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

剪切荷载作用下圆孔孔边裂纹的解

段士杰 刘淑红

段士杰, 刘淑红. 剪切荷载作用下圆孔孔边裂纹的解[J]. 应用数学和力学, 2016, 37(7): 740-747. doi: 10.21656/1000-0887.360352
引用本文: 段士杰, 刘淑红. 剪切荷载作用下圆孔孔边裂纹的解[J]. 应用数学和力学, 2016, 37(7): 740-747. doi: 10.21656/1000-0887.360352
DUAN Shi-jie, LIU Shu-hong. Solutions for a Circular Hole With Edge Cracks Under Shear Load[J]. Applied Mathematics and Mechanics, 2016, 37(7): 740-747. doi: 10.21656/1000-0887.360352
Citation: DUAN Shi-jie, LIU Shu-hong. Solutions for a Circular Hole With Edge Cracks Under Shear Load[J]. Applied Mathematics and Mechanics, 2016, 37(7): 740-747. doi: 10.21656/1000-0887.360352

剪切荷载作用下圆孔孔边裂纹的解

doi: 10.21656/1000-0887.360352
基金项目: 河北省自然科学基金(A2015210089);河北省高等学校科学技术研究重点项目(ZD2015101)
详细信息
    作者简介:

    段士杰(1968—),男,副教授(E-mail: dsj1968@sohu.com);刘淑红(1968—),女,教授,博士,硕士生导师(通讯作者. E-mail: liush@stdu.edu.cn).

  • 中图分类号: O346.1

Solutions for a Circular Hole With Edge Cracks Under Shear Load

  • 摘要: 基于复变函数的方法,研究了在无限远处剪切荷载作用下,含两个径向不等边裂纹圆孔无限大板的平面问题,得到了应力函数和应力强度因子的解析解.通过算例,给出了通过应力函数得到的应力分量沿坐标轴方向和孔边的分布,同时给出了裂纹尖端的应力强度因子.可以看出,应力分量在裂纹尖端、孔附近变化剧烈,离缺陷稍远处趋于所加荷载,符合Saint Venant(圣维南)原理.另外,通过有限元计算了以上数值结果,与解析解的结果进行对比,吻合较好,说明了理论公式推导的正确性.
  • [1] Bowie O L. Analysis of an infinite plate containing radial cracks originating at the boundary of an internal circular hole[J].Journal of Mathematical Physics,1956,35(1/4): 60-71.
    [2] 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.
    [3] 郭怀民, 刘官厅, 皮建东. 带裂纹的椭圆孔口问题的应力分析[J]. 固体力学学报, 2007,28(3): 308-312.(GUO Huai-min, LIU Guan-ting, PI Jian-dong. Stress analysis of an ellipse hole with a straight edge-crack by complex variable method[J].Acta Mechanica Solida Sinica,2007,28(3): 308-312.(in Chinese))
    [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 an elliptical hole with two straight cracks[J].Chinese Journal of Theoretical and Applied Mechanics,2007,39(5): 699-703.(in Chinese))
    [5] 郭怀民, 乔文华. 椭圆孔边两不对称裂纹问题的复变函数解[J]. 力学季刊, 2011,32(3): 444-451.(GUO Huai-min, QIAO Wen-hua. Complex variable function analysis of an elliptic hole with asymmetry edge cracks[J].Chinese Quarterly Mechanics,2011,32(3): 444-451.(in Chinese))
    [6] 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.(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.(in Chinese))
    [7] ZHAO Jin-fang, XIE Li-yang, LIU Jian-zhong, ZHAO Qun. A method for stress intensity factor calculation of infinite plate containing multiple hole-edge cracks[J].International Journal Fatigue,2012,35(1): 2-9.
    [8] 刘淑红, 齐月芹, 冯得得, 史晓佳, 万涛平. 含椭圆孔单边裂纹板的数值分析[J]. 机械工程学报, 2012,48(20): 83-87.(LIU Shu-hong, QI Yue-qin, FENG De-de, SHI Xiao-jia, WAN Tao-ping. Numerical analysis of crack emanating from elliptical hole[J].Journal of Mechanical Engineering,2012,48(20): 83-87.(in Chinese))
    [9] 刘淑红, 李延强, 沈英明. 含椭圆孔压电材料的电弹场[J]. 工程力学, 2012,29(12): 45-50.(LIU Shu-hong, LI Yan-qiang, SHEN Ying-ming. The electro-elastic fields of piezoelectric materials with an elliptic hole[J].Engineering Mechanics,2012,29(12): 45-50.(in Chinese))
    [10] LIU Shu-hong, SHEN Ying-ming, LIU Jin-xi. Exact solutions for piezoelectric materials with an elliptic hole or a crack under uniform internal pressure[J].Chinese Journal of Mechanical Engineering,2012,25(4): 845-852.
    [11] DU Yan-liang, LIU Shu-hong, DUAN Shi-jie, LI Yan-qiang. Electro-elastic fields of piezoelectric materials with an elliptic hole under uniform internal shearing forces[J].Chinese Journal of Mechanical Engineering,2013,26(3): 454-461.
    [12] LIU Shu-hong, DUAN Shi-jie. Analytical solutions of cracks emanating from an elliptical hole under shear[J].Chinese Journal of Aeronautics,2014,27(4): 829-834.
    [13] LIU Shu-hong, DUAN Shi-jie. Analytical solutions of cracks emanating from an elliptic hole in an infinite plate under tension[J].Chinese Journal of Mechanical Engineering,2014,27(5): 1057-1063.
    [14] 周妍, 张财贵, 杨井瑞, 王启智. 圆孔内单边(或双边)裂纹平台巴西圆盘应力强度因子的全面标定[J]. 应用数学和力学, 2015,36(1): 16-30.(ZHOU Yan, ZHANG Cai-gui, YANG Jing-rui, WANG Qi-zhi. Comprehensive calibration of the stress intensity factor for the holed flattened Brazilian disc with an inner single crack or double cracks[J].Applied Mathematics and Mechanics,2015,36(1): 16-30.(in Chinese))
    [15] 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 Guan-ting. Analytical solutions for problems of 1D orthorhombic quasicrystal with semi-infinite crack[J].Applied Mathematics and Mechanics,2015,36(9): 945-955.(in Chinese))
  • 加载中
计量
  • 文章访问数:  736
  • HTML全文浏览量:  34
  • PDF下载量:  696
  • 被引次数: 0
出版历程
  • 收稿日期:  2015-12-24
  • 修回日期:  2016-02-16
  • 刊出日期:  2016-07-15

目录

    /

    返回文章
    返回