{ "title": "Pinched cylinder with rigid diaphragms", "kind": "benchmark", "source": "Belytschko, Stolarski, Liu, Carpenter and Ong, 'Stress projection for membrane and shear locking in shell finite elements', Computer Methods in Applied Mechanics and Engineering 51 (1985) 221–258 (the shell obstacle course); reference 1.8248 × 10⁻⁵ under the load", "quantities": [ { "id": "u", "quantity": "radial displacement under the load, mid-surface", "measure": { "command": "solve.probe", "params": { "step": "Load", "at": [ [ 0, 0, 300 ] ] }, "pointer": "/nodes/0/displacement/2" }, "value": -1.8248e-05, "tolerance": { "relative": 0.02 }, "reason": "a fixed-mesh comparison at the conventional 32 × 32 eighth mesh, the mesh the solver's own in-code benchmark uses: the reference is the thin-shell value Belytschko et al. quote to four figures (1.8248 × 10⁻⁵), while the deflection under a point load has no mesh-converged limit in a Reissner–Mindlin (MITC4) shell, whose transverse shear force is unbounded at the load, so the value keeps rising with refinement (8 × 8, 16 × 16, 24 × 24, 32 × 32, 48 × 48 and 64 × 64 give 1.3559, 1.6942, 1.7735, 1.8038, 1.8275 and 1.8369 × 10⁻⁵, crossing the reference between 32 × 32 and 48 × 48 and staying above it); 2% is the margin the in-code benchmark gates 32 × 32 with, applied here to the same mesh (crates/solver/tests/benchmarks.rs, README)" } ] }