When does a cheaper beam model pick the same design as 3D finite elements?

research/simdesign-fidelity

Cantilever sizing with Euler–Bernoulli, Timoshenko, 2D and 3D finite elements: stress agrees everywhere, deflection differs; cheap models land within ~5% of the 3D depth, unsafe when narrow and stubby (Euler–Bernoulli) and oversized when wide (plane stress). Stylised, assumed material.

6 tests

What it found

A rectangular cantilever is sized for minimum mass under a tip-deflection and a top-fibre stress limit with Euler–Bernoulli and Timoshenko beam theory, 2D plane-stress and 3D finite elements (scikit-fem), and each design is judged by the 3D model. Stress read away from the clamp agrees across models; deflection does not. Over 12 length–width cases the cheap models choose a depth within about 5% of the 3D optimum: Euler–Bernoulli is unsafe for narrow, stubby beams (up to 1.05× the deflection limit), while Timoshenko and plane stress are up to about 5% too heavy for wide ones, where plane strain stiffens the beam. Stylised: assumed material, a coarse 3D reference whose deflection still moves about 0.4% under refinement, no stress concentrations, nothing measured.

A figure from its own output

Figure produced by research/simdesign-fidelity: fidelity — simdesign-fidelity/experiments/fidelity.png, written by the project's own experiment code.

Paper, code and results

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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.