In this paper, the Variational Iteration Method (VIM) or Extended Kantorovich Method (EKM) is formulated for the first time for flexible porous functionally graded (PFGM) plates with different boundary conditions and geometric nonlinearity according to the theory of Theodore von Karman. Its accuracy and efficiency are demonstrated. The plate is subjected to a uniform transversal load and temperature field. The displacement field of the plate is approximated based on the classical plate theory (CTP) or Kirchhoff's plate theory. The governing equations are derived using Hamilton's principle. Modified Coupled Stress Theory (MCST) is used to account for size-dependent effects. The material properties vary with thickness and are temperature dependent. Four porosity distribution patterns are considered in this study. Several examples are solved to demonstrate the proposed algorithm. The results obtained are compared with solutions obtained by the Bubnov-Galerkin Method (BGM) in higher approximations, the Finite Difference Method (FDM) of second order accuracy, as well as with results obtained by the Finite Element Method (FEM) of other authors. The results include an analysis of the effect of size dependent parameters, porosity type pattern, porosity index, functionally graded index, temperature field and different types of boundary conditions on the stress–strain state and bending deflection of plates.

中文翻译：

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温度场中尺寸相关的多孔功能梯度板的非线性变形

本文根据西奥多·冯·卡门的理论，首次针对不同边界条件和几何非线性的柔性多孔功能梯度（PFGM）板制定了变分迭代法（VIM）或扩展康托罗维奇法（EKM）。其准确性和效率得到了证明。板承受均匀的横向载荷和温度场。板的位移场是基于经典板理论（CTP）或基尔霍夫板理论来近似的。控制方程是利用哈密顿原理推导出来的。修正耦合应力理论 (MCST) 用于解释尺寸相关效应。材料特性随厚度变化并且与温度相关。本研究考虑了四种孔隙率分布模式。解决了几个例子来演示所提出的算法。将获得的结果与更高近似值的布布诺夫-伽辽金法 (BGM) 获得的解、二阶精度的有限差分法 (FDM) 以及其他作者的有限元法 (FEM) 获得的结果进行比较。结果包括分析尺寸相关参数、孔隙类型模式、孔隙指数、功能梯度指数、温度场和不同类型的边界条件对板的应力应变状态和弯曲变形的影响。