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 <[email protected]> Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
11 lines
769 B
Markdown
11 lines
769 B
Markdown
# 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.
|