Bending and vibration analysis of functionally graded trapezoidal nanocomposite plates reinforced with graphene nanoplatelets (GPLs)

This paper investigates the bending and vibration behaviors of a novel class of functionally graded trapezoidal plates reinforced with graphene nanoplatelets (GPLs) by employing the finite element method. Modified Halpin-Tsai model and the rule of mixture are used to determine the effective material properties including Young's modulus, mass density and Poisson's ratio of the nanocomposites. A comprehensive parametric study is conducted to examine the effects of the distribution, concentration and dimension of GPL and the plate geometry on the static and dynamic behaviors of GPL reinforced functionally graded trapezoidal plates. The results demonstrate that adding a small amount of GPLs as reinforcing nanofillers can significantly enhance the stiffness of the plate and the most effective reinforcing effect can be achieved by distributing more GPLs with a larger surface area near the top and bottom surfaces of the plate. Also, the bending and vibration behaviors of trapezoidal plates with such a distribution pattern are more sensitive to the GPL weight fraction and plate geometry compared to the other distribution patterns. Moreover, it is found that the static and dynamic deflections of the plate tend to be lower as either of the two base angles becomes smaller