Pesquisa / Cascas e flambagem

Shell obstacle course — Belytschko et al. (1985)

A partir de Ted Belytschko, Henryk Stolarski, Wing Kam Liu, Nicholas Carpenter, Jame S.J. Ong, “Stress projection for membrane and shear locking in shell finite elements”, Computer Methods in Applied Mechanics and Engineering (1985), doi:10.1016/0045-7825(85)90035-0.

Frente ao código do autor
Production-engine comparisons with existing test references; no independent reference solver.
Frente às figuras do artigo
Proposed: numerical values and exact paper table/page locators have not been checked against the paper text.

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

Three curved-shell benchmarks, solved with the production MITC4 engine. Refine each mesh and inspect its measured response; every failure stays visible.

The obstacle course

This page runs existing Stabileo shell tests in the browser. It is a benchmark companion to Belytschko, Stolarski, Liu, Carpenter and Ong (CMAME 51, 1985), not an implementation of their stress-projection element. The production element here is MITC4 with its existing membrane and shear treatment. No solver equations or tolerances were changed for this page.

Models and measurements

Scordelis–Lo roof: R = 25, L = 50, thickness 0.25, 40° half-angle, E = 4.32 × 10⁸, ν = 0, vertical gravity load 90 per area. A quarter model measures |u_z| at the midspan free edge against 0.3024. The existing test's crown pin and corner restraint precedence are retained, including omission of loads at vertically restrained nodes.

Pinched cylinder with rigid diaphragms: R = 300, L = 600, thickness 3, E = 3 × 10⁶, ν = 0.3. The one-eighth geometry carries a 0.25 inward load at midspan. The test calls this a quarter model in its comments. We retain its exact restraints, including corner precedence, and measure |u_y| at the loaded node against 1.8248 × 10⁻⁵.

Hemisphere with an 18° hole: the NAFEMS LE3-labelled variant in shell_benchmark::benchmark_hemisphere_hole_convergence. R = 10, thickness 0.04, E = 6.825 × 10⁷, ν = 0.3; latitude runs from the equator to 72°. The quarter model applies +2 in x and −2 in y and measures |u_x| at the equator against 0.185. The native solid-shell test instead applies ±1 after symmetry reduction and compares with 0.094 (also citing 0.0924). Those conventions are not interchangeable. The unperforated hemisphere is not this case.

All inputs use the tests' consistent benchmark units. The engine input modulus is E/1000. Viewer numbers use those same length units; magnification is visual only. The editor handoff preserves geometry, nodal loads and each constrained degree of freedom.

Refinement and verdicts

The shared engine-owned case file is read by the native tests and this page. Curves show computed/reference versus mesh divisions; the dashed line is 1. Failures or missing results are never interpolated. Refinement need not be monotone and is not a promise of convergence.

The headline counts the finest selected browser meshes only: roof 16×16, cylinder 16×16, hemisphere 16×16. The 16×16 cap bounds each model to 289 nodes. Cylinder 12×12 and 16×16 extend the existing test geometry and restraints; they have no historical regression assertion. This is a conservative workload cap, not a measured browser capacity limit. Every row uses the existing benchmark-page accuracy policy of relative error strictly below 2%; this is not a tolerance attributed to the paper. Native tests retain all their original assertions and much broader regression bounds. Passing those bounds does not mean passing this accuracy target.

Findings and provenance

The findings ledger records accuracy and model limitations. The production registry has no open shell entry; solver-owner triage is still needed. The page cannot establish that a mismatch is solely locking rather than a boundary-condition or reference convention issue.

References are inherited from shell_benchmark.rs and solid_shell_locking.rs; the roof and cylinder values also appear in the shared MacNeal–Harder data. scordelis_lo.rs contains flat plate checks, despite its filename. Crossref verifies the Belytschko citation, not these numerical transcriptions. Published table/page provenance is unresolved, so catalogue status remains proposed. Research, not a design tool.

Coberto apenas no CI nativo

  • Solid-shell roof: Reference 0.3024; original 4/8/16 meshes and accuracy assertions. Solid-shell inputs are not exposed by the production web wrapper. solid_shell_locking::scordelis_lo_roof
  • Solid-shell cylinder: Reference 1.8248e-5; 8/16/32 meshes and original convergence bounds. Solid-shell inputs are not exposed by the production web wrapper. solid_shell_locking::pinched_cylinder_with_diaphragms
  • Solid-shell hemisphere, 18° hole: Reference 0.094, quarter loads ±1; 8/16/32 meshes. The page uses ±2 and reference 0.185, exactly as its MITC4 test. solid_shell_locking::hemisphere_with_hole
  • Unperforated hemisphere: Different pole treatment and geometry; outside this live selection. benchmarks::shell_benchmark::benchmark_pinched_hemisphere_8x8
  • Higher-order shells: MITC9 is not exposed by the production web wrapper. benchmarks::shell_benchmark::benchmark_q9_scordelis_lo
  • Curved shells: Covered by validation CI; not selected for this MITC4 comparison. benchmarks::shell_benchmark::benchmark_curved_shell_hemisphere_hole
  • Flat plate checks: The scordelis_lo.rs file tests flat plates, not the curved roof. benchmarks::scordelis_lo::validation_plate_simply_supported_uniform_pressure

Citar isto

Stabileo Research, “Shell obstacle course — Belytschko et al. (1985)”, reprodução de Ted Belytschko, Henryk Stolarski, Wing Kam Liu, Nicholas Carpenter, Jame S.J. Ong (1985), doi:10.1016/0045-7825(85)90035-0. Implementação: engine/tests/benchmarks no commit 8068cd16ea2c. Motor: o motor do Stabileo no mesmo commit. Estão previstos links permanentes para esta compilação exata.