solver, model, engine: linear buckling steps

Procedure::Buckle {modes, shift}: the step's loads as a linear preload, K_σ from its stresses,
and (K + λ K_σ) φ = 0 by block Lanczos in the K inner product: K⁻¹(−K_σ) on Cholesky without a
shift, the buckling transformation (K + σ K_σ)⁻¹ K on LDLᵀ with one, whose inertia counts the
load factors below σ (Grimes–Lewis–Simon 1994). Lanczos gains an operand and an eigenvalue map
(defaults keep frequency steps bit for bit) and reports converged negative eigenvalues. Results
are frequency results with a `buckling` part; modes display with their load factor.
solve.buckle (in the Static drop-down); Abaqus *BUCKLE, Nastran SOL 105 and LS-DYNA refuse it by
name. Euler columns of hex20 within 0.18 % of Engesser's load.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo

crates/solver/src/lib.rs

@@ -28,6 +28,7 @@
 #![allow(clippy::needless_range_loop)]
 
 pub mod analysis;
+pub mod buckle;
 pub mod cholesky;
 pub mod constraints;
 pub mod discrete;
@@ -43,6 +44,7 @@ pub use analysis::{
     ElementStress, FrequencyOptions, FrequencyResult, Location, MassKind, Mode, PointResult, StaticResult, Stats, StepResult, solve_frequency,
     solve_static,
 };
+pub use buckle::{Buckling, solve_buckle};
 pub use heat::{HeatResult, solve_heat};
 pub use nonlinear::solve_nonlinear;