On the free vibration and bending analysis of functionally graded nanocomposite spherical shells reinforced with graphene nanoplatelets: Three-dimensional elasticity solutions

This paper presents analytical investigations on the free vibration and static bending of functionally graded graphene-reinforced nanocomposite (FG-GPLRC) spherical shells. The GPL nanofillers are dispersed into polymer matrix uniformly and un-uniformly in the thickness direction with a piece-wise type, and UD, FG-O, FG-X, FG-V and FG-A types of GPL distribution patterns are taken into account. The effective material properties of graphenereinforced nanocomposites are estimated by using the modified Halpin-Tsai multi-scaled model and the rule of mixtures. Governing differential equations for free vibration and bending of the FG-GPLRC spherical shells are derived based on the three-dimensional elasticity theory with the aid of the state space method, and the layer wise model is employed to obtain the analytical solutions. The validity of the present method is first examined, followed by the illustrative parametric studies to further scrutinize the free vibration and static bending behaviors of the FG-GPLRC spherical shells with the various reinforcement schemes, including the distribution pattern, the weight fraction, and geometric parameter of GPLs in details.