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/system.rs

@@ -155,6 +155,14 @@ impl Kernel<'_> {
         }
     }
 
+    /// The initial-stress stiffness of stresses at the stiffness points.
+    pub fn geometric_stiffness(&self, stress: &[[f64; 6]]) -> fieldcraft_fem::Result<fieldcraft_fem::dense::Matrix> {
+        match self {
+            Kernel::Solid(s) => s.geometric_stiffness(stress),
+            Kernel::Plane(p) => p.geometric_stiffness(stress),
+        }
+    }
+
     pub fn rule(&self) -> fieldcraft_fem::quadrature::Rule {
         match self {
             Kernel::Solid(s) => s.rule(),