Analytical approximations to large post-buckling deformation of elastic rings under uniform hydrostatic pressure

This paper presents analytical approximations to large post-buckling deformation of a circular, elastic, and inextensional ring under uniform hydrostatic pressure. By combining the Newton's method with the method of harmonic balance, we establish analytical approximations to large deformation of the ring. Unlike the classical method of harmonic balance, the linearization is performed prior to proceeding with harmonic balancing thus resulting in a set of linear algebraic equations instead of one of non-linear algebraic equations. We are hence able to establish analytical approximate solutions. These approximate solutions show excellent agreement with the exact solution, and are valid for small as well as large difference of the curvatures of the undeformed and the deformed ring.