Surface stress size dependency in nonlinear free oscillations of FGM quasi-3D nanoplates having arbitrary shapes with variable thickness using IGA

Abstract

The present study aims to propose a computational package for analyzing the geometrically nonlinear large amplitude vibrations of nanoplates having arbitrary shapes with variable thickness in the presence of surface stress type of size effect. Accordingly, isogeometric analysis (IGA) is employed to achieve exact geometrical description as well as higher-order efficient smoothness with no meshing difficulty. The associated size dependent plate model is constructed for the first time via implementation of the Gurtin-Murdoch surface elasticity to a quasi-3D plate model having the capability to take the thickness stretching into consideration with only four variables. The nanoplates are assumed made of functionally graded materials (FGMs) through the variable thickness, the displacement along which is calculated independently via a trigonometric normal shape function. The variation of plate thickness obeys three different schemes including linear, concave, and convex ones. It is highlighted that by changing the pattern of the thickness variation from convex type to linear one, and then from linear type to concave one, in spite of the higher classical flexural stiffness, the surface elastic-based flexural stiffness of FGM composite nanoplates gets lower, which results in a lower nonlinear frequency corresponding to a very thin nanoplates. Moreover, it is portrayed that by increasing the value of material gradient index, the role of stiffer character of the surface stress in the nonlinear free oscillation behavior of FGM composite nanoplates is pronounced. This anticipation is the same for the both initial and deeper parts of the nonlinear frequency-deflection response.