一维六方准晶中星形静态裂纹和运动裂纹的解析解  

Analytic Solutions of Star Stationary and Moving Cracks Problem in One-Dimensional Hexagonal Quasicrystal

作　　者：赵雪芬[1,2] 李星[1] 

机构地区：[1]宁夏大学数学计算机学院,宁夏银川750021 [2]宁夏大学新华学院,宁夏银川750021

出　　处：《力学季刊》2015年第4期645-654,共10页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金(11362018);宁夏大学新华学院科学研究基金项目(14XHXY02);宁夏高等学校科学研究项目(NGY2015182)

摘　　要：利用复变函数方法研究了一维六方准晶中星形静态裂纹和运动裂纹的反平面剪切问题,得到了星形裂纹尖端处应力强度因子和动应力强度因子的解析解.当裂纹条数给定时,由此可得到直线裂纹,Griffith裂纹,共点均匀分布三裂纹,对称十字形裂纹,米字型裂纹(对称八裂纹)静力学和动力学问题的解析解.当k=4时,用数值算例讨论了声子场-相位子场耦合系数和裂纹运动速度对动应力强度因子的影响.当速度趋于0时,运动裂纹的解可以退化为静态裂纹的解.By means of complex variable method,the anti-plane shear problems of star stationary and moving cracks in one-dimensional hexagonal quasicrystal were discussed,and the analytic solutions of stress intensity factors and dynamic stress intensity factors at star crack tips were obtained. When the number of cracks are given,the analytic solutions of statics and dynamics of straight crack,Griffith crack,three concurrent uniform distribution straight cracks,symmetry cross cracks and eight symmetry straight can be obtained from these. When k=4,the impact of coupling coefficient and crack velocity on dynamic stress intensity factor was discussed using numerical examples. When crack velocity approaches to 0,the solutions of moving cracks can degenerate to those of stationary cracks.

关 键 词：一维六方准晶 星形静态裂纹 星形运动裂纹 应力强度因子 动应力强度因子 复变函数方法 

分 类 号：O343[理学—固体力学]