Structured chaos: redefining the design of buckling-critical cylindrical shells

Experimental studies on axially compressed cylindrical shells have historically shown large variability in buckling loads, often challenging existing theoretical models. Our analysis reveals that this scatter follows a structured, regime-dependent trend—formalized here as the mechanistic design curve (MDC). This curve captures a systematic transition between three dominant failure mechanisms as a function of slenderness: global collapse (Regime 1), transitional recovery (Regime 2) and localized instability (Regime 3). Through large-scale Monte Carlo simulations incorporating measured geometric imperfections and localized buckling triggers, we demonstrate how buckling behaviour evolves across these regimes, exhibiting a characteristic dip–recovery–decline pattern in knockdown factors. The MDC framework is validated using decades of experimental data on both cylindrical and conical shells, revealing consistent regime boundaries despite variations in geometry and manufacturing quality. By unifying physics-based mechanisms with statistical robustness, the MDC replaces empirical lower-bound approaches (e.g. NASA SP-8007) with predictive, regime-aware design rules. Case studies demonstrate weight savings exceeding 14%—and up to 31% in optimized configurations—while maintaining safety, highlighting the MDC's potential to transform lightweight shell design. This work reinterprets historical scatter and reveals that what appeared chaotic is, in fact, governed by hidden structure.