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一维六方压电准晶中正n边形孔边裂纹的反平面问题

刘兴伟 李星 汪文帅

刘兴伟, 李星, 汪文帅. 一维六方压电准晶中正n边形孔边裂纹的反平面问题[J]. 应用数学和力学, 2020, 41(7): 713-724. doi: 10.21656/1000-0887.400334
引用本文: 刘兴伟, 李星, 汪文帅. 一维六方压电准晶中正n边形孔边裂纹的反平面问题[J]. 应用数学和力学, 2020, 41(7): 713-724. doi: 10.21656/1000-0887.400334
LIU Xingwei, LI Xing, WANG Wenshuai. The Anti-Plane Problem of Regular n-Polygon Holes With Radial Edge Cracks in 1D Hexagonal Piezoelectric Quasicrystals[J]. Applied Mathematics and Mechanics, 2020, 41(7): 713-724. doi: 10.21656/1000-0887.400334
Citation: LIU Xingwei, LI Xing, WANG Wenshuai. The Anti-Plane Problem of Regular n-Polygon Holes With Radial Edge Cracks in 1D Hexagonal Piezoelectric Quasicrystals[J]. Applied Mathematics and Mechanics, 2020, 41(7): 713-724. doi: 10.21656/1000-0887.400334

一维六方压电准晶中正n边形孔边裂纹的反平面问题

doi: 10.21656/1000-0887.400334
基金项目: 国家自然科学基金(11561055;11762017;11762016)
详细信息
    作者简介:

    刘兴伟(1993—),男,硕士生(Email: nxu0258@163.com);汪文帅(1980—),男,博士(通讯作者. Email: wws@nxu.edu.cn).

  • 中图分类号: O357.41

The Anti-Plane Problem of Regular n-Polygon Holes With Radial Edge Cracks in 1D Hexagonal Piezoelectric Quasicrystals

Funds: The National Natural Science Foundation of China(11561055;11762017;11762016)
  • 摘要: 利用复变函数方法和Schwarz-Christoffel(SC)变换, 构造了保形映射函数, 研究了一维六方压电准晶中正n边形孔边裂纹的反平面问题.首先由一维六方压电准晶反平面问题的本构方程、平衡方程和几何方程推导得出其控制方程.在电不可导通边界条件下, 应用Cauchy积分公式, 得出任意正n边形孔边裂纹尖端附近应力强度因子和电位移强度因子的解析解, 并针对n=3,5,6时, 给出数值算例, 可以看出这些特殊情形可退化为已有的结果.研究结果表明:等效场强度因子K的值随着孔边长a和裂纹长度L/a的增加而增大; 孔洞的尺寸对等效场强度因子K的影响特别显著, 易导致破坏.该文所给结果对计算等效强度因子具有一般性, 适用于任意正n边形孔边裂纹的求解问题, 从而为工程力学、材料的制备和应用等提供了良好的理论依据.
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出版历程
  • 收稿日期:  2019-11-06
  • 修回日期:  2020-05-12
  • 刊出日期:  2020-07-01

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