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.

本文首次提出了二维应力驱动的非局部积分模型，用于矩形纳米板的弯曲和横向振动。针对笛卡尔坐标系中的二维问题，提出了一个满足所有基本特性的适当核函数。利用莱布尼兹积分法则和汉密​​尔顿原理，推导了曲率矩关系，经典本构和本构边界条件，以及矩形小尺寸板的运动方程。利用两种微分求积技术来实现经典和非经典边界条件，并获得精确的数值解。该解决方案用于模拟纳米板的弯曲和振动。为了比较，还开发了基于拉普拉斯算子的板的非局部应变梯度模型。发现应力驱动的积分模型可以更好地估计具有各种边界条件的小尺寸矩形板的尺寸相关的力学特性。