How wide must the 1.5 mm L-bracket be to clear the buckling floor when the load is reversed?

What it found

A small finite-element sweep (stylised, preliminary; ideal elastic sheet, sharp inner corner, buckling only). Reusing the whole-L 3D eigenbuckling model of simdesign-lbuckle, the reversed-load factor of the 1.5 mm bracket rises from 2.27 at w = 18.4 mm to 3.0 at w ≈ 22.5–22.6 mm (coarse root 22.47, finer-mesh bracket 22.54–22.62), about 0.22 per extra millimetre. The plate mass rises from 30.7 to 36.6 g (+19%). Stress, slenderness and minimum-wall limits were not rechecked at the wider web, the floor of 3 is an assumption, and the corner is sharp.

A figure from its own output

Paper, code and results

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

More in Simulation-first design

• Do the reversed-load buckling widths of the L-bracket change with more element layers through the thickness?More element layers through the thickness (1 to 4) move the L-bracket's reversed-load buckling factor by at most 1.2% and the width needed for the floor of 3 by at most 0.07 mm at 1.5 to 3.0 mm gauges, so the thicker-sheet designs of simdesign-revgauge stand; coarse in-plane mesh, sharp corner, ideal sheet, preliminary.
• Do the reversed-load buckling-limited L-bracket designs also pass the forward-load buckling, stress and deflection checks?Under the forward 100 N load the four reversed-load buckling-limited L-brackets all clear buckling (factor 4.7 to 5.6), but only the 1.5 mm design also meets the 100 MPa and 4 mm limits; the 2.5 and 3.0 mm designs fail by 2 to 8 times, and the 2.0 mm design passes only on the coarse mesh (95.7 vs 144.9 MPa finer). Stylised.
• Is a thicker sheet lighter than a wider 1.5 mm web for clearing the reversed-load buckling floor?At the reversed-load buckling floor of 3, a 2 mm sheet needs a web of about 11.8 mm and weighs 27.5 g against 36.6 g for 1.5 mm at 22.6 mm; 2.5 mm gives 20.5 g; buckling only, one element layer through the thickness, preliminary.
• Does relaxing the 1.2 mm minimum-wall rule open thinner sheet gauges for the laser-cut bracket, or is the buckling floor what binds?Relaxing the 1.2 mm minimum wall of the laser-cut bracket: it does not open 1.0 mm sheet by itself (the buckling floor binds); with floor 1 and wall ≤ 1.0 mm a 24.8 g design appears (unvalidated closed form).
• Does the lightest 1.5 mm bracket design clear buckling in a converged 3D eigenbuckling model?A through-thickness-converged 3D eigenbuckling model agrees with the closed-form buckling factor of the lightest 1.5 mm bracket design to under 1% (3.49 vs 3.47, so it clears the floor of 3); the horizontal-arm formula is about 18% conservative; one design, ideal bar, preliminary.
• What changes when the w/b ≤ 8 slenderness ceiling of the laser-cut bracket is replaced by a buckling-factor floor?Replacing the w/b ≤ 8 ceiling with a closed-form buckling-factor floor makes the 1.5 mm laser-cut gauge feasible (31.0 g, about 13% lighter than the best 2 mm design) and changes nothing at 2 and 3 mm; at 1 mm the minimum-wall rule, not buckling, blocks every design; stylised, unvalidated factor, preliminary.

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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.