| 一维正方准晶沿准周期方向穿透的抛物线裂纹问题 |
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| 引用本文： | 林芳,刘官厅.一维正方准晶沿准周期方向穿透的抛物线裂纹问题[J].数学的实践与认识,2017(3):178-183. |
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| 作者姓名： | 林芳 刘官厅 |
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| 作者单位： | 内蒙古师范大学数学科学学院,内蒙古呼和浩特,010022 |
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| 基金项目： | 国家自然科学基金(11262017;11462020)，内蒙古师范大学“十百千人才工程”研究项目(RCPY-2-2012-K-035)，重大培育专项基金项目(2014ZD03)，内蒙古师范大学研究生科研创新基金项目资助(CXJJS15074) |
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| 摘 要： | 利用广义复变函数方法研究了一维正方准晶材料中周期平面的抛物线裂纹问题,通过建立广义保角映射,将物理平面的抛物线裂纹外映射到数学平面里的单位圆内.得出了声子场和相位子场的应力分量在像平面下的复表示,并且得到了抛物线裂纹尖端的应力强度因子.并在特殊情况下,所得结果与Griffith裂纹的结果一致.
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| 关 键 词： | 一维正方准晶材料 抛物线裂纹 广义保角映射 应力强度因子 |
The Problem of a Parabolic Crack Along the Quasic-periodic Direction in One-dimensional Orthorhombic Quasicrystals |
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| LIN Fang,LIU Guan-ting.The Problem of a Parabolic Crack Along the Quasic-periodic Direction in One-dimensional Orthorhombic Quasicrystals[J].Mathematics in Practice and Theory,2017(3):178-183. |
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| Authors: | LIN Fang LIU Guan-ting |
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| Abstract: | In this paper,by using the generalized complex variable function method,the problem about a parabolic crack in one-dimensional orthorhombic quasicrystals periodical plane was considered.To solve this problem by proposing the generalized conformal mapping the exterior of the parabolic crack in the physical plane was mapped onto the inner of the a unit circle in the mathematical plane.Complex representation of stress in the phonon field and phason field was got in the mathematical plane and the parabolic crack of SIFs at the crack tip were obtained.Under the special condition the result is similar to the SIFs at Griffith crack. |
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| Keywords: | one-dimensional orthorhombic quasicrystals materials parabolic crack generalized conformal mapping stress intensity factor |
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