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Physics Pillar

Imperfection Sensitivity

Small geometric deviations (weld distortion, out-of-roundness, dent) drive shells far below their classical buckling limit. MDC sweeps w/t continuously.

This page is part of the MDC Codex technical documentation series. For the full peer-reviewed methodology, see Wagner et al. (2025), Proc. R. Soc. A, DOI 10.1098/rspa.2025.0196.

Why this matters

Real shells are never perfectly cylindrical. Weld shrinkage, plate rolling tolerance, transport-induced ovality, and fabrication-stage dents all contribute a characteristic imperfection amplitude. Classical elastic buckling predictions assume a perfect geometry and therefore over-predict capacity by 40–80% for thin shells.

The magnitude of the knockdown is not linear in imperfection amplitude: it follows the characteristic hook curve, with a sharp drop at small w/t values and a gentler decline beyond the hook transition. Designing without mapping this curve means accepting either unquantified over-design or unquantified risk.

How MDC handles it

MDC sweeps the normalized imperfection amplitude w/t continuously from 0 to 20 and plots the full knockdown response. Fabrication quality classes (Q=A workshop through Q=C field fabrication, per EN 1993-1-6) are annotated on the curve so you can read the allowable stress at your actual tolerance level — not at a single idealized value.

The framework is calibrated on 1,000+ experimental collapse records and the allowable statistic (A-basis, B-basis, or mean) is user-selectable.

See the imperfection sweep in action.

Open the Codex and drag the w/t slider — the response updates live.