In this paper, for the first time, the bending and free vibration analysis of porous functionally graded sandwich plates with various porosity distributions is investigated using an efficient layerwise model. The present model, proposed recently by the authors, supposes a first-order displacement field for the two face sheets and a higher-order displacement field for the core, thereby ensuring the displacement continuity at the layer's interface. Unlike the conventional layerwise models, the number of degrees of freedom is fixed and does not increase when increasing the number of layers. This is a very important feature compared to the conventional layerwise models and facilitates significantly the engineering analysis. Three different types of porosity distribution including even, logarithmic-uneven, and linear-uneven porosities are considered. The material properties of the FGM sandwich porous plate are graded continuously through the thickness direction according to a power-law function. The numerical analysis is carried out by using an efficient C⁰ continuous eight-node quadrilateral isoparametric element developed for this purpose. The governing equations are derived according to Hamilton’s principle and solved by employing the finite element method. The robustness and accuracy of the proposed formulation are ascertained by comparing its results with those available by other researchers in the existing literature. Further, a comprehensive parametric study is examined in detail to show the effects of material distribution, aspect ratios, porosity coefficient, side-to-thickness ratio, porosity distribution, core-to-face thickness ratio, boundary conditions, volume fraction index, modes shapes on the bending and free vibration behaviors of symmetric and non-symmetric FGM porous sandwich plate. The numerical results show that these parameters play significant roles in the bending and free vibration behaviors of the FGM sandwich porous plates. Many new results are also reported, which will serve as a benchmark for future analysis of FGM sandwich plates with porosity.

在本文中，首次使用有效的分层模型研究了具有不同孔隙率分布的多孔功能梯度夹层板的弯曲和自由振动分析。作者最近提出的当前模型假设两个面板的一阶位移场和核心的高阶位移场，从而确保层界面处的位移连续性。与传统的分层模型不同，自由度的数量是固定的，不会随着层数的增加而增加。与传统的分层模型相比，这是一个非常重要的特征，并且极大地促进了工程分析。三种不同类型的孔隙度分布，包括均匀、对数-不均匀、并考虑线性不均匀孔隙率。FGM 夹层多孔板的材料特性根据幂律函数在厚度方向上连续渐变。数值分析是通过使用一个有效的⁰ _为此目的开发的连续八节点四边形等参单元。控制方程是根据汉密尔顿原理推导出来的，并采用有限元法求解。通过将其结果与现有文献中其他研究人员可获得的结果进行比较，确定了所提出公式的稳健性和准确性。此外，详细检查了全面的参数研究，以显示材料分布、纵横比、孔隙率系数、侧厚比、孔隙率分布、岩心与面厚比、边界条件、体积分数指数、模式的影响形状对对称和非对称 FGM 多孔夹层板的弯曲和自由振动行为的影响。数值结果表明，这些参数在 FGM 夹层多孔板的弯曲和自由振动行为中起重要作用。还报告了许多新结果，这将作为未来分析具有孔隙度的 FGM 夹层板的基准。