The purpose of this study is to present a quasi-three-dimensional (quasi-3D) shear deformation theory for static bending and free vibration analyses of porous sandwich functionally graded (FG) plates with graphene nanoplatelets (GPLs) reinforcement. In addition, we propose a novel sandwich plate model with various outstanding features in terms of structural performance. The quasi-3D theory-based isogeometric analysis (IGA) in conjunction with refined plate theory (RPT) is first exploited to capture adequately the thickness stretching effect for porous sandwich FG plate structures reinforced with GPLs. The Non-Uniform Rational B-Splines (NURBS)-based IGA is employed in order to describe exactly the geometry models as well as approximate the unknown field with higher-order derivatives and continuity requirements while the RPT model includes only four essential variables. The sandwich FG plates consist of a core layer containing internal pores reinforced by GPLs and two functionally graded materials (FGMs) skin layers. Effective mechanical properties can be evaluated by employing the Halpin-Tsai model along with the rule of mixture. Various combinations of two porosity distributions and three GPL dispersions in the core layer are thoroughly investigated. Several numerical investigations are conducted to examine the effects of several key parameters on the static bending and free vibration behaviors of sandwich FG plate structures.

本研究的目的是提出一种准三维 (quasi-3D) 剪切变形理论，用于对具有石墨烯纳米片 (GPL) 增强的多孔夹心功能梯度 (FG) 板进行静态弯曲和自由振动分析。此外，我们提出了一种在结构性能方面具有各种突出特点的新型夹层板模型。基于准 3D 理论的等几何分析 (IGA) 与精细板理论 (RPT) 相结合，首先被用来充分捕捉用 GPL 增强的多孔夹层 FG 板结构的厚度拉伸效应。采用基于非均匀有理 B 样条 (NURBS) 的 IGA 以精确描述几何模型以及用高阶导数和连续性要求逼近未知场，而 RPT 模型仅包含四个基本变量。夹心 FG 板由包含 GPL 增强的内部孔隙的核心层和两个功能梯度材料 (FGM) 表层组成。有效的机械性能可以通过采用 Halpin-Tsai 模型以及混合规则来评估。彻底研究了芯层中两种孔隙率分布和三种 GPL 分散体的各种组合。进行了多项数值研究，以检查几个关键参数对夹层 FG 板结构的静态弯曲和自由振动行为的影响。