A numerical study on the buckling of near-perfect spherical shells

TL;DR

This study uses finite element simulations to analyze how near-perfect spherical shells with small defects buckle differently depending on their shape, revealing the importance of numerical parameters in accurate predictions.

Contribution

It systematically investigates buckling behaviors of near-perfect spherical shells with defects, highlighting the influence of geometry and numerical parameters on buckling modes and knockdown factors.

Findings

Hemispherical shells show boundary-dominated buckling with a knockdown factor of 0.8.

Full spherical shells exhibit localized buckling at the pole with near-unity knockdown factors.

Partial shells transition from boundary to localized buckling modes depending on cap angle.

Abstract

We present the results from a numerical investigation using the finite element method to study the buckling strength of near-perfect spherical shells containing a single, localized, Gaussian-dimple defect whose profile is systematically varied toward the limit of vanishing amplitude. In this limit, our simulations reveal distinct buckling behaviors for hemispheres, full spheres, and partial spherical caps. Hemispherical shells exhibit boundary-dominated buckling modes, resulting in a knockdown factor of 0.8. By contrast, full spherical shells display localized buckling at their pole with knockdown factors near unity. Furthermore, for partial spherical shells, we observed a transition from boundary modes to these localized buckling modes as a function of the cap angle. We characterize these behaviors by systematically examining the effects of the discretization level, solver parameters, and radius-to-thickness ratio on knockdown factors. Specifically, we identify the conditions under which knockdown factors converge across shell configurations. Our findings highlight the critical importance of carefully controlled numerical parameters in shell-buckling simulations in the near-perfect limit, demonstrating how precise choices in discretization and solver parameters are essential for accurately predicting the distinct buckling modes across different shell geometries.