In this article, we present an analytical solution for an imperfect functionally graded plate based on higher order shear deformation theory with cubic variation of in-plane displacements according to thickness and linear/quadratic transverse displacement. The developed solution is used to analyze the static responses of a plate with a porous layer to mechanical loading. Two porosity types and their influences on material properties, displacement, and stress behaviors are considered. The network of pores is assumed to be empty or filled with low-pressure air, and the material properties are calculated using power-law distribution idealization in terms of the volume fractions of constituents. The computed results are presented to illustrate the accuracy of the proposed solutions based on comparisons to previously reported analytical and numerical solutions in the literature. We also analyzed the effects of different volume fractions and thicknesses of porous layers on the mechanical loading and mechanical behavior of the imperfect functionally graded plate.

中文翻译：

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基于线性/二次横向位移的高阶剪切变形理论的多孔中间层功能梯度板静力分析

在本文中，我们提出了基于高阶剪切变形理论的不完美功能梯度板的解析解，面内位移根据厚度和线性/二次横向位移发生三次变化。开发的解决方案用于分析具有多孔层的板对机械载荷的静态响应。考虑了两种孔隙率类型及其对材料特性、位移和应力行为的影响。假设孔隙网络是空的或充满低压空气，材料特性是根据成分的体积分数使用幂律分布理想化计算的。计算结果用于说明基于与文献中先前报告的解析和数值解决方案的比较所提出的解决方案的准确性。我们还分析了不同体积分数和多孔层厚度对不完美功能梯度板的机械载荷和机械性能的影响。