Non-polynomial framework for stress and strain response of the FG-GPLRC disk using three-dimensional refined higher-order theory

This article presents a non-polynomial framework for bending responses of functionally graded-graphene nanoplatelets composite reinforced (FG-GPLRC) disk based upon three-dimensional refined higher-order shear deformation theory (3D-RHOSDT) for various sets of boundary conditions. By employing Hamilton's principle, the structure's governing equations are derived and solved with the aid of the differential quadrature method (DQM). The rule of the mixture and modified Halpin-Tsai model are engaged to provide the effective material constant of the composite layers. Afterward, a parametric study is done to present the effects of weight fraction of GPLs, three kinds of FG patterns, shape mode, three kinds of boundary conditions, and different patterns of applied load on bending characteristics of the FG-GPLRC disk. The results show that in the outer and inner layers of the GPLRC disk, the structure with GPL-X and GPL-O patterns has the highest and lowest value of the shear stress, while in the middle layer, the mentioned relation between GPL patterns and shear stress changes to reverse. Another consequence is that the GPLRC disk has the best bending and static behavior against the sinusoidal pattern of applied load, and the structure shows weaker behavior against the uniform pattern. It is also observed that as the radius ratio increases, the buckled nodes are concentrated along the circumferential direction, and the mentioned issue is more considerable at the higher mode numbers.