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

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

宁夏大学数学统计学院, 银川 750021

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
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- 文章访问数: 1805
- HTML全文浏览量: 394
- PDF下载量: 292
- 被引次数: 0
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

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

School of Mathematics and Statistics, Ningxia University,Yinchuan 750021,P.R.China

Funds: The National Natural Science Foundation of China(11561055;11762017;11762016)

摘要

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.
- 一维六方压电准晶 /
- Schwarz-Christoffel变换 /
- 正n边形孔口 /
- 裂纹 /
- 等效强度因子
Abstract: The heat conduction is a common problem in engineering practice. Compared with those of isotropic materials, the heat conduction problem of anisotropic materials is more complicated, so it is of great significance to accurately predict the internal temperature distribution. The numerical manifold method (NMM) was developed to solve typical continuous and discontinuous heat conduction problems in anisotropic materials. According to the governing differential equation, boundary conditions and variational principles, the NMM discrete equations for such problems were derived. Several representative examples involving continuous and discontinuous situations were analyzed with the uniform mathematical cover independent of all physical boundaries. The results prove the feasibility and accuracy of the method and indicate that the NMM can simulate the heat conduction problem of anisotropic materials well. Besides, the influences of the material properties and crack configurations on the temperatures were also investigated.
- 1D hexagonal piezoelectric quasicrystal /
- Schwarz-Christoffel transformation /
- regular n-polygon hole /
- crack /
- effective intensity factor

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参考文献(36)

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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

doi: 10.21656/1000-0887.400334

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).

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

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留言板

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

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).

计量

出版历程

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

计量

出版历程

目录

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).