留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

一维正交准晶中具有四条裂纹的椭圆孔口问题的解析解

高媛媛 刘官厅

高媛媛, 刘官厅. 一维正交准晶中具有四条裂纹的椭圆孔口问题的解析解[J]. 应用数学和力学, 2019, 40(2): 210-222. doi: 10.21656/1000-0887.390032
引用本文: 高媛媛, 刘官厅. 一维正交准晶中具有四条裂纹的椭圆孔口问题的解析解[J]. 应用数学和力学, 2019, 40(2): 210-222. doi: 10.21656/1000-0887.390032
GAO Yuanyuan, LIU Guanting. Analytical Solutions to Problems of Elliptical Holes With 4 Edge Cracks in 1D Orthorhombic Quasicrystals[J]. Applied Mathematics and Mechanics, 2019, 40(2): 210-222. doi: 10.21656/1000-0887.390032
Citation: GAO Yuanyuan, LIU Guanting. Analytical Solutions to Problems of Elliptical Holes With 4 Edge Cracks in 1D Orthorhombic Quasicrystals[J]. Applied Mathematics and Mechanics, 2019, 40(2): 210-222. doi: 10.21656/1000-0887.390032

一维正交准晶中具有四条裂纹的椭圆孔口问题的解析解

doi: 10.21656/1000-0887.390032
基金项目: 国家重点研发计划(2017YFC1405605);内蒙古自然科学基金(2018MS01005);内蒙古自治区研究生教育创新计划(CXJJS18069)
详细信息
    作者简介:

    高媛媛(1993—),女,硕士生(E-mail: 1223729636@qq.com);刘官厅(1966—),男,教授,博士生导师(通讯作者. E-mail: guantingliu@imnu.cn).

  • 中图分类号: O346.1

Analytical Solutions to Problems of Elliptical Holes With 4 Edge Cracks in 1D Orthorhombic Quasicrystals

Funds: The National Key R&D Program of China(2017YFC1405605)
  • 摘要: 运用广义复变函数方法,通过构造适当的广义保角映射,研究了一维正交准晶中具有四条裂纹的椭圆孔口的平面弹性问题.通过引入应力函数,把平面弹性问题的基本方程简化为一个四阶偏微分方程,从而给出了各个应力分量在像平面的复表示,求得了裂纹尖端的应力强度因子的解析解.当描述缺陷的各参数发生变化时,该文的结果不仅可以还原已有文献中的结论,还可给出多种常见缺陷构型的应力强度因子,为工程力学分析提供了理论依据.
  • [1] 丁棣华, 王仁卉, 杨文革, 等. 准晶的弹性、塑性与位错[J]. 物理学进展, 1998,18(3): 223-260.(DING Dihua, WANG Renhui, YANG Wenge, et al. Elasticity, plasticity and dislocations of quasicrystals[J]. Progress in Physics,1998,18(3): 223-260.(in Chinese))
    [2] FAN T Y. Mathematical Theory of Elaticity of Quasicrystals and Its Applications [M]. Beijing: Science Press, 2010.
    [3] 董闯. 准晶材料[M]. 北京: 国防工业出版社, 1998.(DONG Chuang. The Quasicrystal Material [M]. Beijing: National Defence Industry Press, 1998.(in Chinese))
    [4] LIU G T, FAN T Y. Complex method of the plane elasticity in 2D quasicrystal with point group 10 mm tenfold rotational symmetry and holey problems[J]. Science in China,2003,46(3): 326-336.
    [5] 王仁卉, 胡承正, 桂嘉年. 准晶物理学[M]. 北京: 科学出版社, 2004.(WANG Renhui, HU Chengzheng, GUI Jianian. Quasicrystal Physics [M]. Beijing: Science Press, 2004.(in Chinese))
    [6] ZHOU W M, FAN T Y. Contact problem in decagonal two-dimensional quasicrystal[J]. Journal of Beijing Institute of Technology,2001,10(1): 51-55.
    [7] WANG X, PAN E. Analytical solutions for some defect problems in 1D hexagonal and 2D octagonal quasicrystals[J]. Pramana,2008,70(5): 911-933.
    [8] 刘官厅. 准晶弹性的复变方法与非线性发展方程的显示解[M]. 呼和浩特: 内蒙古人民出版社, 2005.(LIU Guanting. The Complex Variable Function Method of Quasicrystals Elastiaty and Analytic Solutions of Nonlinear Equations [M]. Hohhot: Inner Mongolia People Press, 2005.(in Chinese))
    [9] 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 qsicrystals about problem of a circular hole with asymmetry cracks[J]. Acta Mathematicae Applicatae Sinica,2007,30(6): 1066-1075.(in Chinese))
    [10] 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.
    [11] 杨丽星, 刘官厅. 一维六方准晶中带三条不对称裂纹的圆形孔口问题的解析解[J]. 数学的实践与认识, 2010,40(2): 148-156.(YANG Lixing, LIU Guanting. Analytic solutions of about a circular hole with three unequal straight edge cracks in one-dimensional hexagonal quasicrystals[J].Mathematics in Practice and Theory,2010,40(2): 148-156.(in Chinese))
    [12] 郭俊宏, 刘官厅. 一维六方准晶中带双裂纹的椭圆孔口问题的解析解[J]. 应用数学和力学, 2008,29(4): 439-446.(GUO Junhong, LIU Guanting. Analytical solutions of problem about an elliptic hole with two straight cracks in one-dimensional hexagonal quasicrystals[J]. Applied Mathematics and Mechanics,2008,29(4): 439-446.(in Chinese)).
    [13] 李联和, 刘官厅. 一维六方准晶中螺型位错与楔形裂纹的相互作用[J]. 物理学报, 2012,61(8): 326-330.(LI Lianhe, LIU Guanting. A serew dislocation interacting with a wedge-shaped crack in one-dimensional hexagonal quasicrystals[J]. Acta Physica Sinica,2012,61(8): 326-330.(in Chinese))
    [14] FAN T Y, LI X F, SUN Y F. A moving screw dislocation in a one-dimensional hexagonal quasicrystal[J]. Acta Physica Sinica (Overseas Edition),1999,8(4): 288-295.
    [15] 马小丹, 李星. 一维六方准晶的两类周期接触问题[J]. 应用数学和力学, 2016,37(7): 699-709.(MA Xiaodan, LI Xing. Kinds of periodic contact problems of 1D hexagonal quasicrystals[J]. Applied Mathematics and Mechanics,2016,37(7): 699-709.(in Chinese))
    [16] SLADEK J, SLADEK V, PAN E. Bending analyses of 1D orthorhombic quasicrystal plates[J]. International Journal of Solids and Structures,2013,50(24): 3975-3983.
    [17] LI Y, YANG L Z, GAO Y. An exact solution for a functionally graded multiayered one-dimensional orthorhombic quasicrystal plate[J]. Acta Mechanica,2017: 1-17. DOI: 10.1007/s00707-017-2028-8.
    [18] YANG L Z, GAO Y, PAN E, et al. An exact closed-form solution for a multilayered one-dimensional orthorhombic quasicrystal plate[J]. Acta Mechanica,2015,226(11): 3611-3621.
    [19] ZHANG L L, ZHANG Y M, GAO Y. General solutions of plane elasticity of one-dimensional orthorhombic quasicrystals with piezoelectric effect[J]. Physics Letters A,2014,378(37): 2768-2776.
    [20] 于静, 刘官厅. 一维正方准晶椭圆孔口平面弹性问题的解析解[J]. 固体力学学报, 2010,31(4): 411-416.(YU Jing, LIU Guanting. Analytic solution of plane elasticity of one-dimensional orthorhombic quasicrystals with elliptical hole[J]. Chinese Journal of Solid Mechanics,2010,31(4): 411-416.(in Chinese))
    [21] 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 solutions for problems of 1D orthorhombic quasicrystal with semi-infinite crack[J]. Applied Mathematics and Mechanics,2015,36(9): 945-955.(in Chinese))
    [22] 匡震邦, 马法尚. 裂纹端部场[M]. 西安: 西安交通大学出版社, 2002.(KUANG Zhenbang, MA Fashang. Crack Tip Fields [M]. Xi’an: Xi’an Jiaotong Univercity Press, 2002.(in Chinese))
    [23] 范天佑. 断裂理论基础[M]. 北京: 科学出版社, 2003.(FAN Tianyou. Fracture Theory Basis [M]. Beijing: Science Press,2003.(in Chinese))
  • 加载中
计量
  • 文章访问数:  1056
  • HTML全文浏览量:  175
  • PDF下载量:  483
  • 被引次数: 0
出版历程
  • 收稿日期:  2018-01-22
  • 修回日期:  2018-06-24
  • 刊出日期:  2019-02-01

目录

    /

    返回文章
    返回