热压电材料空间轴对称问题的势函数解法

A GENERAL SOLUTION BASED ON POTENTIAL FUNCTIONS FOR THREE DIMENSIONAL AXISYMMETRIC PROBLEMS OF THERMOPIEZOELECTRICITY

热压电材料因其潜在的应用价值在机敏结构系统中引起极大的关注．因为热－机－电三者相互耦合，热压电弹性理论三维问题的控制微分方程极为复杂，该问题的解极少有文献报导．文中采用引进势函数的方法和傅立叶－汉克尔变换的技巧，得到了横观各向同性热压电材料空间轴对称问题场方程的“通解”．作为通解的应用，求解了热压电陶瓷中圆币形裂纹在稳定热流作用下的应力集中问题，得到了裂纹尖端附近应力场、电位移场的解析表达式．结果表明。

Thermopiezoelectric materials have considerable attracted attention because of their potential use in smart structure systems. Due to the intrinsic coupling effects that take place among thermal, mechanical and electrical fields, the governing equations of a three dimensional thermopiezoelectric medium are much complex, relatively few solutions to such coupled problems are available in the literature. In this paper, we obtain the so called general solution of field equation for three dimensional axisymmetric problem of transversely isotropic thermopiezoelectric materials by means of a method of potential function and Fourier Hankel transformations. As an application of the general solution, a thermopiezoelectric problem of penny shaped crack under an uniform steady flow of heat is analyzed, the analytical expressions of stress field and electric displacement near the crack are obtained. The results show the characteristic r -1/2 singular behaviour of the cack tip stress field and electric displacement.