This work investigates the application of three-dimensional nonlocal elasticity theory to elastic static analysis of nanoplates. Unlike all previous papers that considered two-dimensional Laplacian operator to stress components, this work uses the general three-dimensional nonlocal operator with thickness direction operator. The displacement field of nanoplate is assumed a function of three-dimensional coordinate x, y, z. The principle of virtual work is used to derive the governing equations. A solution procedure is developed for simply supported nanoplate. The solution along the thickness direction is derived using the characteristic equation and application of boundary conditions including free transverse shear stress and applied normal stress. The eigenvalue–eigenvector methodology is used to extract general solution along the transverse direction. The stress and deformation distribution along the transverse direction is presented with changes of significant parameters such as nonlocal parameter and aspect ratio.

这项工作研究了三维非局部弹性理论在纳米板弹性静态分析中的应用。与以前的所有论文都考虑使用二维Laplacian算子来应力分量不同，本论文使用带有厚度方向算子的通用3维非局部算子。假设纳米板的位移场是三维坐标x，y，z的函数。虚拟工作原理用于导出控制方程。针对简单支撑的纳米板开发了一种解决方法。使用特征方程和边界条件的应用（包括自由横向剪切应力和外加法向应力）可以得出沿厚度方向的解。特征值-特征向量方法用于提取横向的一般解。沿横向方向的应力和变形分布随非局部参数和长宽比等重要参数的变化而变化。