Analysis of nano‐reinforced layered plates via classical and refined two‐dimensional theories

Abstract

Purpose

The purpose of this paper is to consider the static analysis of nanocomposite plates. Nanocomposites consist of a small amount of nanoscale reinforcements which can have an observable effect on the macroscale properties of the composites.

Design/methodology/approach

In the present study the reinforcements considered are non‐spherical, high aspect ratio fillers, in particular nanometer‐thin platelets (clays) and nanometer‐diameter cylinders (carbon nanotubes, CNTs). These plates are considered simply supported with a bi‐sinusoidal pressure applied at the top. These conditions allow the solving of the governing equations in a closed form. Four cases are investigated: a single layered plate with CNT reinforcements in elastomeric or thermoplastic polymers, a single layered plate with CNT reinforcements in a polymeric matrix embedding carbon fibers, a sandwich plate with external skins in aluminium alloy and an internal core in silicon foam filled with CNTs and a single layered plate with clay reinforcements in a polymeric matrix. A short review of the most important results in the literature is given to determine the elastic properties of the suggested nanocomposites which will be used in the proposed static analysis. The static response of the plates is obtained by using classical two‐dimensional models such as classical lamination theory (CLT) and first order shear deformation theory (FSDT), and an advanced mixed model based on the Carrera Unified Formulation (CUF) which makes use of a layer‐wise description for both displacement and transverse stress components.

Findings

The paper has two aims: to demonstrate that the use of classical theories, originally developed for traditional plates, is inappropriate to investigate the static response of nanocomposite plates and to quantify the beneficial effect of the nanoreinforcements in terms of static response (displacements and stresses).

Originality/value

In the literature these effects are usually given only in terms of elastic properties such as Young moduli, shear moduli and Poisson ratios, and not in terms of displacements and stresses.

Citation

Brischetto, S. and Carrera, E. (2012), "Analysis of nano‐reinforced layered plates via classical and refined two‐dimensional theories", Multidiscipline Modeling in Materials and Structures, Vol. 8 No. 1, pp. 4-31. https://doi.org/10.1108/15736101211235958