Multiple equilibria of pinned FGP-GPLRC circular arches under a half-span distributed radial load

Abstract

This article presents a theoretical analysis on the multiple equilibria of pinned functionally graded porous graphene platelet reinforced composite (FGP-GPLRC) circular arches subjected to a half-span distributed radial load. The effective material properties of the arch with different porosity distribution modes are approximated via a modified Halpin–Tsai micromechanical model. The decoupled neutral-plane-based governing equations are then built in the framework of the principle of minimum potential energy, from which analytical solutions for the radial displacement at an arbitrary point on the arch axis are derived. Utilizing a perturbation method, the possible buckling modes are discussed. The complete buckling evolution process of bending moment and vertical displacement are followed, meanwhile the critical geometrical parameters that control buckling behaviors switching are identified. To validate the presented analytical solutions, Finite element (FE) analysis is carried out. An in-depth parameter analysis is performed subsequently to evaluate the fluences of porosity distributions, GPL weight fraction, and porosity coefficient on the multiple equilibria path of arches. It was found that the pinned FGP-GPLRC arches could buckle only in a limit point mode under a half-span distributed radial load. When λ ≥ 8.36 , the multiple equilibria phenomenon occurs and the external force corresponding to inflexion point vanishes.