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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。
The governing equations of 6-dimensional quasicrystal anti-plane elasticity problem for point group are derived. Using the complex method, the stress components of anti-plane elasticity problem of 6-dimensional hexagonal quasi- The complex change shows that by introducing the appropriate conformal transformation, the anti-plane elasticity problem with elliptic or semi-infinite cracks in 6-dimensional hexagonal quasi- The analytical solution of the stress intensity factor at the tip of the crack is given. In the limit case, the elliptical orifice is transformed into a Griffith crack and an analytical solution of the stress intensity factor at the crack tip is obtained. When the symmetry of a group of six-dimensional hexagonal quasicrystals increases, the anti-plane elasticity problem of elliptic orifices and semi-infinite cracks is degenerated into a point-group 6mm-dimensional hexagonal quasicrystal with an elliptical aperture and a semi-infinite crack Solution to the problem of elasticity.