一维六方压电准晶中唇形匀速移动裂纹问题的解析解

运用复变函数方法，通过构造保角映射，研究了在电非渗透型边界条件下一维六方压电准晶中唇形快速传播裂纹问题的反平面剪切问题，获得了III型裂纹动态的应力强度因子和电位移强度因子的解析解．研究结果表示，当裂纹传播速度趋于零时，动力学问题就还原为了静力学问题的解．当唇形裂纹的高度趋于零时，所得结果可以退化为Griffth裂纹问题．

Analytic Solutions of a Lip-Shape Uniform Motion Crack in One-Dimensional Hexagonal Piezoelectric Quasicrystals

By using the method of complex variable function, as well as the conformal mapping technique, analyzed was the antiplane problem for a one-dimensional hexagonal piezoelectric quasicrystals with a lip-shape uniform motion crack. Under the electrically impermeable conditions, the analytic solutions of the dynamic stress intensity factors was obtained. The results show that, the analytical solution can be simplified as the solution for static problems when the crack propagation velocity is reduced to zero. When the height of the lip-shape crack approaches zero, the present results are equivalent to the solution of the Griffith crack problem.