This article presents an effective and simple approach based on the four-variable refined plate theory (RPT) and isogeometric analysis (IGA) for bending and free vibration analyses of multilayer functionally graded graphene platelet-reinforced composite (FG GPLRC) nanoplates. The Eringen’s nonlocal elasticity theory is employed to take account of the size-dependent effect of nanoplates. Different distribution patterns of graphene platelets (GPLs) including uniform and non-uniform in the polymer matrix are considered. Governing equations of FG GPLRC nanoplates are then deduced from the principle of virtual work and resolved utilizing NURBS basis functions in the IGA framework. Accordingly, the requirement of third-order derivatives of approximate variables in the nonlocal formulation is fulfilled. Obtained outcomes indicate that the GPLs reinforcement can dramatically improve the stiffness of nanoplates, and GPLs rich at the bottom and the top of the nanoplate can be considered as the best reinforcing effect. Several new results are also considered as benchmark solutions for further studies on the FG GPLRC nanoplates.

本文提出了一种基于四变量精制板理论（RPT）和等几何分析（IGA）的有效且简单的方法，用于多层功能梯度石墨烯血小板增强复合材料（FG GPLRC）纳米板的弯曲和自由振动分析。Eringen的非局部弹性理论被用来考虑纳米板的尺寸依赖性效应。考虑了石墨烯血小板（GPL）在聚合物基质中的均匀分布和不均匀分布的不同分布方式。然后从虚拟工作原理推导FG GPLRC纳米板的控制方程，并利用IGA框架中的NURBS基本函数进行求解。因此，满足了非局部公式中近似变量的三阶导数的要求。获得的结果表明，GPL增强可以显着提高纳米板的刚度，并且在纳米板的底部和顶部富含GPL可以被认为是最佳的增强效果。一些新的结果也被认为是对FG GPLRC纳米板进行进一步研究的基准解决方案。