Regime Analysis

Why this matters

Classical shell-buckling handbooks give you a single knockdown factor and a single allowable stress. That number hides a physics divide: the same shell, under the same load, can fail in three fundamentally different ways depending on its slenderness Z (the Batdorf parameter) and the degree of imperfection present.

In Regime 1 (low Z), failure is dominated by elastic buckling sensitive to initial imperfections — the characteristic hook curve drops steeply from the classical prediction. In Regime 2, the curve briefly recovers as imperfection sensitivity diminishes but plastic interaction has not yet set in. In Regime 3 (high Z, stocky shells), yielding of the material governs and the collapse response follows plastic collapse theory, not elastic stability.

Applying an elastic formula in Regime 3 over-predicts capacity. Applying a plastic formula in Regime 1 under-predicts by a factor that can exceed 2. Regime-awareness is the difference between a sized shell and a correctly sized shell.

How MDC handles it

MDC Codex computes Z from your geometry and material inputs and classifies every analysis point into one of the three regimes. The governing regime and the active collapse criterion are surfaced in every report — not buried in an appendix.

At the regime boundaries, MDC interpolates smoothly using the physics-based η-factor framework rather than a discontinuous empirical switch. The transition-zone handling is calibrated on 400+ experimental collapse records covering Z from ~10 to ~2000.

• Regime 1 (Z ≲ 200): imperfection-sensitive elastic buckling, hook curve applied.
• Regime 2 (200 ≲ Z ≲ 600): transition band, η-interpolation between regimes.
• Regime 3 (Z ≳ 600): plastic-governed collapse, material curve integrated.

The hook-transition point — where the curve bottoms out before the R2 recovery — is flagged explicitly in the output. It tells you whether your design buys its margin from elastic geometry or from material yield.