This paper presents a higher-order shear and normal deformation theory for the static problem of functionally graded porous thick rectangular plates. The effect of thickness stretching in the functionally graded porous plates is taken into consideration. The functionally graded porous material properties vary through the plate thickness with a specific function. The governing equations are obtained via the virtual displacement principle. The static problem is solved for a simply supported plate under a sinusoidal load. The exact expressions for displacements and stresses are obtained. The influences of the functionally graded and porosity factors on the displacements and stresses of porous plates are discussed. Some validation examples are presented to show the accuracy of the present quasi-3D theory in predicting the bending response of porous plates. The effectiveness of the present model is evaluated by numerical results that include displacements and stresses of functionally graded porous plates. The field variables of functionally graded plates are very sensitive to the variation of the porosity factor.

中文翻译：

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功能梯度多孔板的准 3D 细化理论：位移和应力

本文针对功能梯度多孔厚矩形板的静力学问题提出了高阶剪切和法向变形理论。考虑了功能梯度多孔板中厚度拉伸的影响。功能梯度多孔材料特性随具有特定功能的板厚度而变化。控制方程是通过虚拟位移原理获得的。解决了正弦载荷下简支板的静力问题。获得位移和应力的精确表达式。讨论了功能梯度和孔隙度因子对多孔板位移和应力的影响。提供了一些验证示例，以显示当前准 3D 理论在预测多孔板弯曲响应方面的准确性。本模型的有效性通过数值结果进行评估，其中包括功能梯度多孔板的位移和应力。功能梯度板块的场变量对孔隙度因子的变化非常敏感。