Classical and refined shell models for the analysis of nano-reinforced structures

Abstract

The use of nanocomposites could be an interesting innovation in aeronautics and space structures such as multilayered plates and shells. The static analysis of layered shells embedding nanocomposites is here accomplished by means of classical and refined two-dimensional models. The shells analyzed are simply supported with a sinusoidal pressure applied at the top. These boundary and loading conditions allow the governing equations to be solved in a closed form. In nanocomposites a small amount of nanoscale reinforcements is embedded which have effects on the macroscale properties. The reinforcements considered are carbon nanotubes (CNTs) and clays, the former ones are nanometer-diameter cylinders, the second fillers are nanometer-thin platelets. Several types of nanocomposites are used in the static analysis of the shells proposed, their elastic properties have been obtained from a critical literature review. Classical two-dimensional models such as Classical Lamination Theory (CLT) and First order Shear Deformation Theory (FSDT), and a refined mixed model based on Carrera Unified Formulation (CUF) are used to investigate four shell configurations: a single layered cylindrical shell panel with CNT reinforcements in elastomeric or thermoplastic polymers, a single layered shell with CNT reinforcements in a polymeric matrix embedding carbon fibers, a sandwich shell with external skins in aluminium alloy and an internal core in silicon foam filled with CNTs and a single layered shell with clay reinforcements in a polymeric matrix. The aims of the paper are to demonstrate that the use of classical shell theories is inadequate to investigate the static response of nanocomposite shells, to quantify the beneficial effect of the nanoreinforcements in terms of displacements and stresses, to show that the curvature of shells does not give further effects with respect to the plate case.