On size-dependent mechanics of nanoplates

Abstract

In this paper, a two-dimensional stress-driven nonlocal integral model is introduced for the bending and transverse vibration of rectangular nanoplates for the first time. An appropriate kernel function, which satisfies all essential properties, is proposed for two-dimensional problems in the Cartesian coordinate system. Using Leibniz integral rule and Hamilton's principle, the curvature-moment relations, classical and constitutive boundary conditions, as well as the equations of motion of rectangular small-scale plates are derived. Two differential quadrature techniques are utilised to implement both classical and non-classical boundary conditions and obtain an accurate numerical solution. The solution is used to simulate the bending and vibration of nanoplates. The Laplacian-based nonlocal strain gradient model of plates is also developed for the sake of comparison. It is found that the stress-driven integral model can better estimate the size-dependent mechanical characteristics of small-scale rectangular plates with various boundary conditions.