Abstract A meshfree radial point interpolation method (RPIM) based on a higher-order shear deformation theory (HSDT) is here developed to investigate the free vibration and buckling behavior of multilayer functionally graded graphene platelets reinforced composite (FG-GPLRC) perforated plates under an in-plane edge loading. The non-uniform initial stresses in the multilayer FG-GPLRC perforated plates are evaluated accurately by solving the equilibrium equations derived from the same approach. The mixed collocation-Lagrange multiplayer technique is employed to enforce the various boundary conditions. The multilayer FG-GPLRC plates are built up as perfectly-bonded composite layers reinforced with a uniform distribution of graphene platelets (GPLs), randomly oriented. Perforated plates with three different cut-out shapes are analyzed. Several numerical examples are provided to demonstrate the high performance, the fast convergence rate and the high accuracy of the proposed method. Then, we study the influence of different GPLs distribution patterns, GPLs weight fraction, shape and size of cut-outs on the free vibration and buckling behavior of the multilayer FG-GPLRC perforated plates under an in-plane edge loading.

中文翻译：

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面内载荷作用下FG-GPLRC穿孔板振动屈曲分析的无网格径向点插值法

摘要 本文开发了一种基于高阶剪切变形理论 (HSDT) 的无网格径向点插值法 (RPIM) 来研究多层功能梯度石墨烯片增强复合材料 (FG-GPLRC) 穿孔板在不同条件下的自由振动和屈曲行为。面内边缘加载。多层 FG-GPLRC 穿孔板中的非均匀初始应力通过求解从相同方法导出的平衡方程来准确评估。采用混合搭配-拉格朗日多人游戏技术来强制执行各种边界条件。多层 FG-GPLRC 板构建为完美结合的复合层，由均匀分布的石墨烯薄片 (GPL) 增强，随机取向。分析了具有三种不同切割形状的穿孔板。提供了几个数值例子来证明所提出的方法的高性能、快速收敛速度和高精度。然后，我们研究了不同 GPLs 分布模式、GPLs 重量分数、切口形状和尺寸对平面内边缘载荷下多层 FG-GPLRC 穿孔板的自由振动和屈曲行为的影响。