集中力作用下一维六方准晶双材料界面共线裂纹反平面问题  

Antiplane Problem of Collinear Cracks Between One Dimensional Hexagonal Quasicrystal Bi-Material Interface Under Concentrated Forces

作　　者：赵雪芬 马园园 卢绍楠 ZHAO Xue-fen;MA Yuan-yuan;LU Shao-nan(School of Information Engineering,Ningxia University,Yinchuan 750021,China;School of Mathematical Statistics,Ningxia University,Yinchuan 750021,China)

机构地区：[1]宁夏大学信息工程学院,宁夏银川750021 [2]宁夏大学数学统计学院,宁夏银川750021

出　　处：《数学的实践与认识》2025年第2期209-220,共12页Mathematics in Practice and Theory

基　　金：国家自然科学基金(12062021);宁夏自然科学基金项目(2024AAC03008);宁夏大学新华学院院级科学研究基金项目(23XHKY01)。

摘　　要：界面裂纹对准晶双材料的力学性能有极大的影响,研究准晶双材料界面裂纹断裂问题具有重要的理论意义和实际应用价值.文章利用复分析理论中分离复势函数奇性主部以及解析延拓复势函数的方法,分析了一维六方准晶双材料界面处共线裂纹在集中力作用下的反平面弹性断裂问题,得到了问题的一般解.在施加不同类型集中或均布载荷条件下,求出了准晶双材料界面含单条和两条裂纹时应力强度因子(包括声子场和相位子场)的精确解.数值结果部分分析研究了耦合系数之比、外载荷和集中力作用位置对应力强度因子的影响.该研究结果对准晶双材料界面抗断裂优化设计有一定参考价值.Interface cracks have a great influence on the mechanical properties of quasicrystal bi-material.Therefore,it is of great theoretical and practical significance to study the fracture of quasicrystal bi-material with interface cracks.By using the method of separating the singular principal parts of the complex potential function and analytic continuation in complex analysis theory,the anti-plane elastic fracture problem of collinear cracks at the interface of one-dimensional hexagonal quasicrystal bi-material under concentrated force was analyzed,and the general solutions of the problem were obtained.The exact solutions for the stress intensity factors(including phonon field and phason field)of quasicrystal bi-material with single and two cracks at the interface were derived under different types of concentrated or uniformly distributed loads.The numerical results analyzed and studied the effects of external load,coupling coefficient and the position of concentrated force on stress intensity factors.The conclusions are useful for the optimal design of interface fracture resistance of quasicrystal bi-material.

关 键 词：一维六方准晶双材料 共线界面裂纹 应力强度因子 奇性主部分析 解析延拓方法 

分 类 号：O17[理学—数学]