The main contribution of this study is to propose an efficient and straightforward numerical model for exploring size-dependent geometrically nonlinear static and dynamic characteristics of functionally graded microplates reinforced by graphene nanofillers. To accomplish this purpose, modified couple stress theory including only one material length scale parameter is utilized to capture the size-dependent effect while the displacement field of small-scale structures is calculated by using four-variable refined plate theory and von-Kármán assumptions within the framework of isogeometric analysis. In this study, four dispersion patterns of graphene-based nanofillers along the thickness direction of microplate models are investigated under various static or dynamic loads. Solutions of nonlinear governing equation of motion can be obtained based on the Newton–Raphson iterative procedure and Newmark's time integration scheme. The Rayleigh damping is included, for the first time, to explore the influence of damping on the oscillations of functionally graded microplates reinforced by graphene nanofillers under three dynamic loads including step, triangular and half-sine pulses. Herein, several numerical examples are conducted to investigate the influences of a wide range of significant parameters on the geometrically nonlinear behaviors of functionally graded microplates with graphene nanofillers reinforcement. The significant outcomes of the present study can be referred to as benchmark results as well as provide valuable guides for designing small-scale structures with excellent features in the future.

本研究的主要贡献是提出了一种有效且直接的数值模型，用于探索石墨烯纳米填料增强的功能梯度微板的尺寸相关几何非线性静态和动态特性. 为了实现这一目的，使用仅包含一个材料长度尺度参数的修正耦合应力理论来捕捉尺寸相关效应，而小尺度结构的位移场通过使用四变量精炼板理论和 von-Kármán 假设计算等几何分析的框架。在这项研究中，在各种静态或动态载荷下，研究了石墨烯基纳米填料沿微板模型厚度方向的四种分散模式。非线性运动控制方程的解可以基于Newton-Raphson迭代过程和Newmark的时间积分方案获得。瑞利阻尼第一次被包括在内，探索阻尼对石墨烯纳米填料增强的功能梯度微板在三种动态载荷（包括步进、三角形和半正弦脉冲）下振荡的影响。在此，通过几个数值例子来研究各种重要参数对几何形状的影响。石墨烯纳米填料增强的功能梯度微板的非线性行为。本研究的重要成果可作为基准结果，为未来设计具有优良特性的小型结构提供有价值的指导。