中文摘要：

运用广义复变函数方法,通过构造适当的广义保角映射,研究了含有沿准周期方向穿透的半无限裂纹的一维正方准晶的反平面弹性问题,给出了在部分裂纹面上受均匀面外剪切时应力场和裂纹尖端应力强度因子的解析解.将此方法进一步推广到半无限裂纹垂直于一维正方准晶的准周期方向穿透的情形中,得到了相应的平面弹性问题的解析解.当准晶体的对称性增加时,还可以得出一维四方准晶相应问题的解析解.

英文摘要：

The anti-plane elasticity problem of the ID orthorhombic quasicrystal with a semi-in- finite crack penetrating along the quasiperiodic direction was investigated through introduction of a new generalized conformal mapping and with the generalized complex variable method. The analytical solutions of the stress fields and the stress intensity factors under the action of the u- niform out-of-plane shear load on the partial crack surface were obtained. In addition, this method was applied to solve the plane elasticity problem of the 1 D orthorhombic quasicrystal with a semi-in/mite crack penetrating perpendicular to the quasiperiodic direction and the ana- lytical solutions were derived. Under the condition of higher symmetry, the analytical solutions for the corresponding problem of the 1D tetragonal quasicrystal were also obtained.