
|
]
|
|
end
|
|
|
|
function get_interpolation_polynomial(::Type{Tri7}, xi, ::Type{Val{:partial_derivatives}})
|
|
[
|
|
0 1 0 2*xi[1] xi[2] 0 2*xi[1]*xi[2]^2
|
|
0 0 1 0 xi[1] 2*xi[2] 2*xi[1]^2*xi[2]
|
|
]
|
|
end
|
|
|
|
#
|
|
|
|
type Quad4 <: AbstractElement
|
|
end
|
|
|
|
function description(::Type{Quad4})
|
|
"4 node quadrangle"
|
|
end
|
|
|
|
function size(element::Element{Quad4})
|
|
return (2, 4)
|
|
end
|
|
|
|
function length(element::Element{Quad4})
|
|
return 4
|
|
end
|
|
|
|
function get_reference_coordinates(::Type{Quad4})
|
|
Vector{Float64}[
|
|
[-1.0, -1.0], # N1
|
|
[ 1.0, -1.0], # N2
|
|
[ 1.0, 1.0], # N3
|
|
[-1.0, 1.0]] # N4
|
|
end
|
|
|
|
function get_interpolation_polynomial(::Type{Quad4}, xi)
|
|
[
|
|
1.0 xi[1] xi[2] xi[1]*xi[2]
|
|
]
|
|
end
|
|
|
|
function get_interpolation_polynomial(::Type{Quad4}, xi, ::Type{Val{:partial_derivatives}})
|
|
[
|
|
0 1 0 xi[2]
|
|
0 0 1 xi[1]
|
|
]
|
|
end
|
|
|
|
#
|
|
|
|
type Quad8 <: AbstractElement
|
|
end
|
|
|
|
function description(::Type{Quad8})
|
|
"8 node Serendip quadrangle"
|
|
end
|
|
|
|
function size(element::Element{Quad8})
|
|
return (2, 8)
|
|
end
|
|
|
|
function length(element::Element{Quad8})
|
|
return 8
|
|
end
|
|
|
|
function get_reference_coordinates(::Type{Quad8})
|
|
Vector{Float64}[
|
|
[-1.0, -1.0], # N1
|
|
[ 1.0, -1.0], # N2
|
|
[ 1.0, 1.0], # N3
|
|
[-1.0, 1.0], # N4
|
|
[ 0.0, -1.0], # N5
|
|
[ 1.0, 0.0], # N6
|
|
[ 0.0, 1.0], # N7
|
|
[-1.0, 0.0]] # N8
|
|
end
|
|
|
|
function get_interpolation_polynomial(::Type{Quad8}, xi)
|
|
[
|
|
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]
|
|
]
|
|
end
|
|
|
|
function get_interpolation_polynomial(::Type{Quad8}, xi, ::Type{Val{:partial_derivatives}})
|
|
[
|
|
0 0 1 0 xi[2] 2*xi[1] xi[2]^2 2*xi[1]*xi[2]
|
|
0 1 0 2*xi[2] xi[1] 0 2*xi[1]*xi[2] xi[1]^2
|
|
]
|
|
end
|
|
|
|
#
|
|
|
|
type Quad9 <: AbstractElement
|
|
end
|
|
|
|
function description(::Type{Quad9})
|
|
"9 node quadrangle"
|
|
end
|
|
|
|
function size(element::Element{Quad9})
|
|
return (2, 9)
|
|
end
|
|
|
|
function length(element::Element{Quad9})
|
|
return 9
|
|
end
|
|
|
|
function get_reference_coordinates(::Type{Quad9})
|
|
Vector{Float64}[
|
|
[-1.0, -1.0], # N1
|
|
[ 1.0, -1.0], # N2
|
|
[ 1.0, 1.0], # N3
|
|
[-1.0, 1.0], # N4
|
|
[ 0.0, -1.0], # N5
|
|
[ 1.0, 0.0], # N6
|
|
[ 0.0, 1.0], # N7
|
|
[-1.0, 0.0], # N8
|
|
[ 0.0, 0.0]] # N9
|
|
end
|
|
|
|
function get_interpolation_polynomial(::Type{Quad9}, xi)
|
|
[
|
|
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
|
|
]
|
|
end
|
|
|
|
function get_interpolation_polynomial(::Type{Quad9}, xi, ::Type{Val{:partial_derivatives}})
|
|
[
|
|
0 0 1 0 xi[2] 2*xi[1] xi[2]^2 2*xi[1]*xi[2] 2*xi[1]*xi[2]^2
|
|
0 1 0 2*xi[2] xi[1] 0 2*xi[1]*xi[2] xi[1]^2 2*xi[1]^2*xi[2]
|
|
]
|
|
end
|
|
|
|
### 3d elements
|
|
|
|
type Tet4 <: AbstractElement
|
|
end
|
|
|
|
function description(::Type{Tet4})
|
|
"4 node tetrahedral element"
|
|
end
|
|
|
|
function size(element::Element{Tet4})
|
|
return (3, 4)
|
|
end
|
|
|
|
function length(element::Element{Tet4})
|
|
return 4
|
|
end
|
|
|
|
function get_reference_coordinates(::Type{Tet4})
|
|
Vector{Float64}[
|
|
[0.0, 0.0, 0.0], # N1
|
|
[1.0, 0.0, 0.0], # N2
|
|
[0.0, 1.0, 0.0], # N3
|
|
[0.0, 0.0, 1.0]] # N4
|
|
end
|
|
|
|
function get_interpolation_polynomial(::Type{Tet4}, xi)
|
|
[
|
|
1.0 xi[1] xi[2] xi[3]
|
|
]
|
|
end
|
|
|
|
function get_interpolation_polynomial(::Type{Tet4}, xi, ::Type{Val{:partial_derivatives}})
|
|
[
|
|
0.0 1.0 0.0 0.0
|
|
0.0 0.0 1.0 0.0
|
|
0.0 0.0 0.0 1.0
|
|
]
|
|
end
|
|
|
|
#
|
|
|
|
type Tet10 <: AbstractElement
|
|
end
|
|
|
|
function description(::Type{Tet10})
|
|
"10 node tetrahedral element"
|
|
end
|
|
|
|
function size(element::Element{Tet10})
|
|
return (3, 10)
|
|
end
|
|
|
|
function length(element::Element{Tet10})
|
|
return 10
|
|
end
|
|
|
|
function get_reference_coordinates(::Type{Tet10})
|
|
Vector{Float64}[
|
|
[0.0, 0.0, 0.0], # N1
|
|
[1.0, 0.0, 0.0], # N2
|
|
[0.0, 1.0, 0.0], # N3
|
|
[0.0, 0.0, 1.0], # N4
|
|
[0.5, 0.0, 0.0], # N5
|
|
[0.5, 0.5, 0.0], # N6
|
|
[0.0, 0.5, 0.0], # N7
|
|
[0.0, 0.0, 0.5], # N8
|
|
[0.5, 0.0, 0.5], # N9
|
|
[0.0, 0.5, 0.5]] # N10
|
|
end
|
|
|
|
function get_interpolation_polynomial(::Type{Tet10}, xi)
|
|
[
|
|
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
|
|
]
|
|
end
|
|
|
|
function get_interpolation_polynomial(::Type{Tet10}, xi, ::Type{Val{:partial_derivatives}})
|
|
[
|
|
0 0 0 1 0 0 0 xi[3] xi[2] 2*xi[1]
|
|
0 0 1 0 0 xi[3] 2*xi[2] 0 xi[1] 0
|
|
0 1 0 0 2*xi[3] xi[2] 0 xi[1] 0 0
|
|
]
|
|
end
|
|
|
|
#
|
|
|
|
type Wedge6 <: AbstractElement
|
|
end
|
|
|
|
function description(::Type{Wedge6})
|
|
"6 node prismatic element (wedge)"
|
|
end
|
|
|
|
function size(element::Element{Wedge6})
|
|
return (3, 6)
|
|
end
|
|
|
|
function length(element::Element{Wedge6})
|
|
return 6
|
|
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 description(::Type{Wedge15})
|
|
"15 node prismatic element (wedge)"
|
|
end
|
|
|
|
function size(element::Element{Wedge15})
|
|
return (3, 15)
|
|
end
|
|
|
|
function length(element::Element{Wedge15})
|
|
return 15
|
|
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 description(::Type{Hex8})
|
|
"8 node hexahedral element"
|
|
end
|
|
|
|
function size(element::Element{Hex8})
|
|
return (3, 8)
|
|
end
|
|
|
|
function length(element::Element{Hex8})
|
|
return 8
|
|
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 description(::Type{Hex20})
|
|
"20 node hexahedral element"
|
|
end
|
|
|
|
function size(element::Element{Hex20})
|
|
return (3, 20)
|
|
end
|
|
|
|
function length(element::Element{Hex20})
|
|
return 20
|
|
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 description(::Type{Hex27})
|
|
"27 node hexahedral element"
|
|
end
|
|
|
|
function size(element::Element{Hex27})
|
|
return (3, 27)
|
|
end
|
|
|
|
function length(element::Element{Hex27})
|
|
return 27
|
|
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 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{Hex8}, Type{Hex20}, Type{Hex27}}, xi)
|
|
return all(-1.0 .<= xi .<= 1.0)
|
|
end
|
|
|
|
function inside(::Union{Type{Tri3}, Type{Tri6}, Type{Tri7}, Type{Tet4}, Type{Tet10}}, xi)
|
|
return all(xi .>= 0.0) && (sum(xi) <= 1.0)
|
|
end
|
|
|
|
function get_reference_coordinates{E}(element::Element{E})
|
|
get_reference_coordinates(E)
|
|
end
|
|
|