摘要
研究了点群10十次对称二维准晶平面弹性问题的复变函数解法。首先将该问题的位移势函数用4个解析函数表示出来,再利用解析函数的性质,经过大量的推导,给出了准晶声子场和相位子场的位移、应力及边界条件的复变函数表示,从而建立了十次对称二维准晶平面弹性问题的复变解法的理论基础。作为应用,借助于复变函数中的保角变换,求解了该准晶中的裂纹问题.一定条件下,本文可还原为点群10mm十次对称二维准晶的情形。
The complex method of plane elasticity in two-dimensional decagonal quasicrystal is proposed and established.First the displacement potential function in the quasicrystal is represented by four analytic functions.Then by using the properties of analytic function and through a great deal of derivation,the complex representations of stresses and displacements components of phonon fields and phason fields in the quasicrystal are given,which are the theoretical foundation of the method.As its application,mode I crack problem is studied by the help of conformal transformations in the theory of complex function and its analytic solutions of stress fields are obtained.In some conditions,the results can give one of the point group 10mm two-dimensional decagonal quasicrystal.
出处
《内蒙古农业大学学报（自然科学版）》
CAS
北大核心
2009年第4期264-272,共9页
Journal of Inner Mongolia Agricultural University(Natural Science Edition)
基金
国家自然科学基金项目(19761005)
关键词
十次对称二维准晶
平面弹性
保角变换
Two-dimensional decagonal quasicrystal
plane elasticity
conformal transformation
