Within the framework of a variational mixed formation and higher-order shear deformation theory (HSDT), a numerical approach is developed in this research to investigate the buckling and post buckling behaviors of variously-shaped plates made of functionally graded graphene platelet-reinforced composites (FG-GPLRCs) taking the effect of porosity into account. By the proposed approach, which can be named as VDQ-FEM, thick and moderately thick plate-type structures with different shapes (e.g. rectangular, skew, or quadrilateral) with arbitrary-shaped cutout (e.g. circular or rectangular) can be studied. Various types for porosity distribution scheme and GPL dispersion pattern including uniform and different functionally graded patterns are considered along the thickness of plate. In the computation of material properties, the closed-cell Gaussian Random field scheme and Halpin–Tsai micromechanical model are utilized. One of the key novelties of proposed approach is developing an efficient way according to the mixed formulation to accommodate the continuity of first-order derivatives on the common boundaries of elements for the used HSDT model. Several numerical examples are given to analyze the influences of porosity coefficient/distribution pattern, GPL weight fraction/dispersion pattern, cutout and boundary conditions on the buckling and postbuckling characteristics of FG-GPLR porous composite plates.

中文翻译：

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具有不同形状和边界条件的 FG-GPL 增强多孔纳米复合材料板的屈曲和后屈曲

在变分混合形成和高阶剪切变形理论（HSDT）的框架内，本研究开发了一种数值方法来研究由功能梯度石墨烯片状增强复合材料制成的各种形状板的屈曲和后屈曲行为。 FG-GPLRCs）考虑了孔隙率的影响。通过所提出的方法，可以命名为VDQ-FEM，可以研究具有任意形状切口（例如圆形或矩形）的不同形状（例如矩形、斜向或四边形）的厚板型结构和中等厚板型结构。沿着板的厚度考虑了各种类型的孔隙率分布方案和 GPL 分散模式，包括均匀和不同的功能梯度模式。在计算材料特性时，使用闭孔高斯随机场方案和 Halpin-Tsai 微机械模型。所提出方法的一个关键创新是根据混合公式开发一种有效的方法，以适应所用 HSDT 模型元素公共边界上的一阶导数的连续性。给出了几个数值例子，分析了孔隙率系数/分布模式、GPL重量分数/分散模式、切口和边界条件对FG-GPLR多孔复合板屈曲和后屈曲特性的影响。所提出方法的一个关键创新是根据混合公式开发一种有效的方法，以适应所用 HSDT 模型元素公共边界上的一阶导数的连续性。给出了几个数值例子，分析了孔隙率系数/分布模式、GPL重量分数/分散模式、切口和边界条件对FG-GPLR多孔复合板屈曲和后屈曲特性的影响。所提出方法的一个关键创新是根据混合公式开发一种有效的方法，以适应所用 HSDT 模型元素公共边界上的一阶导数的连续性。给出了几个数值例子，分析了孔隙率系数/分布模式、GPL重量分数/分散模式、切口和边界条件对FG-GPLR多孔复合板屈曲和后屈曲特性的影响。