具有压电材料薄板弯曲控制的有限元法

Finite element method on bending control of thin plate with piezoelectric material

考虑一均匀各向同性薄板结构，在其上下表面离散分布着压电执行元件。在横向外载和电压共同作用下，分析板的弯曲变形，并通过变化作用于执行元件上的电压对板的变形进行控制。根据逆压电效应将电压转换成作用于板上的等效作用量，用Ｈａｍｉｌｔｏｎ原理导出压电结构板弯曲变形的有限元公式，并对环形板的情况进行了数值计算。

An uniform distribution, isotropic thin plate, on which both surface there are discrete distribution piezoelectric actuators, is considered. Under action both cross force and voltage altogether, bending of the plate is analyzed. And by means of variant voltage that is exerted on actuators, the bending of plate is controlled. According to the inverse piezoelectric effect, equivalent action of the actuators are obtained. By use to Hamilton's principle, the finite element formula of bending deformation of the piezoelectric structure is obtained. And the bending of annular plate with piezoelectric material under four boundary conditions are calculated.