Does the minimum feature of a robust topology-optimised beam follow the filter radius when the mesh is refined?

What it found

Repeats the simdesign-robustradius sweep on 60×20 and 180×60 meshes with the filter radius held at 1/30, 1/20 and 1/15 of the beam length, plain Heaviside against the robust eroded / blueprint / dilated design (12 runs, one each). On the 180×60 mesh the minimum solid feature is 5 pixels (2.8% of the beam) at all three radii, 6, 9 and 12 elements; on 60×20 it is 1–3 pixels. With the earlier 120×40 runs the feature in pixels grows with the mesh (1, 3, 5) and not with the radius, so it is set by the grid here, not by the filter (negative for radius control; one problem, coarse integer measure). Two robust runs on the 60×20 mesh ended at poor blueprints (compliance about 740 against about 195), reported as such. Stylised: 2D, dimensionless.

A figure from its own output

Paper, code and results

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

More in Simulation-first design

• 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).
• Can penalty continuation free SIMP topology-optimisation starts that stay stuck in a different local optimum?Can penalty continuation free SIMP starts stuck in a different local optimum? No: it sends all 5 stuck starts of 20 to one design (c 204.01) worse than the 202.83 three reach by running longer at p = 3. Stylised.
• Is the start-dependence of fixed-penalty SIMP topology optimisation just slow convergence?Is the start-dependence of fixed-penalty SIMP just slow convergence? Over 1200 iterations the median of 20 random starts reaches the uniform-start design (0.0% of elements differ, from 3.9% at 150), but the compliance spread only falls 1.43% → 0.85% (stylised, 2D, one mesh).
• How much does a SIMP topology optimisation depend on its starting density field, and does penalty continuation remove it?How much does a SIMP topology optimisation depend on its starting density field? With a fixed penalty, final compliance spreads 1.4–2.8% over 30 random starts and 2–23% of elements change state; with penalty continuation the spread is 0–0.4% (stylised, 2D, 150 iterations).

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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.