Keystone v14: continuum linear buckling & stability studio

[kkd16]

What this adds

A sixth studio tab for Keystone (projects/keystone-fea-b3k9/): continuum linear (Euler) buckling — the elastic-instability failure mode the static Q4/Q8 solver was blind to. A slender 2-D part under compression snaps sideways far below its yield stress; this is the eigenvalue problem that catches it.

The physics is the generalized eigenproblem (K + λ K_g) φ = 0, where K_g = ∫ Gᵀ τ G dΩ is the geometric (initial-stress) stiffness built from a reference plane-stress field. The smallest positive load multiplier λ_cr is the buckling factor; φ is the buckled shape.

Implementation

• src/engine/buckling.ts — assemble K, run the reference static solve for the pre-buckling stress field, recover Gauss-point stresses, assemble the stress stiffness S = −K_g, and solve for the lowest critical load factors + mode shapes. Because K_g is indefinite, the v9 SPD-mass subspace solver can't be reused: the eigensolver runs a K-orthonormal subspace iteration on A = K⁻¹(−K_g) (self-adjoint in the K-inner-product) with a standard symmetric Rayleigh–Ritz reduction (jacobiEig) and relative rank-revealing deflation — so the indefinite / rank-deficient stress stiffness never breaks the reduction. Plus eulerLoad = π²EI/(KL)².
• src/engine/bucklingpresets.ts — material table (steel / Al 6061 / Ti-6Al-4V, with σ_y), three scenarios (fixed–free flagpole K=2, fixed–pinned braced strut K≈0.699, compression panel), and a builder returning section properties (I, r, Euler load, slenderness KL/r) for the analytical column.
• src/ui/BucklingStudio.tsx — the new tab. Two views on one solve: the buckled shape (breathing lateral bow over axial load-path shading, base hatching + load arrows) and the column curve (FE critical stress dropped onto the Euler hyperbola σ_cr = π²E/λ² with its yield cut-off + transition slenderness). Mode-pill selector, a Q8/Q4 toggle that visibly shows shear locking, and a debounced slenderness slider.
• Wired into App.tsx (tab + segmented option), state.ts (persisted tab type), validate.ts + components.tsx (badge category), plus CSS.

Validation

Three new closed-form benchmarks, badge 81 → 84, all green:

Check	Reference	Rel. error
Fixed–free Euler column	π²EI/(2L)²	0.05%
Fixed–pinned Euler column	π²EI/(0.699L)²	0.5%
Cantilever mode ladder	λ₂/λ₁ = 3²/1² = 9	0.25%

Verified end-to-end in headless Chromium — all six studio tabs render, the flagpole reproduces Euler to 0.08% with the 1 : 8.97 : 24.79 mode ladder, the braced strut shows the fixed–pinned half-wave, the panel buckles into a 2-D bulge, and the column curve seats the design point on the hyperbola. Scope + conformance + lint + build all pass the exact CI gate; zero runtime errors.

🤖 Generated with Claude Code

https://claude.ai/code/session_01RGnTxnxKH7Fmj125T54jqg

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Generated by Claude Code

[github-actions]

✅ Scope + lint + build passed.