Does a topology-optimised beam survive a 0.2 threshold error, and what does the robust formulation cost?
research/simdesign-robust
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).
What it found
Adds the eroded / blueprint / dilated robust projection formulation to the SIMP code of simdesign-heaviside and tests both on a half-MBB beam at three mesh sizes, each design judged at projection thresholds 0.7, 0.5 and 0.3. The plain Heaviside design fails when eroded on every mesh (a member disconnects; compliance 105–109 against about 190), while the robust design stays at 224–226 eroded, 14–16% above its nominal value. The nominal compliance costs 0.8–3.4% more and the run about 2.5× the time. A minimum-length-scale gain was not shown (negative): feature sizes match Heaviside’s to within a pixel. Stylised: 2D dimensionless compliance, one problem, one run per setting, a density threshold standing in for etch error.
A figure from its own output
Paper, code and results
More in Simulation-first design
- 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).
- 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.
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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.