Topology-Optimization-in-Julia

Julia Codes for Structural Topology Optimization Design

Codes

A personal Julia code is given mainly based on a compact and efficient Matlab implementation top99neo of compliance topology optimization (TO) for 2D continua¹, which is a v3.0 version of the celebrated top99 Matlab code developed by Sigmund² and top88 by its heir³.

Assemble just one half of the sysmetric stiffness matrix, thus substantial speedups are acheived.

top_oc/ and top_mma/ contain corresponding files related to the TO with OC and MMA algorithms, respectively.

Running codes could be tried out as:

include("./top99neo_mma.jl")
setup = SetUp() # problem setup
mat = Mat() # material property
disfeature = DiscretizationFeature(setup, mat) # model discretization
load = LoadsSupportsBCs(setup, disfeature) # boudary conditions
ini = Initialization(setup, disfeature, mat) # initial conditions
filter = Filter(setup) # filtering
xPhys, opt_hist, vf_hist, anim = Optimization(setup, mat, load, filter, ini, disfeature) # optimization process
gif(anim, "./res/des_hist.gif", fps=20) # design result visulization

Results

A benchmark MBB example is presented. TO design results are saved in ./res/ folder and a evolution history is shown as below.

👍 💯

Packages

Run the Julia REPL, enter ] to bring up Julia's package manager, and add the listed packages:

julia> ]

(@v1.7) pkg> add #pkg_name#

• Scientific computing
  • LinearAlgebra
  • SparseArrays
  • Statistics : mean
• Image process
  • ImageFiltering: imfilter
• Modelling
  • Gmsh
• FEM
  • Gridap
• AD
  • ForwardDiff
  • Zygote
• Optimization
  • NLopt
• Visualization
  • Plots

TODOs

• top99neo.jl top99neo.m rewritten in Julia
• MMA.jl MMA algorithm (mmasub.m + subsolve.m) rewritten in Julia
• top99neo_mma.jl 2D code (top99neo + MMA) written in Julia
• top99neo_AD.jl Sensitivity Analysis using Automatic Differentiation
• top99neo_NLopt.jl Optimization solved with NLopt
• top3D.jl 3D code (top3D125 + MMA) written in Julia
• top_flux.jl Combine TO with machine learning through Flux

Acknowledgements

• TopOpt Group 🇩🇰 Matlab codes for topology optimization

  • v1.0 top99.m Educatianal TO enlightenment for every beginners
  • v2.0 top88.m Loop vectorization and memory preallocation
  • v3.0 top99neo.m Half matrix assembly operation, filter implementation and volume-preserving density projection

• Prof. Krister Svanberg 🇸🇪

  • Freely available Matlab code for CCSA/MMA⁴ and GCMMA

Author ©️

📧 Please contact to [email protected]

⚠️ Disclaimer: The author reserves all rights but does not guarantee that the code is free from errors. Furthermore, we shall not be liable in any event.

Name	Info.	Hobby	Food
Yu Li	🇨🇳 🎓 1️⃣9️⃣9️⃣0️⃣ ♑	🎧 🃏 🎮 🏀 🏊 🏃 🚴‍♂️	🍦 🦞 🍣 🌽 🍌

@misc{Yu2022,
  author = {Yu Li},
  title = {Topology Optimization in Julia},
  year = {2022},
  publisher = {GitHub},
  journal = {GitHub repository},
  howpublished = {\url{https://github.com/yuloveyet/Topology-Optimization-in-Julia}},
  }

References

Footnotes

1. Ferrari, F., & Sigmund, O. (2020). A new generation 99 line Matlab code for compliance topology optimization and its extension to 3D. Structural and Multidisciplinary Optimization, 62(4), 2211-2228. ↩

2. Sigmund, O. (2001). A 99 line topology optimization code written in Matlab. Structural and multidisciplinary optimization, 21(2), 120-127. ↩

3. Andreassen, E., Clausen, A., Schevenels, M., Lazarov, B. S., & Sigmund, O. (2011). Efficient topology optimization in MATLAB using 88 lines of code. Structural and Multidisciplinary Optimization, 43(1), 1-16. ↩

4. Svanberg, K. (2002). A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization, 12(2), 555-573. ↩