How much stiffness does a topology-optimised cantilever lose when the real load points a different way than the model assumed?

What it found

Optimises a 48×24 cantilever (volume fraction 0.4) for a straight-down tip load and for weighted sums over several load directions, then analyses each design under load angles from −90° to 90° against the design optimised for that angle alone. The nominal design is within 5% for tilts up to 30°, but 1.57× off at 60° and 2.58× at horizontal. A {0, ±60°} multi-load design cuts the worst case to 2.00× for 0.6% on the nominal load, and {0, ±90°} to 1.88× for 2.9%; no single topology is stiff in every direction. Stylised 2D, one mesh, one run per design; preliminary.

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 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).
• 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).

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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.