A size-dependent functionally graded nanocomposite Mindlin plate model based on consistent generalized continuum theory

Abstract

This paper presents an effective consistent-continuum model to analyse the behaviour of functionally graded nanocomposite (FG-NC) Mindlin plates based on the consistent couple stress theory (CCST) and the non-classical finite element method. A novel unified form is presented based on the Halpin–Tsai model to capture the small-scale heterogeneity, which can simultaneously consider the grading effects of the matrix and reinforcement phases along with the dispersion distribution through the plate thickness. To meet the C¹ continuity requirements of the couple stress theory, a four-node rectangular element is adopted by using the Hermitian approach and in the way of a sub-parametric manner. The element has 20 degrees of freedom (DOF) at each node, which is reduced to 12 DOF in a bending mode without stretching deformation. FG-NC plates’ bending, free vibration, and buckling behaviour are investigated. Graphene oxide (GO), reduced graphene oxide (rGO), and silver-reduced graphene oxide (Ag-rGO) are considered for the dispersed phase. Size-dependent optimal values for the material and geometrical properties of the FG-NC plate model are presented, which minimize its mass with the frequency constraint. The effects of various parameters such as grading index, weight fraction, dispersion pattern, filler aspect/thickness ratio, and length scale parameter are examined, and benchmark examples are provided.