Pesquisa / Métodos numéricos

Mattiasson (1981): cantilever elastica

A partir de Kjell Mattiasson, “Numerical results from large deflection beam and frame problems analysed by means of elliptic integrals”, International Journal for Numerical Methods in Engineering (1981), doi:10.1002/nme.1620170113.

Frente ao código do autor
Production engine only; no independently reproduced reference solver.
Frente às figuras do artigo
The numerical transcription has not been checked against the paper text. Status: proposed.

Pesquisa, não uma ferramenta de projeto. Nada aqui é um resultado de engenharia.

A cantilever under increasing tip force, traced by Stabileo’s production corotational solver. References use independently checked elliptic-integral values; failures remain visible.

Model and load path

A fixed-root cantilever has L = 2 m, 16 frame elements, E = 200000 MPa, A = 0.01 m² and I = 10⁻⁴ m⁴. The engine converts E to kN/m². Downward tip force P is parametrized by PL²/EI; u/L = −ux/L is shortening and v/L = −uz/L is downward displacement. The viewer uses actual nodal displacements at scale 1.

Twenty independent incremental solves trace force parameters 0.5 through 10. Each uses the production solveCorotational2D wrapper with 50 iterations, residual tolerance 10⁻⁶ and 10 increments. Playback loops through these live results and stops on interaction. It is not an exact reference shape or an interpolated solver path.

References and accuracy

The four reference pairs use the exact elliptic-integral values documented in BENCHMARK_REFERENCES.md on fix/845-elastica (#849): PL²/EI = 1, 2, 5, 10 gives (u/L, w/L) = (0.056433, 0.301721), (0.160642, 0.493457), (0.387628, 0.713792), (0.554996, 0.810609). The original paper table locator remains unverified.

The exploratory accuracy target is relative error strictly below 2% for both signed components. This new page target is separate from every existing native assertion, tolerance and regression bound. Intermediate steps have no accuracy reference. Nonconvergence or incomplete loading is a failure, never an accuracy pass.

Tip moment

The separate moment case uses M = EI/L = 10000 kN·m, matching the native end-moment test exactly. That test checks convergence and significant rotation. It does not establish full-circle rolling or elliptic-integral accuracy; the page makes neither claim. Under our downward-positive convention its upward displacement gives a negative v/L.

One case file and findings

The shared engine-owned JSON supplies the native end-moment test, native comparison runner and live page. Research CI compares fresh native and WASM results, including failures. No research solver is used.

Findings ledger and unresolved provenance: disagreement may involve transcription, model assumptions or solver accuracy. Solver-owner triage and the original numerical table are needed before attributing a defect. No runtime issue identifier is invented.

Coberto apenas no CI nativo

  • benchmarks::corotational_benchmarks::validation_corotational_small_load_equals_linear: Native regression: corotational/linear ratio within 5%; not an elliptic-integral accuracy target.
  • benchmarks::corotational_benchmarks_extended::validation_corotational_cantilever_end_moment: Same moment input shown live; rotation and convergence assertions run only in native CI.

The corotational API is available in production WASM. The native-only designation above applies to regression assertions, not to an unavailable solve.

Citar isto

Stabileo Research, “Mattiasson (1981): cantilever elastica”, reprodução de Kjell Mattiasson (1981), doi:10.1002/nme.1620170113. Implementação: engine/tests/benchmarks no commit 8068cd16ea2c. Motor: o motor do Stabileo no mesmo commit. Estão previstos links permanentes para esta compilação exata.