功能梯度板弯曲和自由振动分析的简单精化板理论

论文提出了一种可用于分析功能梯度板弯曲和自由振动行为的简单精化板理论.该理论分析功能梯度板的弯曲时只需三个未知量，而分析功能梯度板的自由振动时只需一个未知量.与包含三个未知量的经典板理论相比，论文提出的简单精化板理论考虑了横向剪切效应，提高了计算准确度.与一阶剪切变形板理论不同，该简单精化板理论引入了多项式型剪切应变函数，满足板上下表面剪切应力为零的边界条件，因此不需要剪切修正.通过与已有文献的比较，验证了该简单精化板理论的准确性和便捷性，并基于该简单精化板理论研究了功能梯度板的弯曲和自由振动力学行为.

SIMPLE REFINED PLATE THEORY FOR FUNCTIONALLY GRADED PLATE BENDING AND FREE VIBRATION ANALYSIS

In this paper, a simple refined plate theory that can be used to analyze the bending and free vibration behavior of functionally graded plates is proposed. This theory requires only three unknowns for analyzing the bending of a functionally graded plate and only one for analyzing the free vibration of a functionally graded plate. Compared with the classical plate theory which contains three unknown quantities, the simple refined plate theory proposed in this paper takes into account the transversely shear effect and improves the accuracy of the calculation. Unlike the first-order shear deformation plate theory, this simple refined plate theory introduces a polynomial-type shear strain function that satisfies the boundary condition of zero shear stress on the upper and lower surfaces of the plate, so no shear correction is required. The accuracy and convenience of this simple refined plate theory were verified by comparing with existing literature, and the bending and free vibration mechanical behaviors of functionally graded plates were investigated based on this simple refined plate theory.