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Moonwalker777 2022-06-06 13:08:48 +02:00
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commit eb4e741ebb
21 gewijzigde bestanden met toevoegingen van 61439 en 0 verwijderingen

Diff onderdrukt omdat het te groot bestand Laad Diff

Diff onderdrukt omdat het te groot bestand Laad Diff

Diff onderdrukt omdat het te groot bestand Laad Diff

Diff onderdrukt omdat het te groot bestand Laad Diff

Diff onderdrukt omdat het te groot bestand Laad Diff

Diff onderdrukt omdat het te groot bestand Laad Diff

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Exercise_04/Abgabe/report/baseline.png (Opgeslagen met Git LFS) Normal file

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Group 1
12134031, Bianchi Riccardo
01128052, Kapla Daniel
01630056, Kuen Jakob
01620740, Müller David

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Exercise_04/Abgabe/report/report.pdf (Opgeslagen met Git LFS) Normal file

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Exercise_04/Abgabe/report/variation1.png (Opgeslagen met Git LFS) Normal file

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Exercise_04/Abgabe/report/variation2.png (Opgeslagen met Git LFS) Normal file

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Exercise_04/Abgabe/report/variation3.png (Opgeslagen met Git LFS) Normal file

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Exercise_04/Abgabe/report/variation4_div.png (Opgeslagen met Git LFS) Normal file

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Exercise_04/Abgabe/report/variation4_mul.png (Opgeslagen met Git LFS) Normal file

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module Parameters
export k, hz, L, q, T, e, elₘ
k = 429.
hz = 0.0005
L = 0.01
q = 2000000.
T = 293.
c = 10.
elₘ = [41,42,43,44,45,46,47,59,60,61,62,63,77,78,79,95]
end

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FEM solver
- programmed in Julia
- run using `julia run.jl`
- this generates output txt files in ./txt/ and plots in ./plots/ for all 5 variants
- the script requires the Julia packages GeometryBasics, GLMakie for plotting, and Fmt (https://github.com/bicycle1885/Fmt.jl) for print_HTP functionality3

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module FEM
export Node, Element, stiffness, tri_tiles, gradient, center, normalize, p
include("./Parameters.jl")
using GeometryBasics
using GeometryBasics.LinearAlgebra
struct Node
x::Float64
y::Float64
index::UInt
end
p(n::Node) = Point2f(n.x, n.y)
struct Element
nodes::Vector{Node}
a::Vector{Float64}
b::Vector{Float64}
c::Vector{Float64}
Δ::Float64
function Element(n::Vector{Node})
xs = map(nd->nd.x,n)
ys = map(nd->nd.y,n)
a = cross(xs, ys)
b = cross(ys, ones(3))
c = cross(ones(3), xs)
Δ = dot(xs,b) / 2
new(n,a,b,c,Δ)
end
end
function stiffness(e::Element)::Matrix{Float64}
# tensor product
Hₑ = e.b .* e.b'
Hₑ += e.c .* e.c'
Hₑ *= Parameters.hz*Parameters.k/4e.Δ
return Hₑ
end
function tri_tiles(L::Float64, divisions::Int, trapezoidal::Bool=false, biased::Bool=false, ring::Bool=false)::Tuple{Vector{Node}, Vector{Element}}
nodes = Matrix{Node}(undef, divisions+1, divisions+1)
i = 1
for y in 0:divisions
for x in 0:divisions
xₑ = L*x/divisions
yₑ = L*y/divisions
if biased
B = yₑ/2Parameters.L
xₑ = xₑ*(xₑ*B/Parameters.L - B + 1)
end
if trapezoidal
xₑ *= 1 - 0.5*(y/divisions)
end
if ring
r = Parameters.L*(1 + x/divisions)
θ = (π/4)*(y/divisions)
xₑ = r*cos(θ)
yₑ = r*sin(θ)
xₑ -= Parameters.L
end
nodes[x+1,y+1] = Node(xₑ,yₑ,i)
i += 1
end
end
elements = []
for y in 1:divisions
for x in 1:divisions
# lower/upper triangle
push!(elements, Element([nodes[x,y], nodes[x+1,y], nodes[x,y+1]]))
push!(elements, Element([nodes[x+1,y+1], nodes[x,y+1], nodes[x+1,y]]))
end
end
return vec(nodes), elements
end
function gradient(e::Element, T::Vector{Float64})::Vec2f
return Vec2f([
e.b[1] e.b[2] e.b[3] ;
e.c[1] e.c[2] e.c[3]
] * [
T[e.nodes[1].index]
T[e.nodes[2].index]
T[e.nodes[3].index]
] / 2e.Δ)
end
center(e::Element)::Point2f = Point2f(sum([n.x for n in e.nodes])/3.0, sum([n.y for n in e.nodes])/3.0)
normalize(v::Vec2f)::Vec2f = v / sqrt(v[1]^2 + v[2]^2)
end

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using Fmt
function print_HTP(H::Matrix{Float64}, T::Vector{Float64}, P::Vector{Float64}, filename="output.txt")
# Print matrices to .txt-file (name of file = filename).
# H... overall assembled stiffness matrix
# T... nodal temperature vector
# P... nodal force vector
# Make sure, that your system of equations is sorted by
# ascending node numbers, i.e., N1 N2 ... N100.
open(filename, "w") do io
write(io, "Stiffness matrix H: \n")
for row in H
for col in row
outline = f"{$col:+8.4e},"
write(io, f"{$outline:11s}")
end
write(io, "\n")
end
write(io, "Temperature T: \n")
for row in T
for col in row
outline = f"{$col:+8.4e},"
write(io, f"{$outline:11s} \n")
end
end
write(io, "Force vector P: \n")
for row in P
for col in row
outline = f"{$col:+8.4e},"
write(io, f"{$outline:11s} \n")
end
end
end
end

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include("./fem.jl")
include("./Parameters.jl")
include("./print_HTP.jl")
using .FEM
using GLMakie
using Makie.GeometryBasics
@enum Variation BASIC V1 V2 V3 V4_div V4_mul
function solve(name::String, variation::Variation)
div = 9
H = zeros(Float64,(div+1)^2, (div+1)^2)
(nodes, elements) = tri_tiles(Parameters.L, div, variation==V1, variation==V2, variation==V3)
for (index, el) in enumerate(elements)
Hₑ = stiffness(el)
if variation == V4_div && index in Parameters.elₘ
Hₑ /= Parameters.c
elseif variation == V4_mul && index in Parameters.elₘ
Hₑ *= Parameters.c
end
for i in 1:3
for j in 1:3
H[el.nodes[i].index, el.nodes[j].index] += Hₑ[i,j]
end
end
end
P = zeros(Float64, 90)
# impose neumann conditions on top edge
# adapted from https://mathoverflow.net/questions/5085/how-to-apply-neuman-boundary-condition-to-finite-element-method-problems
# maybe check if this actually makes sense
nᵧ = -Parameters.q / Parameters.k
# skip=2 since only every second element has a edge along the bottom: ◺◹
for ∂_el in elements[1:2:18]
n1 = ∂_el.nodes[1]
n2 = ∂_el.nodes[2]
l = abs(n2.x - n1.x)
P[n1.index] += nᵧ*l/2
P[n2.index] += nᵧ*l/2
end
rhs = P - H[1:90,91:100]*fill(Parameters.T, 10,1)
T = vec(H[1:90,1:90]\rhs)
append!(T, fill(Parameters.T, 10))
reaction_forces = H[91:100,:]*T
centers = center.(elements)
gradients = map(el -> gradient(el, T), elements)
flux = gradients .* -1
norm = maximum(map(g-> sqrt(g[1]^2 + g[2]^2), gradients))/(Parameters.L/div)*2.5
gradients ./= norm
flux ./= norm
set_theme!(theme_black())
f = Figure(resolution = (1536, 1024))
tris = map(e->Polygon([p(e.nodes[1]), p(e.nodes[2]), p(e.nodes[3])]), elements)
poly(f[1, 1], tris, color=:transparent, linestyle=:solid, strokewidth=0.8, strokecolor=:white, transparency=true)
xs = map(n->n.x, nodes)
ys = map(n->n.y, nodes)
xs = reshape(xs, (div+1, div+1))
ys = reshape(ys, (div+1, div+1))
Ts = reshape(T, (div+1, div+1))
surface(f[2, 1], xs, ys, Ts, colormap=:matter, axis=(type=Axis3,))
contour(f[1:2,2:3], map(n->n.x,nodes), map(n->n.y,nodes), T, levels=16, colormap=:matter)
arrows!(f[1:2,2:3], centers, gradients, arrowcolor=:red, linecolor=:red)
arrows!(f[1:2,2:3], centers, flux, arrowcolor=:blue, linecolor=:blue)
save("plots/$name.png", current_figure())
# print_HTP(H, T, P, "txt/htp_$name.txt")
end
solve("baseline", BASIC)
solve("variation1", V1)
solve("variation2", V2)
solve("variation3", V3)
solve("variation4_div", V4_div)
solve("variation4_mul", V4_mul)