The nonlinear buckling behavior of a complete spherical shell under uniform external pressure and homogenous natural curvature

TL;DR

This paper investigates how combined external pressure and natural curvature influence the buckling stability of spherical shells, revealing that natural curvature can either destabilize or reinforce shells depending on its sign.

Contribution

It introduces a novel analysis of shell stability considering both external pressure and natural curvature, highlighting the destabilizing or strengthening effects of curvature.

Findings

Positive natural curvature can destabilize shells.

Negative natural curvature can reinforce shells.

Shell buckling limits can be exceeded through natural curvature design.

Abstract

In this work, we consider the stability of a spherical shell under combined loading from a uniform external pressure and a homogenous natural curvature. Non-mechanical stimuli, such as one that tends to modify the rest curvature of an elastic body, are prevalent in a wide range of natural and engineered systems, and may occur due to thermal expansion, changes in pH, differential swelling, and differential growth. Here, we investigate how the presence of both an evolving natural curvature and an external pressure modifies the stability of a complete spherical shell. We show that due to a mechanical analogy between pressure and curvature, positive natural curvatures can severely destabilize a thin shell, while negative natural curvatures can strengthen the shell against buckling, providing the possibility to design shells that buckle at or above the theoretical limit for pressure alone, i.e. a knock-up factor. These results extend directly from the classical analysis of the stability of shells under pressure, and highlight the important role that non-mechanical stimuli can have on modifying the the membrane state of stress in a thin shell.