A theoretical study on nonlinear in-plane buckling of shallow angle-ply laminated arches with elastic supports

Abstract

This paper presents, for the first time, an analytical study on the nonlinear in-plane buckling of angle-ply laminated shallow arches with elastic supports under a uniform radial loading. To decouple internal forces and facilitate theoretical derivations, the nonlinear equilibrium path and buckling equation are established based on neutral plane formulation by using a virtual work method, from which the closed-form solutions for limit point buckling and bifurcation buckling are determined. The buckling mode of the laminated arch is characterized by introducing the modified slenderness ratio. The present analysis is verified through direct comparisons with finite element results. The effects of radial and circumferential stiffnesses of the elastic supports on the buckling behaviors are discussed in detail. It is found that the laminated arch may buckle in either a limit point mode or a bifurcation mode and its buckling behavior is highly sensitive to the support stiffness. The effects of ply-angle on the critical buckling load are also researched. It is found that the buckling loads of laminated arches decrease with an increase of flange and web ply-angles, and the influence of flange ply-angle on buckling load is more pronounced than that of web ply-angle.