基于物理中面的压电功能梯度板几何非线性弯曲分析

GEOMETRIC NONLINEAR BENDING ANALYSIS OF PIEZOELECTRIC FUNCTIONALLY GRADED PLASES BASED ON NEUTRAL SURFACE

基于物理中面的概念,建立了压电功能梯度板(FGM)几何非线性静力弯曲的基本方程,利用Ritz法研究了材料性质、梯度指数等对FGM板考虑几何非线性时弯曲变形的影响,并通过不同的电压施加方式探讨了压电材料对FGM板变形控制的规律。与已有文献结果对比分析表明,本文建立的方程和采用的方法是可靠的;基于几何非线性方程求解功能梯度材料板的静力变形时,计算偏差随着物理中面与几何中面位置偏差的增大而增大,在利用压电材料对FGM板的变形进行控制时,宜采用物理中面。

According to the concept of neutral surface,the basic equation for geometric nonlinear static bending of functionally graded material（ FGM） plates was established. By Ritz method,the effects of gradient index and material properties taking into account of the geometric nonlinear on bending deformation of FGM plates were analyzed.Also,the variation of deformation control was explored when FGM plates were subjected to different electric fields.The accuracy of the present equation and method is veried by comparing them with known results. The static deformation of FGM plates was solved by the geometric nonlinear equation. Analysis results show that the difference increases with the increase of neutral axis shift. The neutral surface should be considered when using piezoelectric material to control the deformation of FGM plates.