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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
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@@ -280,6 +280,9 @@ fn solution(steps: &[&Step]) -> std::result::Result<u32, String> {
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if let Some(s) = steps.iter().find(|s| matches!(s.procedure, Procedure::ExplicitDynamic(_))) {
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return Err(format!("step `{}`: explicit dynamic steps (Nastran's linear solutions have none)", s.name));
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}
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if let Some(s) = steps.iter().find(|s| matches!(s.procedure, Procedure::Buckle { .. })) {
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return Err(format!("step `{}`: buckling steps (Nastran's SOL 105; this writer writes SOL 101 and 103 so far)", s.name));
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}
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if let Some(s) = steps.iter().find(|s| matches!(s.procedure, Procedure::NonlinearStatic(_))) {
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return Err(format!("step `{}`: nonlinear static steps (Nastran's SOL 400; this writer writes SOL 101 and 103 so far)", s.name));
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}
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