具有压电材料薄板稳定性的有限元法

Finite Element Method of Stability for Thin Plate of Piezoelectric Material

考虑一均匀各向同性薄板结构，在板面内受面力作用，且在板的上下表面离散分布着压电执行元件．设每块压电片具有相同的材料，且作用相同电压．不考虑压电元件对整体结构刚度的影响；只考虑执行元件对板的逆压电效应，而不考虑板弯曲对执行元件中电场强度的影响．根据压电材料的逆压电效应，利用三角形三节点单元，用变分原理导出压电结构板平面应力问题位移法的有限元表达式以及在大挠度小变形情况下的稳定性有限元特征方程．可利用子空间迭代法求出结构在电压和面内外力共同作用下的稳定性特征值．通过调节作用于执行元件上的电压，可使结构的稳定性得到有效的控制．

A homogeneous isotropic thin plate, on which the surface force acts and there are many actuators of discrete distribution, is considered. Suppose all piezoelectric lamellas are made of the same material, thickness and have the same voltage acting on all actuators. The effect of the piezoelectric material on the stiffness of the total structure is not considered; only the inverse piezoelectric effect of actuating components on the plate is taken into account;the piezoelectric effect of deformations on the actuating components is not considered. According to the inverse piezoelectric effect of piezoelectric material, the finite element expression of the plane stress problem of the piezoelectric plate and the finite element characteristic equation of the structure stability under large deflection and small deformation are obtained. By taking advantage of subspace iteration method, the characteristic values are obtained under voltage and surface force combined. By means of regulating the voltage in actuators, the structure stability can be controlled effectively.