一维六方准晶粘结接触问题的复变函数方法（英文）  

The adhesive contact problem in one-dimensional hexagonal quasicrystals with complex variable function method

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,银川750021 [2]宁夏大学新华学院,银川750021

出　　处：《上海师范大学学报（自然科学版）》2016年第3期305-312,共8页Journal of Shanghai Normal University(Natural Sciences)

基　　金：Natural Science Foundation of China(11362018,11261045,11261401);Pecialized Research Fund for the Doctoral Program of Higher Education of China(20116401110002);Science and Technology Research Project of Ningxia High School(NGY2015182)

摘　　要：本文考虑了一维六方准晶非周期平面的粘结接触问题.利用复变函数的方法,把粘结接触问题转化为Riemann-Hilbert边值问题.通过边值问题的求解,得到了刚性平底压头作用下应力函数和接触应力的显式表达式.结果表明:(1)接触位移与压入载荷成比例关系;(2)接触应力在接触边缘有振荡型奇异性.由于一维六方准晶声子场与相位子场的耦合性,接触问题压头下方接触应力分布不同于弹性体中应力分布的结果.当忽略相位子场作用时,所得结果与弹性材料相应结果一致.This paper considers the adhesive contact problem in aperiodical plane of one-dimensional hexagonal quasicrystals. By complex variable method, the adhesive contact problem is converted into a Riemann-Hilbert boundary problem. By solving that, we obtain the explicit expressions of stress functions and contact stress for a rigid flat punch. The results show that： （1） the contact displacement is proportional to the indentation force under a flat rigid punch; （2） The contact stress exhibits the oscillatory singularities at the edge of the contact zone. Because phonon field and phason field are coupled in one-dimensional hexagonal quasicrystals, the distribution of contact stress under punch is different from the results of contact problems in the classical elasticity theory. Without the contribution of phason field, the above solutions degenerate into the classical ones. Here is the abstract of your article.

关 键 词：一维六方准晶 非周期平面 粘结接触问题 奇异性 RIEMANN-HILBERT边值问题 

分 类 号：O346.1[理学—固体力学]