From Euler buckling to an equilibrium jump
A flat-clamped arch stores end shortening in its shape. A preferred-curvature pattern couples to its buckling modes. Equations (2) and (3), arXiv v2 pages 3–4, give the shallow-angle equilibrium and compression spectrum. We restrict this experiment to a centered rectangular pattern.
The production Stabileo 2D frame buckling solver computes 16 modes on 64 elements. A research layer projects the curvature onto these modes and solves the paper’s compression constraint. The same Rust code runs here as WASM and generates the replay.
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Validation and sources
At a stimulated width of 70%, the paper gives α/√ε = 21,52 (arXiv v2 page 3, following Eq. 2). The overlay is regenerated from the authors’ shallow-angle software in Zenodo record 18256271, licensed CC-BY-4.0. It is a numerical reference, not experimental validation.
- Published threshold at 70% width
- 21,52
- Stabileo modes + shallow-arch equations
- 21,51730
- Zenodo curve: maximum relative error
- 0,1821% · Tolerance 0,3%
- Mesh and mode refinement
- 0,04% · Tolerance 0,1%
- First Euler load
- 0,0000129% · Tolerance 0,001%
- Second Euler load
- 0,00005393% · Tolerance 0,001%
Paper and supplementary equations · Zenodo data and software
This is a shallow, inextensible equilibrium model. The jump connects equilibria; it does not simulate snap dynamics or reproduce laboratory measurements. Arc-length in the production engine rejects prescribed displacements and thermal loading, so it is not used for this curvature-driven path. Only centered patterns and small end shortening are covered.
Cite this
Stabileo Research, “Snapping arches by curvature patterning”, reproduction of Michał Zmyślony, Ammar Khan, John S. Biggins (2026), doi:10.1103/56f8-8gsx. Implementation: research/mechanics/biggins-2026 at commit 8068cd16ea2c. Engine: the Stabileo engine at the same commit. Permanent links to this exact build are planned.