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

Roshanbakhsh M. Z., Tavakkoli S. M.

Archives of Mechanics

2024

Vol. 76, nr 1-2

93--141

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.