Can Sigmund's 99-line topology optimisation be reproduced in Python and carried through to a printable part?
research/simdesign-topopt
Python reproduction of Sigmund's 99-line SIMP topology optimisation (cantilever, half-MBB; filter removes 11.5% checkerboards) with the density field exported as a mirrored, extruded STL; stylised 2D compliance only.
What it found
A Q4 plane-stress SIMP code with the 99-line sensitivity filter and optimality-criteria update, tested against Hooke's law and finite-difference sensitivities. It gives truss-like cantilever (compliance 351.9 → 52.4) and half-MBB (1007.0 → 203.3) designs. Without the filter 11.5% of 2×2 cells are checkerboards; with it none, at the same compliance within 0.03%. The thresholded MBB design is one connected body and is written as an extruded, mirrored STL. Stylised: dimensionless 2D compliance only, no stress or 3D check, not compared with the published codes.
A figure from its own output
Paper, code and results
More in Simulation-first design
- How much stiffness does a topology-optimised cantilever lose when the real load points a different way than the model assumed?How much stiffness a topology-optimised cantilever loses when the real load direction differs from the modelled one: 1.57× at 60° and 2.58× at horizontal for the nominal design; a multi-load design at 0, ±60° cuts the worst case to 2.00× for 0.6% nominal cost; stylised 2D, preliminary.
- Does a density filter with Heaviside projection close the gap between a topology-optimised density field and the black-and-white part?Density filter and Heaviside projection added to the SIMP code: the optimiser's compliance matches the thresholded part's to 0.1% (sensitivity filter: 10% off) but the parts are equally stiff within 0.9%; β continuation needed (β=64 from the start: 344.8 vs 192.1); a minimum-length-scale check found no advantage (negative); stylised 2D.
- Does a topology-optimised beam survive a 0.2 threshold error, and what does the robust formulation cost?Does a topology-optimised beam survive a 0.2 threshold error? The plain Heaviside design disconnects when eroded on all three meshes; the robust eroded/blueprint/dilated design stays at 224–226 (14–16% above nominal) for 0.8–3.4% more nominal compliance, but shows no minimum-length-scale gain (negative; stylised).
- Does the filter radius or the threshold gap set the minimum feature size of a robust topology-optimised beam?Does the filter radius or the threshold gap set a robust beam's minimum feature size? A gap of 0.1 already stops the erosion failure (eroded compliance 255–276 against 187–200 nominal; plain design disconnects), but solid feature size is 3 px at both radius 4 and 6 (negative; stylised, one mesh).
- Does the minimum feature of a robust topology-optimised beam follow the filter radius when the mesh is refined?Does the minimum feature follow the filter radius once the mesh is refined? No: at 180×60 it is 5 px at radii of 6, 9 and 12 px; across meshes it grows with the grid (1, 3, 5 px), not the radius (negative; two poor 60×20 robust runs reported; stylised).
- Does the optimality-criteria move limit decide whether a robust topology optimisation survives its beta steps?Does the move limit decide whether a robust topology optimisation survives its β steps? Yes here: at 0.2 five of nine cases failed (blueprint compliance up to 4× the best), at 0.1 and 0.05 none (stylised; mechanism not tested).
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Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.