1维6方压电准晶带4条裂纹的圆形孔口问题的解析解

The Analytic Solutions of a Circular Hole with Four Cracks of One-Dimensional Hexagonal Piezoelectric Quasicrystals

利用复变函数方法与保角变换技巧,探讨了1维6方压电准晶中带有4条裂纹的圆形孔口的反平面III型裂纹问题,得出了应力强度因子和电位移强度因子的解析解.由该解析解得出极限情形下的对称4裂纹圆形孔口、3条裂纹的圆形孔口、共线双裂纹圆形孔口、单裂纹圆形孔口、十字裂纹、T形裂纹对应的III型裂纹应力强度因子和电位移强度因子的解析表达式.

By using the complex variable function method and the conformal mapping technique,the antiplane problem of one-dimensional hexagonal piezoelectric quasicrystals with a circular hole with four cracks is analyzed. The solutions of the stress intensity factors and electric displacement intensity factor is given in analytical form. For some special cases,such as a circular hole with symmetrical four cracks,a circular hole with three cracks,a circular hole with two collinear cracks,a circular hole with a single crack,a cross crack and a T shape crack in one-dimensional hexagonal piezoelectric quasicrystals,the analytic expressions of the stress intensity factor and the electric displacement intensity factor can be obtained by taking a limiting process from our present solution.