Investigation of uncertainty modeling in predicting the buckling of a metal hemisphere formed by the spinning process under uniform external pressure

**“The main objective of this study is to model uncertainty in predicting the critical buckling pressure of metallic hemispherical shells by considering thickness scatter, radius variations, and the effects of the spinning manufacturing process. In this regard, random geometric and material quantities—including thickness variation as a function of the angle θ, local radius fluctuations, and the dispersion of mechanical properties—were introduced using statistical models such as normal, log‑normal, and Weibull distributions, and a Monte Carlo analysis was performed to simulate the statistical response of the critical pressure.

In the first step, smooth functions for thickness and radius variations with respect to the angle θ, from the pole to the base of the hemisphere, were defined so that geometric imperfections and random distortions could be incorporated into the numerical model. Statistical analysis of the simulated datasets showed that even small fluctuations in thickness and radius can lead to a significant reduction in critical pressure, and that classical deterministic models are unable to accurately predict the real behavior of the shells.

From an experimental viewpoint, actual thickness and radius data of the manufactured shells were collected using 3D scanning and a thickness‑gauge probe to ensure that the statistical distributions used in the numerical model reflect real conditions. This combination of experimental methods and non‑deterministic numerical modeling enables an accurate assessment of the critical pressure and the determination of buckling reduction factors, thereby improving safe design, weight optimization, and the reliability of advanced structures.

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