一维六方准晶非周期平面内的平面应变理论

The plane strain theory for one-dimensional hexagonal quasicrystals in aperiodical plane

针对一维六方准晶中一种新平面弹性问题,即非周期平面内的平面弹性问题,通过引入应力势函数,建立了一维六方准晶中非周期平面内的平面应变理论.作为应用,求解了一维六方准晶中垂直于准周期方向的椭圆孔口问题,得到了其弹性应力场的解析解.在极限情形下,可给出裂纹问题的解.

Considering the plane elastic problem of one-dimensional hexagonal quasicrystals with point group 6mm, the theory about plane strain parallel to aperiodic direction is proposed and established. As an application of this theory, the analytic solutions of elastic fields of the quasicrystals with an elliptical cavity perpendicular to quasi-periodical direction are given in the form of general complex variable. In the limit case, our solutions degenerate into the ones of crack problems.