一维正方准晶椭圆孔口平面弹性问题的解析解

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.

ANALYTIC SOLUTION OF PLANE ELASTICITY OF ONE-DIMENSIONAL ORTHORHOMBIC QUASICRYSTALS WITH ELLIPTICAL HOLE

By introducing the generalized conformal transformation and using the complex variable function method , the analytic solution of the plane elasticity problem of elliptical hole in one-dinensional orthorhombic quasicrystals were obtained and derived complex repesentation of stress displacement . In some special conditions,the elliptical hole can be turned into a Griffith crack and the SIFs of crack tips can be obtained. The plane elasticity problem of elliptical hole in 1D orthorhombic QCs could extended for 1D tetragonal QCs and the analytic solution of plane elasticity problem of elliptical hole in 1D tetragonal QCs. The elliptical hole can be also turned into a Griffith crack in specical conditions and the SIFs also be obtained.