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中文摘要：
利用复变方法,引入广义保角映射,研究了一维正方准晶中具有椭圆孔口的平面弹性问题,给出了各应力分量的复变表示,并在特殊情况下转化为Griffith裂纹,得到该裂纹尖端处的应力强度因子的解析解.当准晶体的对称性增加时,正方准晶椭圆孔口平面弹性问题退化为一维四方准晶中具有椭圆孔口的平面弹性问题,同样在特殊情况下转化为Griffith裂纹,得到裂纹尖端处的应力强度因子的解析解.
英文摘要：
By introducing the generalized conformal transformation and using the complex variable function method,the analytic solution of the plane elasticity problem of one-dimensional（1D） orthorhombic quasicrystals（QCs） with an elliptical hole was obtained.Complex representation of stress was also derived.In special case,the elliptical hole can be reduced to the Griffith crack and the stress intensity factors（SIFs） at the crack tip can be easily obtained.Under conditions of more symmetry,the plane elasticity problem of 1D orthorhombic QCs with an elliptical hole can degenerate to that of 1D tetragonal QCs and the corresponding analytic solution of stress was also given.In this case,the elliptical hole can be also reduced to the Griffith crack and the SIFs at the crack tip also can be obtained.
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