压电材料空间轴对称问题的通解及其应用  

A General Solution And the Applicatlon of Space Axisymmetric Problem in Piezoelectric Material

作　　者：王子昆[1] 陈庚超[1] 

机构地区：[1]西安交通大学

出　　处：《应用数学和力学》1994年第7期587-598,共12页Applied Mathematics and Mechanics

摘　　要：本文根据横观各向同性压电材料空间轴对称问题场方程的结构特点，利用逐次引进势函数的方法，最后得到将位移分量和电势函数用满足特定偏微分方程的单一势函数表示的所谓通解，推导过程表明这种形式的通解是完备的，作为应用举例，文中用通解求解了压电材料半无限体表面受集中力的问题，得到位移、应力、电位移分量及电势函数的解析表达式，本文所提供的通解可作为分析含空腔、夹杂或币形裂纹等缺陷的压电材料的机－电耦合行为的工具，算例所得结果可直接用于求解压电体相互间或压电体与普通弹性体间的接触问题。According to the structure feature of the governing equations of space axisym- metric problem in transversely isotropic piezoelectric material,using method of introducing potential function one by one,in this paper we obtain the so-called general solution of displacement and electric potential function denoted by uinque potential function which satisfies specific partiality equations.As an applying example of the general solution,we solve problem of semi-infinite body made of piezoelectric material,on the surface of the semi-infinite body a concentrative force is applied,and get the analytic formulations of stress and electric displa- cement components.The general solution provided by this paper can be used as a tool to analyse the mechanical-electrical coupling behavior of piezoelectric mate- rial which contains defects such as cavity,inclusion,penuy-shape crack.and so on. The result of the solved problem can be used directly to analyse contact problems which take place between two piezoelectric bodies or piezoelectric body and elastic body.

关 键 词：压电材料 空间轴对称 通解 

分 类 号：TM201[一般工业技术—材料科学与工程]