含圆孤裂纹系的压电材料反平面应变问题

应用复变函数解析延展原理，并通过求解Ｒｉｅｍａｎｎ－Ｈｉｌｂｅｒｔ问题，得到了含圆弧裂纹压电材料反平面应变问题的一般解，对单个圆弧裂纹的情形，给出了封闭形式的复函数解和场强度因子，结果表明，当无限远处或裂纹表面同时受机械载荷（应力τ＾∞或Ｔｚ）和电载荷（电位移Ｄ＾∞或电荷ｑ）联合作用时，应力强度因子仅与机械载荷有关，而电位移动强度因子仅与电载荷有关。

ON ANTI-PLANE STRAIN PROBLEMS OF CIRCULAR-ARC CRACKS IN PIEZOELETRIC MATERIALS

In this paper, a general solution of the anti-plane strain problem in piezoelectric materials with circular-arc crack using the continuation principle of function of complex variables together with the solution of the Riemann-Hilbert problems is given. Solutions in closed form of the complex potentials and the field intensity factors are given for a single circular-arc crack. It is shown from the results obtained in this paper that the stress intensity when mechanical loading and the electrical loading act jointly of infinity or of surface of the cracks is only dependent on the mechanical loading and the electric displacement intensity factor is only dependent on the electricol loading.