Plane Elasticity and Dislocation of One-Dimensional Hexagonal Quasicrystals with Point Group 6

Plane elasticity theory of one-dimensional hexagonal quasicrystals with point group 6 is proposed and established. As an application of this theory, one typical example of dislocation problem in the quasicrystals is investigated and its exact analytic solution is presented. The result obtained indicates that the stress components of (elastic) fields of a straight dislocation in the quasicrystals still first order singularity, which is the same as the (general crystals,) but are related with the Burgers vector of phason fields, which is different from the general (crystals.)

点群6一维六方准晶中唇形裂纹的反平面问题

通过引入适当的保角映射,利用复变方法,研究了裂纹面受剪切作用下无限大点群6一维六方准晶中唇形裂纹的断裂行为,给出唇形裂纹在裂纹尖端处的应力强度因子公式,得到了裂纹尖端处应力强度因子的解析解.当唇形裂纹高度趋于0时,该解析解退化为无限大点群6一维六方准晶中有限长Griffith裂纹问题的解.

点群6一维六方准晶狭长体中有限长Griffith裂纹的反平面问题

利用复变函数法,通过构造新的保角变换,研究了裂纹面受剪切作用下点群6一维六方准晶狭长体中有限长Griffith裂纹的断裂行为,得到了裂纹尖端处应力强度因子的解析解.当狭长体高度趋于无穷时,该解析解退化为无限大点群6一维六方准晶中有限长Griffith裂纹问题的解.

点群6一维六方准晶椭圆孔口与半无限裂纹反平面弹性问题的解析解

导出了点群6-维六方准晶反平面弹性问题的控制方程.利用复变方法,给出了点群6-维六方准晶在周期平面内的反平面弹性问题的应力分量以及边界条件的复变表示,通过引入适当的保角变换,研究了点群6-维六方准晶中带有椭圆孔口与半无限裂纹的反平面弹性问题,得到了椭圆孔口问题应力场的解析解,给出了半无限裂纹问题在裂纹尖端处的应力强度因子的解析解.在极限情形下,椭圆孔口转化为Griffith裂纹,并得到该裂纹在裂尖处的应力强度因子的解析解.当点群6-维六方准晶体的对称性增加时,其椭圆孔口与半无限裂纹的反平面弹性问题的解退化为点群6mm-维六方准晶带有椭圆孔口与半无限裂纹的反平面弹性问题的解。