一维正方准晶中半无限裂纹问题的解析解

高健; 刘官厅

doi:10.3879/j.issn.1000-0887.2015.09.006

一维正方准晶中半无限裂纹问题的解析解

doi: 10.3879/j.issn.1000-0887.2015.09.006

高健¹,
刘官厅²

¹内蒙古民族大学数学学院, 内蒙古通辽 028043;²内蒙古师范大学数学科学学院, 呼和浩特 010022

基金项目: 国家自然科学基金（11262017）

详细信息

作者简介:
高健（1986—），男，内蒙古通辽人，讲师，硕士（通讯作者. E-mail: gaojianimun@yeah.net）；刘官厅（1966—），男，内蒙古包头人，教授，博士，博士生导师（E-mail: guantingliu@imnu.cn）.

中图分类号: O346.1
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出版历程
- 收稿日期: 2015-01-14
- 修回日期: 2015-04-26
- 刊出日期: 2015-09-15

Analytical Solutions to Problems of 1D Orthorhombic Quasicrystal With SemiInfinite Cracks

GAO Jian¹,
LIU Guan-ting²

¹College of Mathematics, Inner Mongolia University for the Nationalities, Tongliao, Neimenggu 028043, P.R.China;²College of Mathematical Science, Inner Mongolia Normal University, Hohhot 010022, P.R.China

Funds: The National Natural Science Foundation of China(11262017)

摘要

摘要: 运用广义复变函数方法，通过构造适当的广义保角映射，研究了含有沿准周期方向穿透的半无限裂纹的一维正方准晶的反平面弹性问题，给出了在部分裂纹面上受均匀面外剪切时应力场和裂纹尖端应力强度因子的解析解.将此方法进一步推广到半无限裂纹垂直于一维正方准晶的准周期方向穿透的情形中，得到了相应的平面弹性问题的解析解.当准晶体的对称性增加时，还可以得出一维四方准晶相应问题的解析解.
- 一维正方准晶 /
- 半无限裂纹 /
- 广义保角映射 /
- 应力场 /
- 应力强度因子
Abstract: The anti-plane elasticity problem of the 1D orthorhombic quasicrystal with a semi-infinite crack penetrating along the quasiperiodic direction was investigated through introduction of a new generalized conformal mapping and with the generalized complex variable method. The analytical solutions of the stress fields and the stress intensity factors under the action of the uniform out-of-plane shear load on the partial crack surface were obtained. In addition, this method was applied to solve the plane elasticity problem of the 1D orthorhombic quasicrystal with a semi-infinite crack penetrating perpendicular to the quasiperiodic direction and the analytical solutions were derived. Under the condition of higher symmetry, the analytical solutions to the corresponding problem of the 1D tetragonal quasicrystal were also obtained.
- 1D orthorhombic quasicrystal /
- semi-infinite crack /
- generalized conformal mapping /
- stress field /
- stress intensity factor

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参考文献(24)

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一维正方准晶中半无限裂纹问题的解析解

doi: 10.3879/j.issn.1000-0887.2015.09.006

作者简介:
高健（1986—），男，内蒙古通辽人，讲师，硕士（通讯作者. E-mail: gaojianimun@yeah.net）；刘官厅（1966—），男，内蒙古包头人，教授，博士，博士生导师（E-mail: guantingliu@imnu.cn）.

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Analytical Solutions to Problems of 1D Orthorhombic Quasicrystal With SemiInfinite Cracks

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留言板

一维正方准晶中半无限裂纹问题的解析解

doi: 10.3879/j.issn.1000-0887.2015.09.006

作者简介: 高健（1986—），男，内蒙古通辽人，讲师，硕士（通讯作者. E-mail: gaojianimun@yeah.net）；刘官厅（1966—），男，内蒙古包头人，教授，博士，博士生导师（E-mail: guantingliu@imnu.cn）.

计量

出版历程

Analytical Solutions to Problems of 1D Orthorhombic Quasicrystal With SemiInfinite Cracks

计量

出版历程

目录

作者简介:
高健（1986—），男，内蒙古通辽人，讲师，硕士（通讯作者. E-mail: gaojianimun@yeah.net）；刘官厅（1966—），男，内蒙古包头人，教授，博士，博士生导师（E-mail: guantingliu@imnu.cn）.