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.

本研究旨在提出一种计算包，用于在存在表面应力类型的尺寸效应的情况下分析具有任意形状和可变厚度的纳米板的几何非线性大振幅振动。因此，采用等几何分析 (IGA) 来实现精确的几何描述以及高阶有效平滑度，而没有网格划分困难。通过将 Gurtin-Murdoch 表面弹性实施到准 3D 板模型中，首次构建了相关的尺寸相关板模型，该模型能够仅用四个变量来考虑厚度拉伸。假设纳米板由不同厚度的功能梯度材料 (FGM) 制成，通过三角法向形状函数独立计算的位移。板厚的变化服从线性、凹面和凸面三种不同的方案。强调的是，通过将厚度变化模式从凸型变为线性，然后从线性变为凹型，尽管经典弯曲刚度较高，但 FGM 复合纳米板的表面弹性弯曲刚度降低，这导致对应于非常薄的纳米片的较低非线性频率。此外，它描绘了通过增加材料梯度指数的值，表面应力的刚性特性在 FGM 复合纳米板的非线性自由振荡行为中的作用是显着的。