Does a density filter with Heaviside projection close the gap between a topology-optimised density field and the black-and-white part?

What it found

Adds a density filter, a tanh Heaviside projection and β continuation to the SIMP code of simdesign-topopt. On a 90×30 half-MBB beam the sensitivity and density filters leave 26–34% grey elements and a model compliance 10–15% above the thresholded part’s; with projection the two agree to 0.1% (192.1 vs 192.0). The thresholded parts are equally stiff within 0.9% (190.3–192.0), so the gain is an honest model, not a stiffer part. Starting at β = 64 without continuation gives 344.8 against 192.1. A minimum-length-scale check did not separate the formulations (negative): a single projection does not by itself fix a physical minimum feature. Stylised: 2D dimensionless compliance, one problem, one run per setting.

A figure from its own output

Paper, code and results

• README and method
• Experiments and results
• Code
• Tests

More in Simulation-first design

• 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).
• Can an adaptive move limit that shrinks after a compliance spike rescue a robust topology optimisation as well as a fixed small one?Can a move limit that halves after a compliance spike rescue a robust topology optimisation? Partly: fixed 0.2 failed 5 of 9 cases, fixed 0.05 none, the adaptive rule 2 of 9, because it reacts after the damaging step (stylised, one run per cell).
• Does rolling back a robust topology-optimisation step that spikes compliance, and redoing it at half the move, beat shrinking the move afterwards?Does rolling back a robust topology-optimisation step that spikes compliance and redoing it at half the move beat shrinking the move afterwards? Mostly: fixed 0.2 failed 5 of 9 cases, adaptive 2, retry 1, fixed 0.1/0.05 none, but retry never beat fixed 0.05 (stylised, one run per cell).

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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.