Nonlinear in-plane buckling of fixed FGP-GPLRC arches subjected to a half-span distributed radial load

In this work, nonlinear in-plane buckling analysis of fixed functionally graded porous graphene nanoplatelet reinforced composite (FGP-GPLRC) shallow arches under a half-span distributed radial load is presented. Material properties of the arch with different porosity distribution modes are determined via a modified Halpin-Tsai micromechanical model. Neutral plane-based nonlinear governing equations of motion are established based on the principle of virtual work from which analytical solutions for the critical buckling load are derived and the complete equilibrium path is traced. Possible buckling modes of fixed FGP-GPLRC arches are determined by employing a perturbation technique. Key parameters controlling the buckling configuration switching are also proposed. FE analysis is then carried out to verify the accuracy of the presented solutions. Effects of porosity distributions, GPL weight fraction, and porosity coefficient on the buckling behaviors are comprehensively examined. It was found that under the action of a half-span distributed radial load, the fixed FGP-GPLRC shallow arches buckle in a limit point configuration only, and the equilibrium path especially the per-buckling branch is significantly affected by porosity coefficient.