Chin. Phys. B ›› 2013, Vol. 22 ›› Issue (1): 16102-016102.doi: 10.1088/1674-1056/22/1/016102

• CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES • 上一篇    下一篇

Elliptic hole in octagonal quasicrystals

李联和   

  1. College of Mathematical Science, Inner Mongolia Normal University, Huhhot 010022, China
  • 收稿日期:2012-03-17 修回日期:2012-06-07 出版日期:2012-12-01 发布日期:2012-12-01
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 11026175, 11262017, and 10761005), the Key Project of Ministry of Education of China (Grant No. 212029), the Natural Science Foundation of Inner Mongolia, China (Grant Nos. 2009MS0102 and 2009BS0104), and the Natural Science Foundation of Inner Mongolia Department of Public Education, China (Grant Nos. NJzy08024 and NJ10047).

Elliptic hole in octagonal quasicrystals

Li Lian-He (李联和)   

  1. College of Mathematical Science, Inner Mongolia Normal University, Huhhot 010022, China
  • Received:2012-03-17 Revised:2012-06-07 Online:2012-12-01 Published:2012-12-01
  • Contact: Li Lian-He E-mail:nmglilianhe@163.com
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 11026175, 11262017, and 10761005), the Key Project of Ministry of Education of China (Grant No. 212029), the Natural Science Foundation of Inner Mongolia, China (Grant Nos. 2009MS0102 and 2009BS0104), and the Natural Science Foundation of Inner Mongolia Department of Public Education, China (Grant Nos. NJzy08024 and NJ10047).

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摘要： The stress potential function theory for plane elasticity of octagonal quasicrystals is developed. By introducing stress functions, a large number of basic equations involving elasticity of octagonal quasicrystals are reduced to a single partial differential equation. Furthermore, we develop the complex variable function method (Lekhnitskii method) for anisotropic elasticity theory to that for quasicrystals. With the help of conformal transformation, an exact solution for the elliptic hole of quasicrystals is presented. The solution of the Griffith crack problem, as a special case of the results, is obtained. As a consequence, the phonon stress intensity factor is derived analytically.

关键词: quasicrystals, plane elasticity, elliptic hole, stress potential

Abstract: The stress potential function theory for plane elasticity of octagonal quasicrystals is developed. By introducing stress functions, a large number of basic equations involving elasticity of octagonal quasicrystals are reduced to a single partial differential equation. Furthermore, we develop the complex variable function method (Lekhnitskii method) for anisotropic elasticity theory to that for quasicrystals. With the help of conformal transformation, an exact solution for the elliptic hole of quasicrystals is presented. The solution of the Griffith crack problem, as a special case of the results, is obtained. As a consequence, the phonon stress intensity factor is derived analytically.

Key words: quasicrystals, plane elasticity, elliptic hole, stress potential

中图分类号:  (Quasicrystals)

  • 61.44.Br
62.20.D- (Elasticity) 02.30.Em (Potential theory)