Analytical Prediction for Nonlinear Buckling of Elastically Supported FG-GPLRC Arches under a Central Point Load.

Zhicheng Yang,Jiyang Fu,Siu-Kai Lai,Jiangen Lv,Airong Liu,Jie Yang

doi:10.3390/ma14082026

Abstract

In this paper, we present an analytical prediction for nonlinear buckling of elastically supported functionally graded graphene platelet reinforced composite (FG-GPLRC) arches with asymmetrically distributed graphene platelets (GPLs). The effective material properties of the FG-GPLRC arch are formulated by the modified Halpin–Tsai micromechanical model. By using the principle of virtual work, analytical solutions are derived for the limit point buckling and bifurcation buckling of the FG-GPLRC arch subjected to a central point load (CPL). Subsequently, the buckling mode switching phenomenon of the FG-GPLRC arch is presented and discussed. We found that the buckling modes of the FG-GPLRC arch are governed by the GPL distribution pattern, rotational restraint stiffness, and arch geometry. In addition, the number of limit points in the nonlinear equilibrium path of the FG-GPLRC arch under a CPL can be determined according to the bounds of successive inflexion points. The effects of GPL distribution patterns, weight fractions, and geometric configurations on the nonlinear buckling behavior of elastically supported FG-GPLRC arches are also comprehensively discussed.

Highlights

Graded material (FGM) structures, characterized by a continuous change in the material compositions along one or multiple directions, have attracted extensive attention from both research and industrial communities owing to their excellent stiffness and strength-to-weight properties as compared with homogeneous composite structures [1,2,3]
Nguyen et al [8] studied the mechanical buckling of stiffened Functionally graded material (FGM) plates by using the finite element method
The solutions of the limit point load and nonlinear equilibrium path of FG-GPLRC arches under a central point load (CPL) can be determined by solving Equations (21) and (27)

Summary

Introduction

Graded material (FGM) structures, characterized by a continuous change in the material compositions along one or multiple directions, have attracted extensive attention from both research and industrial communities owing to their excellent stiffness and strength-to-weight properties as compared with homogeneous composite structures [1,2,3]. By introducing GPLs to FGM materials, novel FG GPLs-reinforced composite (FG-GPLRC) structures have been developed recently and have since attracted extensive attention in both research and engineering communities [24]. Yang and his co-workers conducted pioneering studies on the mechanical behaviors of FG-GPLRC structures, such as beams [25,26,27,28], shells [29,30], and plates [31,32]. The presence of analytical solutions is useful to engineers and researchers for benchmarking the convergence and validity of numerical methods for arch buckling analysis

Configuration ofof anan elastically supported functionally graded

Limit Point Buckling

Bifurcation Buckling

Numerical Studies and Discussion

As metric parameters the buckling are presented in Figure

Conclusions