压电介质中受拉伸与弯曲联合作用的圆币形裂纹问题

Penny-Shaped Crack Problems in A Piezoelectric MediumUnder Venture Action by Tension and Bending Loads

以弹性位移分量和电势函数为基本未知量时，横观各向同性压电介质非轴对称三维问题的控制微分方程是四个二阶线性偏微分方程相联立的方程组。本文导出了用四个调和函数表示位移及电势的该方程组的势函数通解。作为通解的应用举例，文中求解了压电陶瓷材料中受拉伸与弯曲联合作用的圆币形裂纹问题，得到了裂纹尖端附近应力场及电位移场的解析表达式。结果表明裂尖场以及应力强度因子和电位移强度因子均表现出复杂的机－电耦合行为。

While the displacement components and electric potential functions are the essential unknowns,the governing equations of three-dimensional problems in transversely isotropic piezoelectric media arecomposed of four second order linear partial differential equations obtained with the aid of four har-monic functions which are used to express the components of displacements and the electric potentialfunctions.As an application of the general solution,the penny-shaped crack problems in piezoelectricceramic materials under venture action by tension and bending loads are solved and the analytic ex-pressions of stresses and electric displacement near the crack top are gotten. The results demonstratethat the crack top field and force intensity and electric displacement intensity all appear the complicat-ed coupling effects that take place between electric fields and mechanical deformation.