压电、压磁弹性体平面问题的通解

General Solution of the Plane Problem in Piezoelectric, Piezomagnectic and Elastic Media

从压电、压磁和电磁耦合弹性介质材料平面问题的平衡方程、梯度方程、本构方程出发,通过引入位移函数导出该材料平面问题的位移、电势和磁势通解.同时针对特征根的不同情况,将通解化为简单形式,即用4个调和的位移函数来表示所有的物理量.该解可以用来求解压电、压磁和电磁耦合弹性介质材料楔形体和半无限平面体受集中力、点电荷和点电流作用下的问题.

Fundamental equations of the plane problem for transversely isotropy piezoelectric-piezomagnetic and elastic media were observed. By means of drawing one displacement potential function the general solution for the plane problem of transversely isotropic magneto-electro-elastic was derived. Moreover, this general solution can be simplified under the distinct situation of latent root,namely the all physical quantities are expressed by four harmonic functions. That solution can be used to solve the problem that the wedge shape body and the semi plane infinity body are acted by a point force, a point charge and a point electric current for piezoelectric-piezomagnetic and elastic media.