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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2015, Vol. 32 ›› Issue (6): 835-844.doi: 10.3969/j.issn.1005-3085.2015.06.005

• • 上一篇    下一篇

一维六方准晶有限板中心裂纹反平面问题的边界配置法

方  丹,   李  星   

  1. 宁夏大学数学计算机学院，银川 750021
  • 收稿日期:2014-04-17 接受日期:2015-01-23 出版日期:2015-12-15 发布日期:2016-02-15
  • 通讯作者: 李 星 E-mail: li_x@nxu.edu.cn
  • 基金资助:
    国家自然科学基金 (11362018; 51061015).

The Boundary Collocation Method for Anti-plane Problems with Central Cracks in the Finite Plate of One-dimensional Hexagonal Quasicrystals

FANG Dan,   LI Xing   

  1. School of Mathematics and Computer Science, Ningxia University, Yinchuan 750021
  • Received:2014-04-17 Accepted:2015-01-23 Online:2015-12-15 Published:2016-02-15
  • Contact: X. Li. E-mail address: li_x@nxu.edu.cn
  • Supported by:
    The National Natural Science Foundation of China (11362018; 51061015).

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摘要： 采用边界配置法，本文研究了一维六方准晶有限板中心直裂纹反平面问题．利用解析函数的性质，选取适当的位移函数，在问题的边界条件下，得到了应力函数的表达式．进而给出了声子场与相位子场的应力强度因子表达式．利用有限板的对称性，只需在半个矩形上配置边界点，板的边界条件即可满足．通过数值算例，讨论了各种因素对应力强度因子的影响．本文所采用的方法可以推广到其他一维六方准晶材料断裂问题的研究中．

关键词: 一维六方准晶, 中心裂纹, 反平面剪切, 边界配置法, 应力强度因子

Abstract:

The anti-plane problems of one-dimensional hexagonal quasicrystals with the central straight cracks in the finite plate are investigated by using the boundary collocation method．The stress functions can be expressed by selecting an appropriate displacement function under the boundary conditions and by using the properties of analytic functions. Then, the related stress intensity factor in the phonon and quantum fields can be obtained from the stress functions．It is shown that only the plate boundary conditions on the half rectangle are needed to be satisfied approximatively when employing the boundary collocation method due to the geometric symmetry. The influence of the stress intensity factor is investigated through numerical examples. The proposed method can be extended to other fracture problems in the one-dimensional hexagonal quasicrystals.

Key words: one-dimensional hexagonal quasicrystals, central crack, anti-planar shear, boundary collocation method, stress intensity factor

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