forked from 1b-agent/fieldcraft-upstream
jyvikoandClaude Opus 5.5
9f6afe7a89
arc-shallow-arch: a sinusoidal arch of 40 × 2 × 1 hex20 under a sinusoidal dead load scaled to the one-mode closed form's upper limit load: the upper limit point at 0.992 (−0.8 %), the lower at 0.219 (0.8 % of the peak load) and exactly one negative eigenvalue between them. ROADMAP and parity updated, docs/oracle.md regenerated. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
769 B
769 B
Snap-through of a shallow arch by arc length
A shallow sinusoidal arch y₀ = a sin(πx/L), L = 100, depth 1, unit width (40 × 2 × 1 hex20, E = 10⁴, ν = 0), pinned at mid-depth at both ends, under a sinusoidal dead load q₀ sin(πx/L) applied per element on its top face, in a nonlinear static step with arc-length control. With a/r = 3.5 the symmetric path has two limit points and the antisymmetric mode does not bifurcate before them. The load is scaled to the closed form's upper limit load, so the path peaks at load factor 1; the step snaps through, passes the lower limit point and stops at a midspan deflection of 2.2 a. Measured: both limit points' load factors (from the change of the tangent's inertia) and the one negative eigenvalue between them.