中文摘要：

利用一种数值方法分析压电材料切口尖端包括奇异应力场和奇异电位移场在内的双重奇异性。基于切口尖端的位移场按幂级数渐近展开假设,从应力平衡方程和Maxwell方程出发,推导出关于压电材料切口奇性指数的特征方程组,同时将切口的力学和电学边界条件转化为奇性指数和特征函数的组合表达,从而将压电材料双重奇性分析问题转化为在相应边界条件下微分方程组的特征值求解问题,采用插值矩阵法,可以一次性地计算出压电材料切口的各阶奇性指数。裂纹作为切口的特例,其尖端的电弹性奇性指数亦可以根据本法求出。

英文摘要：

A new method is proposed to analyze the stress singularity and the electricity singularity at the piezoelectric notch tip.Based on the assumption that the displacement field at the notch tip was expanded as the power series asymptotic expansion,the governing equations on the notched structure,i.e.,the stress equilibrium equations and the Maxwell equation,were turned into the characteristic equations respects to the singularity orders.The mechanic and electric boundary conditions on the notch surfaces were transformed into the combination of the singularity order and the corresponding eigen-functions.The analysis of the piezoelectric notch singularity orders was turned into calculating the eigen-values of the ordinary differential equations under corresponding boundary conditions.The interpolate matrix method was introduced to solving the established differential equations.Numerical results show that all the singularity orders at the piezoelectric notch can be evaluated in the present method.As a special case of the notch,the singularity orders of cracks can also be obtained by the present method.