Abstract This work proposes a novel quasi three-dimensional (3D) approach for the bending analysis of moderately thick plates with a functionally graded material (FGM), in presence of porosities due to some incorrect manufacturing processes. Such porosities can appear within the plate in two forms, namely, even and uneven distributions. The modeled system has a polymer matrix where both shear and transverse factors coexist. The bending equations of the problem are obtained from the Hamiltonian principle. In order to apply the quantum effects for the nanosystem, the well-known nonlocal theory of Eringen is here assumed, while checking for its numerical accuracy. A physically-consistent analysis of the nanostructures would investigate possible surrounding effects. Thus, the thermal and humidity influence is accounted for the 3D problem, whose governing equations are solved through a semi-analytical polynomial method (SAPM), as recently proposed in literature for different applications. The proposed method is based on a simple procedure with very accurate numerical outcomes, whose performance is checked against the available literature. After computing the deflection relations, a systematic study is performed for the bending response of nanoporous FGMs in a hygro-thermal surrounding environment, with promising results for practical applications.

中文翻译：

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湿热环境下中等厚度多孔功能梯度板的非局部弹性分析

摘要 这项工作提出了一种新的准三维 (3D) 方法，用于对具有功能梯度材料 (FGM) 的中等厚度板进行弯曲分析，由于某些不正确的制造工艺而存在孔隙。这种孔隙可以以两种形式出现在板内，即均匀分布和不均匀分布。建模系统具有聚合物基体，其中剪切和横向因素共存。问题的弯曲方程是从哈密顿原理得到的。为了将量子效应应用于纳米系统，这里假设了著名的 Eringen 非局域理论，同时检查其数值精度。纳米结构的物理一致性分析将调查可能的周围影响。因此，热和湿度的影响被解释为 3D 问题，其控制方程通过半解析多项式方法 (SAPM) 求解，正如最近在文献中针对不同应用提出的那样。所提出的方法基于具有非常准确的数值结果的简单程序，其性能根据可用文献进行检查。在计算偏转关系后，对湿热周围环境中纳米多孔 FGM 的弯曲响应进行了系统研究，在实际应用中取得了有希望的结果。