| 一维六方准晶压电材料中幂函数型曲线裂纹的反平面问题 |
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| 引用本文： | 林芳,刘官厅.一维六方准晶压电材料中幂函数型曲线裂纹的反平面问题[J].数学的实践与认识,2017(7):216-220. |
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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(CXJJS15074) |
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| 摘 要： | 依据一维六方准晶压电材料反平面问题的基本方程,利用复变函数方法,通过引入适当的保角映射,研究了一维六方准晶压电材料中幂函数型曲线裂纹的反平面问题,并利用Cauchy积分理论,得到电不可通和电可通边界条件下的应力场和位移场的复表示以及裂纹尖端场强度因子的解析表达式.
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| 关 键 词： | 一维六方准晶压电材料 幂函数型曲线裂纹 保角映射 场强度因子 |
Anti-Plane Analysis of Power Function Curved Crack in Piezoelectricity of One-Dimensional Hexagonal Quasicrystals |
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| LIN Fang,LIU Guan-ting.Anti-Plane Analysis of Power Function Curved Crack in Piezoelectricity of One-Dimensional Hexagonal Quasicrystals[J].Mathematics in Practice and Theory,2017(7):216-220. |
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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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