## 留言板

 引用本文: 白巧梅, 丁生虎. 一维六方压电准晶中正六边形孔边裂纹的反平面问题[J]. 应用数学和力学, 2019, 40(10): 1071-1080.
BAI Qiaomei, DING Shenghu. An Anti-Plane Problem of Cracks at Edges of Regular Hexagonal Holes in 1D Hexagonal Piezoelectric Quasicrystals[J]. Applied Mathematics and Mechanics, 2019, 40(10): 1071-1080. doi: 10.21656/1000-0887.390362
 Citation: BAI Qiaomei, DING Shenghu. An Anti-Plane Problem of Cracks at Edges of Regular Hexagonal Holes in 1D Hexagonal Piezoelectric Quasicrystals[J]. Applied Mathematics and Mechanics, 2019, 40(10): 1071-1080.

## 一维六方压电准晶中正六边形孔边裂纹的反平面问题

##### doi: 10.21656/1000-0887.390362

###### 作者简介:白巧梅（1994—），女，硕士生（E-mail: 1642721043@qq.com）;丁生虎(1980—)，男，教授，博士(通讯作者. E-mail: dshnx2006@163.com).
• 中图分类号: O346.1

## An Anti-Plane Problem of Cracks at Edges of Regular Hexagonal Holes in 1D Hexagonal Piezoelectric Quasicrystals

Funds: The National Natural Science Foundation of China（11762016；11762017；11832014）
• 摘要: 研究了一维六方压电准晶中正六边形孔边裂纹的反平面问题，利用复变函数中的Cauchy积分公式，通过构造保角映射函数，在电非渗透型的边界条件下得到了孔边裂纹尖端的应力分布以及场强度因子的解析解.通过数值算例，讨论了正六边形的边长和裂纹长度以及剪应力对场强度因子的影响.
•  [1] SHECHTMAN D, BLECH I, GRATIAS D, et al. Metallic phase with long-range orientational order and no translational symmetry[J]. Physical Review Letters,1984,53(20): 1951-1953. [2] ZHANG Z, URBAN K. Transmission electron microscope observations of dislocations and stacking faults in a decagonal Al-Cu-Co alloy[J]. Philosophical Magazine Letters,1989,60(3): 97-102. [3] LIU G T, GUO R P, FAN T Y. On the interaction between dislocations and cracks in one-dimensional hexagonal quasi-crystals[J]. Chinese Physics,2003,12(10): 1149-1155. [4] LIU G T, FAN T Y, GUO R P. Governing equations and general solutions of plane elasticity of one-dimensional quasicrystals[J]. International Journal of Solids and Structures,2004,41(14): 3949-3959. [5] FAN T Y. The Mathematical Theory of Elasticity of Quasicrystals and Its Applications [M]. Beijing: Springer-Verlag, 2010. [6] 马晴, 王桂霞, 李联合. 八次对称二维准晶Ⅱ型单边裂纹的动力学问题[J]. 应用数学和力学, 2018,39(10): 1180-1188.(MA Qing, WANG Guixia, LI Lianhe. Dynamic problems of mode Ⅱ cracks in 2D octagonal quasicrystals[J]. Applied Mathematics and Mechanics,2018,39(10): 1180-1188.(in Chinese)) [7] GUO J H, LU Z X. Exact solution of four cracks originating from an elliptical hole in one-dimensional hexagonal quasicrystals[J]. Applied Mathematics & Computation,2011,217(22): 9397-9403. [8] 邵阳, 郭俊宏. 一维六方准晶中正方形孔边双裂纹的反平面问题[J]. 内蒙古工业大学学报, 2014,33(2): 81-87.(SHAO Yang, GUO Junhong. Anti-plane analysis of double cracks originating from a square hole in one-dimensional hexagonal quasicrystals[J]. Journal of Inner Mongolia University of Technology,2014,33(2): 81-87.(in Chinese)) [9] LIU G T, YANG L Y. Interaction between infinitely many dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal[J]. Chinese Physics,2017,26(9): 280-284. [10] 高健, 刘官厅. 一维正方准晶中半无限裂纹问题的解析解[J]. 应用数学和力学, 2015,36(9): 945-955.(GAO Jian, LIU Guanting. Analytical solution for problems of 1D orthorhombic quasicrystal with semi-infinite crack[J]. Applied Mathematics and Mechanics,2015,36(9): 945-955.(in Chinese)) [11] LI X Y, LI P D, WU T H, et al. Three-dimensional fundamental solutions for one-dimensional hexagonal quasicrystal with piezoelectric effect[J]. Physics Letters A,2014,378(10): 826-834. [12] 李星, 霍华颂, 时朋朋. 一维六方压电准晶对称条形体中共线双半无限快速传播裂纹的解析解[J]. 固体力学学报, 2014,〖STHZ〗 35(2): 135-141.(LI Xing, HUO Huasong, SHI Pengpeng. Analytic solutions of two collinear fast propagating cracks in a symmetrical strip of one-dimensional hexagonal piezoelectric quasicrystals[J]. Chinese Journal of Solid Mechanics,2014,35(2): 135-141.(in Chinese)) [13] YANG J, LI X, DING S H. Anti-plane analysis of a circular hole with three unequal cracks in one-dimensional hexagonal piezoelectric quasicrystals[J]. Chinese Journal of Engineering Mathematics,2016,33(2): 184-198. [14] 徐文帅, 杨连枝, 高阳. 二维十次对称压电准晶含Griffith裂纹的平面问题[J]. 浙江大学学报（工学版）, 2018,52(3): 487-496.(XU Wenshuai, YANG Lianzhi, GAO Yang. Plane problems of 2D decagonal quasicrystals of piezoelectric effect with Griffith cracks[J]. Journal of Zhejiang University (Engineering Science),2018,52(3): 487-496.(in Chinese)) [15] WANG X, PAN E. Analytical solutions for some defect problems in 1D hexagonal and 2D octagonal quasicrystals[J]. Pramana,2008,70(5): 911-933. [16] 刘官厅, 何青龙, 郭瑞平. 一维六方准晶非周期平面内的平面应变理论[J]. 物理学报, 2009,58(S1): 118-123.(LIU Guanting, HE Qinglong, GUO Ｒuiping. The plane strain theory for one-dimensional hexagonal quasicrystals in aperiodical plane[J]. Acta Physica Sinica,2009,58(S1): 118-123.(in Chinese)) [17] 路见可. 平面弹性复变方法[M]. 武汉: 武汉大学出版社, 2002.(LU Jianke. Plane Elastic Complex Method [M]. Wuhan: Wuhan University Press, 2002.(in Chinese)) [18] 侯祥林, 王家祥, 贾连光. 正六边形孔角裂纹应力强度因子复变函数解[J]. 应用力学学报, 2018,35(3): 484-488.(HOU Xianglin, WANG Jiaxiang, JIA Lianguang. Complex variable function solutions of stress intensity factors for cracks emanating from a hexagonal hole in an infinite plane[J]. Chinese Journal of Applied Mechanics,2018,35(3): 484-488.(in Chinese)) [19] 郭俊宏, 刘官厅. 一维六方准晶中具有不对称裂纹的圆形孔口问题的解析解[J]. 应用数学学报, 2007,30(6): 1066-1075.(GUO Junhong, LIU Guanting. Analytic solutions of the one-dimensional hexagonal quasicrystals about problem of a circular hole with asymmetry cracks[J]. Acta Mathematicae Applicatae Sinica,2007,30(6): 1066-1075.(in Chinese))

##### 计量
• 文章访问数:  735
• HTML全文浏览量:  96
• PDF下载量:  383
• 被引次数: 0
##### 出版历程
• 收稿日期:  2018-12-29
• 修回日期:  2019-08-30
• 刊出日期:  2019-10-01

/

• 分享
• 用微信扫码二维码

分享至好友和朋友圈