Do the closed-form buckling factors of the laser-cut bracket arms agree with a 3D eigenbuckling model?
research/simdesign-webshell
A 3D scikit-fem eigenbuckling check of the bracket-arm closed forms (stylised, mesh not converged): within about 1% for the governing vertical arm, conservative by 6–29% for the horizontal arm at the 2 mm gauge.
What it found
A stylised, preliminary comparison of two idealised models (mesh not fully converged). A 3D scikit-fem linear-buckling model of each bracket arm, checked against the Euler column, gives a critical load within about 1% of the closed form for the governing vertical arm (end moment) at web widths of 8–25 mm at the 2 mm gauge. For the horizontal arm (tip load) the closed form is conservative: the 3D model is 6% higher at w = 8 mm and 29% higher at 25 mm. The governing safety factors (3.2, 7.0, 11.9) therefore support the conclusion of simdesign-webbuckle. Imperfections, residual stress, corner flexibility and plasticity are left out. Simulated only.
Paper, code and results
More in Simulation-first design
- Does refining the mesh of the 3D eigenbuckling check change how the closed-form bracket-arm buckling factors compare?Mesh refinement of the 3D eigenbuckling check of the bracket arms (stylised): refining length, width and thickness lowers every FE/closed-form ratio by 0.9–1.3 points, so the governing vertical arm agrees with the closed form to within 1% (ratio 0.99–1.00 at the finest mesh).
- At what bar slenderness does the 3D eigenbuckling model agree with the slender-beam closed form?How the 3D eigenbuckling model compares with the slender-beam closed form as a bar gets longer (stylised): the finite-element load is 14.5%, 7.4%, 3.8% and 2.1% above it at l/w = 3, 6, 12, 24.
- How much stiffer than a uniformly thinned plate is a topology-optimised part, and how does that depend on volume fraction?How much stiffer a thresholded topology-optimised part is than a uniformly thinned plate across volume fractions (stylised): 26–31% lower compliance at v = 0.3–0.5, shrinking to 14% at 0.8, and disconnected designs below that on coarse grids.
- At what rate does the 3D eigenbuckling model converge under uniform mesh refinement?Observed convergence order of the 3D eigenbuckling model on a short bar (stylised): three uniform meshes give order ≈ 2.6 and a Richardson limit FE/closed-form ratio 1.137, so the gap to the closed form is not discretisation error.
- What does it cost to replace the w/b ≤ 8 rule of the laser-cut bracket with a buckling-factor guard?Replacing the w/b ≤ 8 slenderness rule of the laser-cut bracket with a lateral-torsional buckling factor ≥ 3 lets the optimiser use the 1.5 mm gauge at w ≈ 18.7 mm, 31.3 g instead of 35.9 g (about 12% lighter), and the guard does not bind at that optimum; the result depends on the assumed factor (no feasible design for factors ≥ 5 at that gauge); stylised, preliminary.
- When does the buckling guard of the laser-cut bracket start to bind as load and arm length change?Sweeping tip load (50–400 N) and arm length (60–120 mm) of the laser-cut bracket: the buckling-factor ≥ 3 guard binds only at 120 mm arms (unguarded optimum has factor 1.9; 69 g vs 59 g), while the old w/b ≤ 8 rule costs 14–25% in mass in five of six cases (stylised, two seeds).
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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.