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

插值矩阵法分析正交各向异性板切口应力奇异性

葛仁余 程长征 杨智勇 牛忠荣

葛仁余, 程长征, 杨智勇, 牛忠荣. 插值矩阵法分析正交各向异性板切口应力奇异性[J]. 应用数学和力学, 2014, 35(4): 459-470. doi: 10.3879/j.issn.1000-0887.2014.04.011
引用本文: 葛仁余, 程长征, 杨智勇, 牛忠荣. 插值矩阵法分析正交各向异性板切口应力奇异性[J]. 应用数学和力学, 2014, 35(4): 459-470. doi: 10.3879/j.issn.1000-0887.2014.04.011
GE Ren-yu, CHENG Chang-zheng, YANG Zhi-yong, NIU Zhong-rong. Singularity Analysis for Notches in Orthotropic Composite Plates With the Interpolating Matrix Method[J]. Applied Mathematics and Mechanics, 2014, 35(4): 459-470. doi: 10.3879/j.issn.1000-0887.2014.04.011
Citation: GE Ren-yu, CHENG Chang-zheng, YANG Zhi-yong, NIU Zhong-rong. Singularity Analysis for Notches in Orthotropic Composite Plates With the Interpolating Matrix Method[J]. Applied Mathematics and Mechanics, 2014, 35(4): 459-470. doi: 10.3879/j.issn.1000-0887.2014.04.011

插值矩阵法分析正交各向异性板切口应力奇异性

doi: 10.3879/j.issn.1000-0887.2014.04.011
基金项目: 国家自然科学基金(11272111;11372049)
详细信息
    作者简介:

    葛仁余(1969—),男,合肥人,博士(通讯作者. E-mail: gerenyu@sina.com).

  • 中图分类号: O343.4

Singularity Analysis for Notches in Orthotropic Composite Plates With the Interpolating Matrix Method

Funds: The National Natural Science Foundation of China(11272111;11372049)
  • 摘要: 基于切口尖端附近区域位移场渐近展开,提出了分析正交各向异性复合材料板切口奇异性的新方法.将位移场的渐近展开式的典型项代入弹性板的基本方程,得到关于正交各向异性板切口奇异性指数的一组非线性常微分方程的特征值问题;再采用变量代换法,将非线性特征问题转化为线性特征问题,用插值矩阵法求解获得的正交各向异性板切口若干阶应力奇异性指数和相应特征函数.该法可由相应的特征角函数对板切口的平面应力和反平面奇异特征值加以区分,并将计算结果与现有结果对照,表明了该文方法的有效性.
  • [1] Li Y T, Song M. Method to calculate stress intensity factor of V-notch in bi-materials[J].Acta Mechanica Solida Sinica,2008,21(4): 337-346.
    [2] Williams M L. Surface stress singularities resulting from various boundary conditions in angular corners of plates under bending[C]// Proceedings of the First US National Congress of Applied Mechanics. Chicago, 1951: 325-329.
    [3] Sih G C, Paris P C, Erdogan F. Crack-tip, stress-intensity factors for plane extension and plate bending problems[J].Journal of Applied Mechanics,1962,29(2): 306-312.
    [4] Knowles J K, Wang N M. On the bending of an elastic plate containing a crack[J].Journal of Mathematics and Physics,1960,39(5): 223-236.
    [5] 柳春图. 承受弯曲的板在裂纹顶端附近的应力和变形[J]. 固体力学学报, 1983,9(3): 441-448.(LIU Chun-tu. Stresses and deformations near the crack tip for bending plate[J].Acta Mechanica Solida Sinica,1983,9(3): 441-448.(in Chinese))
    [6] Delate F, Erdogan F. The effect of transverse shear in a cracked plate under skew-symmetric loading[J].Journal of Applied Mechanics,1979,46(3): 618-624.
    [7] Murthy M V V, Raju K N, Viswanath S. On the bending stress distribution at the tip of a stationary crack from Reissner’s theory[J].International Journal of Fracture,1981,17(6): 537-552.
    [8] Boduroglu H, Erdogan F. Internal and edge cracks in a plate of finite width under bending[J].Journal of Applied Mechanics,1983,50(3): 621-629.
    [9] Sosa H A, Eischen J W. Computation of stress intensity factors for plate bending via a path-independent integral[J].Engineering Fracture Mechanics,1986,25(4): 451-462.
    [10] Hui C Y, Zehnder A T. A theory for the fracture of thin plates subjected to bending and twisting moments[J].International Journal of Fracture,1993,61(3): 211-229.
    [11] Young M J, Sun C T. Cracked plates subjected to out-of-plane tearing loads[J].International Journal of Fracture,1993,60(1): 1-18.
    [12] Su R K L, Leung A Y T. Mixed mode crack in Reissner plates[J].International Journal of Fracture,2001,107(3): 235-257.
    [13] Sih G C, Rice J R. The bending of plates of dissimilar materials with cracks[J].Journal of Applied Mechanics,1964,31(3): 477-482.
    [14] Sih G C. Flexural problems of cracks in mixed media[C]// Proceedings of the First International Conference on Fracture. Sendai, 1965,1: 391-409.
    [15] Ang D D, Williams M L. Combined stresses in an orthotropic plate having a finite crack[J].Journal of Applied Mechanics,1961,28(3): 372-378.
    [16] Sih G C, Chen E P.Cracks in Composite Materials [M].Mechanics of Fracture .6. Hague, Boston, London: Martinus Nijhoff Publishers,1981: 76-87.
    [17] Yuan F G, Yang S. Asymptotic crack-tip fields in an anisotropic plate subjected to bending, twisting moments and transverse shear loads[J].Composites Science and Technology,2000,60(12/13): 2489-2502.
    [18] Li J. Singularity analysis of near-tip fields for notches formed from several anisotropic plates under bending[J].International Journal of Solids and Structures,2002,39(23): 5767-5785.
    [19] 牛忠荣. 轴对称变厚度扁球壳的非线性弯曲问题[J]. 应用数学和力学, 1993,14(11): 971-978.(NIU Zhong-rong. Nonlinear bending of the shallow spherical shells with variable thickness under axisymmetrical loads[J].Applied Mathematics and Mechanics,1993,14(11): 971-978.(in Chinese))
    [20] NIU Zhong-rong, GE Da-li, CHENG Chang-zheng, YE Jian-qiao, Recho N. Evaluation of the stress singularities of plane V-notches in bonded dissimilar materials[J].Applied Mathematical Modelling,2009,33(3): 1776-1792.
    [21] CHENG Chang-zheng, NIU Zong-rong, Recho N. Effect of non-singular stress on the brittle fracture of V-notched structure[J].International Journal of Fracture,2012,174(2): 127-138.
  • 加载中
计量
  • 文章访问数:  880
  • HTML全文浏览量:  10
  • PDF下载量:  855
  • 被引次数: 0
出版历程
  • 收稿日期:  2013-08-08
  • 修回日期:  2013-09-24
  • 刊出日期:  2014-04-15

目录

    /

    返回文章
    返回