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
11 lines
769 B
Markdown
11 lines
769 B
Markdown
# Snap-through of a shallow arch by arc length
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A shallow sinusoidal arch y₀ = a sin(πx/L), L = 100, depth 1, unit width (40 × 2 × 1 hex20,
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E = 10⁴, ν = 0), pinned at mid-depth at both ends, under a sinusoidal dead load q₀ sin(πx/L)
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applied per element on its top face, in a nonlinear static step with arc-length control. With
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a/r = 3.5 the symmetric path has two limit points and the antisymmetric mode does not bifurcate
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before them. The load is scaled to the closed form's upper limit load, so the path peaks at load
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factor 1; the step snaps through, passes the lower limit point and stops at a midspan deflection
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of 2.2 a. Measured: both limit points' load factors (from the change of the tangent's inertia)
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and the one negative eigenvalue between them.
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