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.

Elastic models coupling the cellulose nanofibril to the macroscopic film level

“…27 Each ply represents one specic orientation of the bres and the off-axis stiffness matrix can be calculated through coordinate transformation. CLT analogies are also used to describe the in-plane elasticity of non-layered materials, such as short-bre composites, 25 paper sheets, 21 liquid crystals 26 and nanocomposites.…”

Numerical simulation of the mechanical behavior of a carbon nanotube bundle

“…This includes the investigation of their properties as well as the consideration of this material for versatile applications, e.g., from medicine and electronics to applications for lightweight construction [2]. In particular, the outstanding mechanical properties of carbon nanotubes are desirable for many technical applications, e.g., in composites [3] and for nanoscale reinforcements [4]. The fabrication of fibers from carbon nanotubes is one specific example of utilizing the characteristics for technical lightweight applications [5].…”

Quasi-3D Stability and Vibration Analyses of Sandwich Piezoelectric Plates with an Embedded CNT-Reinforced Composite Core

“…Lin and Xiang 43 investigated the nonlinear free vibration of FG CNTRC beams using the FSDT and HSDT with p-Ritz method, in which the di®erences in natural frequencies and the nonlinear to linear frequency ratios between the FSDT and HSDT were examined. The above-mentioned equivalent singlelayered plate theories have also been applied to the free vibration analysis of FG plates by Zenkour 44 and Jha et al 45 Finally, Brischetto and Carrera 46,47 investigated the static behaviors of nanoreinforced layered plates and shells using the classical lamination theory (CST), FSDT and an advanced mixed model based on the Carrera uni¯ed formulation (CUF), [48][49][50] which is a technique being capable of handling a large variety of plate and shell models in a uni¯ed manner. Their results demonstrated the use of CSTs is inappropriate for obtaining the static response of nanocomposite structures.…”