用“调和函数”表示的压电介质平面问题的通解  

General Solution of Plane Problem of Piezoelectric Media Expressed by“Harmonic Functions”

作　　者：丁皓江[1] 王国庆[1] 陈伟球[1] 

机构地区：[1]浙江大学力学系,杭州310027

出　　处：《应用数学和力学》1997年第8期703-710,共8页Applied Mathematics and Mechanics

基　　金：国家自然科学基金

摘　　要：本文首先从压电介质平面问题基本方程出发，引入一个位移函数，导出其通解，然后利用推广的Almansi定理，将通解化为简单形式，即通过三个“调和函数”来表示所有的物理量，其次，推导了楔形体顶端受集中力和点电荷作用时有限形式的解，退化可得半无限平面直线边界受集中力和点电荷的解。First, based on the basic equations of two-dimensional piezoelectroelasticity, a displacement function is introduced and the general solution is then derived. Utilizing the generalized Almansi's theorem, the general solution is so simplified that all physical quantities can be expressed by three 'harmonic functions'.Second, solutions of problems of a wedge loaded by point forces and point charge at the apex are also obtained in the paper. These solutions can be degenerated to those of problems of point forces and point charge acting on the line boundary of a piezoelectric half-plane.

关 键 词：压电介质 平面问题 通解 调和函数 压电材料 

分 类 号：TM22[一般工业技术—材料科学与工程]