中文摘要：

利用复变函数方法，通过构造拱形映射函数，研究了一维六方准晶中幂函数类裂纹的反平面剪切问题，给出了Ⅲ型裂纹问题的应力强度因子的一般解，当幂次取不同的自然数时，可以退化为已有的结果。通过数值计算，讨论了一维六方准晶中幂函数类曲线裂纹的系数、幂次及在X轴上的投影长度对Ⅲ型应力强度因子的影响规律。

英文摘要：

By means of the complex variable function method and using the technique of conformal mapping, the an- ti - plane shear problem for power function curved cracks in one-dimensional hexagonal quasicrystals was investiga- ted and the general solutions of the stress intensity factor（SIFs）of mode III was found out. The present results can be reduced to the well-known solutions when the power of power function is prescribed to different natural numbers. Numerical examples are conducted to reveal the effects of opening orientation,power and projected length along x- axis of the power function curved crack on the SIFs for mode III in one-dimensional hexagonal quasicrystals.