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幂函数型曲线裂纹平面问题的一般解

郭俊宏 袁泽帅 卢子兴

郭俊宏, 袁泽帅, 卢子兴. 幂函数型曲线裂纹平面问题的一般解[J]. 应用数学和力学, 2011, 32(5): 533-540. doi: 10.3879/j.issn.1000-0887.2011.05.003
引用本文: 郭俊宏, 袁泽帅, 卢子兴. 幂函数型曲线裂纹平面问题的一般解[J]. 应用数学和力学, 2011, 32(5): 533-540. doi: 10.3879/j.issn.1000-0887.2011.05.003
GUO Jun-hong, YUAN Ze-shuai, LU Zi-xing. General Solutions of Plane Problem for Power Function Curved Cracks[J]. Applied Mathematics and Mechanics, 2011, 32(5): 533-540. doi: 10.3879/j.issn.1000-0887.2011.05.003
Citation: GUO Jun-hong, YUAN Ze-shuai, LU Zi-xing. General Solutions of Plane Problem for Power Function Curved Cracks[J]. Applied Mathematics and Mechanics, 2011, 32(5): 533-540. doi: 10.3879/j.issn.1000-0887.2011.05.003

幂函数型曲线裂纹平面问题的一般解

doi: 10.3879/j.issn.1000-0887.2011.05.003
基金项目: 国家自然科学基金资助项目(10932001;11072015;10761005);北京市教育委员会共建项目建设计划资助项目(KZ201010005003);高等学校博士学科点专项科研基金资助项目(201011021100167)
详细信息
    作者简介:

    郭俊宏(1981- ),男,内蒙古乌兰察布人,博士生(E-mail:guojunhong@ase.buaa.edu.cn);卢子兴(1960- ),男,河北枣强人,教授,博士生导师(联系人.Tel:+86-10-82317507;Fax:+86-10-82328501;E-mail:luzixing@buaa.edu.cn).

  • 中图分类号: O346.1

General Solutions of Plane Problem for Power Function Curved Cracks

  • 摘要: 通过构造一个新的、精确的和通用的保角映射,利用Muskhelishvili复势法研究了任意自然数次幂的幂函数型曲线裂纹的平面弹性问题,给出了远处受单向拉伸载荷下裂纹尖端Ⅰ型和Ⅱ型应力强度因子的一般解.当幂次取不同的自然数时,可以退化为若干已有的结果.通过数值算例,讨论了幂函数型曲线裂纹的系数、幂次及在x轴上的投影长度对Ⅰ型和Ⅱ型应力强度因子的影响规律.
  • [1] SHEN Da-wei, FAN Tian-you. Exact solutions of two semi-infinite collinear cracks in a strip[J]. Engineering Fracture Mechanics, 2003, 70(6): 813-822. doi: 10.1016/S0013-7944(02)00083-8
    [2] Muskhelishvili N I. Some Basic Problems of Mathematical Theory of Elasticity[M]. Gorningen, Holland: P Noordhoff, 1975.
    [3] YAN Xiang-qiao. A numerical analysis of cracks emanating from an elliptical hole in a 2-D elasticity plate[J]. European Journal of Mechanics A/Solids, 2006, 25(1): 142-153. doi: 10.1016/j.euromechsol.2005.06.005
    [4] 郭俊宏, 刘官厅. 带双裂纹的椭圆孔口问题的应力分析[J].力学学报, 2007, 39(5): 699-703.(GUO Jun-hong,LIU Guan-ting. Stress analysis for elliptical hole with two straight cracks[J]. Chinese Journal of Theoretical and Applied Mechanics, 2007, 39(5): 699-703. (in Chinese))
    [5] Abdelmoula R, Semani K, Li J. Analysis of cracks originating at the boundary of a circular hole in an infinite plate by using a new conformal mapping approach[J]. Applied Mathematics and Computation, 2007, 188(2): 1891-1896. doi: 10.1016/j.amc.2006.11.052
    [6] CHEN Yi-zhou. Stress intensity factors for curved and kinked cracks in plane extension[J]. Theoretical and Applied Fracture Mechanics, 1999, 31(3): 223-232. doi: 10.1016/S0167-8442(99)00016-6
    [7] 胡元太,赵兴华. 沿抛物线分布的各向异性曲线裂纹问题[J]. 应用数学和力学,1995, 16(2):107-115.(HU Yuan-tai, ZHAO Xing-hua. Curve crack lying along a parabolic curve in anisotropic body[J]. Applied Mathematics and Mechanics(English Edition), 1995, 16(2): 115-124.)
    [8] 魏雪霞, 董健. 含轴对称抛物线曲裂纹平面弹性问题的解析解[J]. 北京理工大学学报, 2004, 24(5): 380-382.(WEI Xue-xia,DONG Jian. An analytical solution for the elastic plane problem with a symmetric parabolic crack[J]. Transactions of Beijing Institute of Technology, 2004, 24(5): 380-382. (in Chinese))
    [9] 郭怀民, 刘官厅, 皮建东. 若干含幂函数类对称曲线裂纹平面弹性问题的解析解[J]. 内蒙古师范大学学报(自然科学汉文版), 2007, 36(5): 533-536.(GOU Huai-min, LIU Guan-ting, PI Jian-dong. Analytical solutions for the elastic plane problem with symmetric power function cracks[J]. Journal of Inner Mongolia Normal University (Natural Science Edition), 2007, 36(5): 533-536. (in Chinese))
    [10] 范天佑. 断裂理论基础[M]. 北京:科学出版社,2003. (FAN Tian-you. Foundation of Fracture Theory[M]. Beijing: Science Press, 2003. (in Chinese))
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  • 被引次数: 0
出版历程
  • 收稿日期:  2010-12-09
  • 修回日期:  2011-03-15
  • 刊出日期:  2011-05-15

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