Exact analytic solutions for an elliptic hole with asymmetric collinear cracks in a one-dimensional hexagonal quasi-crystal  

作　　者：郭俊宏 刘官厅 

机构地区：[1]College of Mathematics Science,Inner Mongolia Normal University

出　　处：《Chinese Physics B》2008年第7期2610-2620,共11页中国物理B（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant No 10761005);the Inner Mongolia Natural Science Foundation of China (Grant No 200607010104)

摘　　要：Using the complex variable function method and the technique of conformal mapping, the anti-plane shear problem of an elliptic hole with asymmetric colfinear cracks in a one-dimensional hexagonal quasi-crystal is solved, and the exact analytic solutions of the stress intensity factors （SIFs） for mode Ⅲ problem are obtained. Under the limiting conditions, the present results reduce to the Griffith crack and many new results obtained as well, such as the circular hole with asymmetric collinear cracks, the elliptic hole with a straight crack, the mode T crack, the cross crack and so on. As far as the phonon field is concerned, these results, which play an important role in many practical and theoretical applications, are shown to be in good agreement with the classical results.Using the complex variable function method and the technique of conformal mapping, the anti-plane shear problem of an elliptic hole with asymmetric colfinear cracks in a one-dimensional hexagonal quasi-crystal is solved, and the exact analytic solutions of the stress intensity factors （SIFs） for mode Ⅲ problem are obtained. Under the limiting conditions, the present results reduce to the Griffith crack and many new results obtained as well, such as the circular hole with asymmetric collinear cracks, the elliptic hole with a straight crack, the mode T crack, the cross crack and so on. As far as the phonon field is concerned, these results, which play an important role in many practical and theoretical applications, are shown to be in good agreement with the classical results.

关 键 词：one-dimensional hexagonal quasi-crystals elliptic hole with asymmetric collinear cracks stress intensity factor complex variable function method 

分 类 号：O753.3[理学—晶体学]