An edge-based smoothed finite element method (ES-FEM) combined with the mixed interpolation of tensorial components technique (MITC) for triangular elements, named as ES-MITC3, was recently proposed to enhance the accuracy of the original MITC3 for analysis of plates and shells. In this study, the ES-MITC3 is extended to the static and vibration analysis of functionally graded (FG) porous plates reinforced by graphene platelets (GPLs). In the ES-MITC3, the stiffness matrices are obtained by using the strain smoothing technique over the smoothing domains created by two adjacent triangular elements sharing an edge. The effective material properties are variable through the thickness of plates including Young’s modulus estimated via the Halpin–Tsai model and Poisson’s ratio and the mass density according to the rule of mixture. Three types of porosity distributions and GPL dispersion pattern into the metal matrix are examined. Numerical examples are given to demonstrate the performance of the present approach in comparison with other existing methods. Furthermore, the effect of several parameters such as GPL weight fraction, porosity coefficient, porosity distribution, and GPL dispersion patterns on the static and free vibration responses of FG porous plates is discussed in detail.

中文翻译：

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基于高阶剪切变形理论的ES-MITC3有限元方法用于GPL加固FG多孔板的静，自由振动分析

最近提出了一种基于边缘的平滑有限元方法（ES-FEM）与张量分量混合混合插值技术（MITC）结合使用三角形元素的方法，称为ES-MITC3，以提高原始MITC3用于板分析的准确性和贝壳。在这项研究中，ES-MITC3扩展到了功能梯度（FG）石墨烯血小板（GPL）增强的多孔板的静态和振动分析。在ES-MITC3中，刚度矩阵是通过使用应变平滑技术在由共享一个边的两个相邻三角形元素创建的平滑域上获得的。有效的材料特性会随板的厚度而变化，包括通过Halpin-Tsai模型估算的杨氏模量和泊松比以及根据混合法则的质量密度。检查了三种类型的孔隙率分布和GPL在金属基体中的分散方式。数值示例说明了本方法与其他现有方法相比的性能。此外，详细讨论了GPL重量分数，孔隙率系数，孔隙率分布和GPL分散模式等参数对FG多孔板的静态和自由振动响应的影响。