Collapse and folding of pressurized rings in two dimensions

TL;DR

This paper analyzes how pressurized rings in two dimensions buckle and fold, especially focusing on the effects of variable bending stiffness and symmetry on stability and collapse patterns.

Contribution

It introduces a stability analysis for rings with non-uniform bending moduli and explores how symmetry influences buckling and folding behaviors.

Findings

Segments with weakened bending modulus lower the critical buckling pressure.

4-fold symmetric rings are more prone to collapse.

Initial post-buckling patterns include various folding configurations.

Abstract

Hydrostatically pressurized circular rings confined to two dimensions (or cylinders constrained to have only z-independent deformations) undergo Euler type buckling when the outside pressure exceeds a critical value. We perform a stability analysis of rings with arc-length dependent bending moduli and determine how weakened bending modulus segments affect the buckling critical pressure. Rings with a 4-fold symmetric modulation are particularly susceptible to collapse. In addition we study the initial post-buckling stages of the pressurized rings to determine possible ring folding patterns.