一维六方准晶压电材料中唇形裂纹反平面问题的解析解

本文在准晶压电材料基本方程的基础上，根据点群的对称性和一维六方准晶的线性压电效应，导出了一维六方准晶压电材料反平面问题的控制方程.利用复变函数的方法，通过引入适当的保角映射，研究了准晶压电材料中唇形裂纹的反平面问题，并利用Cauchy积分理论，得到在电不可通边界条件下的裂纹尖端场强度因子与机械应变能释放率的解析表达式.

Anti-plane Analysis of a lip-shape crack of piezoelectricity of one-dimensional hexagonal quasicrystals

Based on the fundamental equations of peizoelasticity of quasicrystal materials, by using the symmetry operations of point groups, the linear piezoelasticity behavior of one-dimensional hexagonal quasicrystals is investigated, the control equations of anti-plane problems are derived, variable function method and the technique of conformal mapping in the anti-plane problem of a lip shape cracks of piezoelectricity of one-dimensional hexagonal quasicrystals is adopted. By using Cauchy integral formula, the analytical expressions of the field intensity factors and the mechanical strain energy release rate were presented with the assumption that the crack were electrically impermeable.