A finite strain theory for incompressible rubber-like circular arches with an application

Abstract

A theory for incompressible rubber-like circular arches, undergoing finite strains and rotations, with an application to the stability of Mooney-Rivlin, doubly fixed, thin beams having initially small circular imperfections under uniformly distributed radial loads, is presented. The essence of considering transverse normal strain is emphasized for an incompressible rubber-like material. The effects of the thickness, initial curvature, and perturbation terms of the pseudo strain components on the buckling loads and central deflections are investigated. The thresholds of buckling are observed to depend on the values of the curvature of the initially imperfect beam for the chosen nonlinear material.