Topology-Optimization-in-Julia

Julia Codes for Structural Topology Optimization Design

Codes

An educational 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 liyu_npu@outlook.com

⚠️ 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.

@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

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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. ↩︎