Do the reversed-load buckling widths of the L-bracket change with more element layers through the thickness?

What it found

A small finite-element check (stylised, preliminary; ideal elastic sheet, sharp inner corner, coarse in-plane mesh). Raising the number of hexahedral layers through the sheet from one to four moves the whole-L reversed-load buckling factor at the simdesign-revgauge root widths by at most 1.2% (3.0 mm gauge; under 0.7% at 1.5 to 2.5 mm) and the width needed for a factor of 3 by 0.07 mm or less (2.0 mm: 11.84 to 11.77 mm, 27.4 g). The thicker-sheet mass ranking of that project is not an artefact of a single through-thickness layer; its other doubt, a web barely wider than the sheet is thick, stands.

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-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.
• Does lateral-torsional buckling justify the w/b ≤ 8 slenderness rule of the 2 mm laser-cut bracket?A closed-form lateral-torsional buckling check of the laser-cut bracket arms (stylised, unvalidated by FE): at 2 mm gauge the governing safety factor is 6.9–9.0 for w = 16–20 mm, so the widths of simdesign-widerweb are not buckling-limited, and the factor rises with w, opposite to the w/b ≤ 8 rule; at 1 mm the old rule admits designs below 1.

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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.