一维正方准晶非周期平面弹性有限摩擦接触问题  

The Frictional Contact Problem for Aperiodical Plane in One-Dimensional Orthorhombic Quasicrystals

作　　者：赵雪芬[1,2] 李星 ZHAO Xuefen;LI Xing(Xinhua College, Ningxia University, Yinchuan 750021, Ningxia, China;School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, Ningxia, China)

机构地区：[1]宁夏大学新华学院,宁夏银川750021 [2]宁夏大学数学统计学院,宁夏银川750021

出　　处：《力学季刊》2019年第1期183-192,共10页Chinese Quarterly of Mechanics

基　　金：宁夏自然科学基金(NZ17042;NZ17009)

摘　　要：利用平面弹性复变方法和解析函数边值理论,讨论了一维正方准晶材料非周期平面上的有限摩擦接触问题.基于一维正方准晶非周期平面内应力和位移分量的广义复变函数表示,有限摩擦接触问题被转换为Riemann-Hilbert边值问题.对于平底压头,得到了压头下方接触应力的显式表达式,并用数值算例分析了摩擦系数和声子场-相位子场耦合系数对压头下方接触应力分布的影响.结果表明:(1)摩擦系数对接触应力大小和分布规律的影响几乎可以忽略;(2)耦合系数对接触应力的分布规律无影响,对声子场接触应力值的影响微乎其微,对相位子场接触应力大小的影响比较明显.特殊条件下,本文所得结论可退化为一维四方准晶和一维六方准晶非周期平面内有限摩擦接触问题的解.当摩擦系数等于0时,还可以得到对应无摩擦接触问题的解.By means of plane elastic complex method and theory of boundary value of analytic function, the frictional contact problem for aperiodical plane in one-dimensional orthorhombic quasicrystals was discussed. Based on the generalized complex function representation of the stress and displacement components in aperiodical plane, the frictional contact problem was converted into Riemann-Hilbert boundary value problem. Especially, for the flat punch, the explicit expressions of contact stress under a rigid punch were obtained, and the effects of the friction coefficient and the phonon-phason coupling coefficients on contact stress distribution were studied by numerical examples. The results showed that:(1) the influence of the friction coefficient on the contact stress is barely perceptible;(2) the phonon-phason coupling coefficients have nearly no efficacy on distributions of the phonon and phason field contact stress. The influence of coupling constants on the contact stress magnitude is barely perceptible in phone field, and is evident in phason field. As special cases, the results can be reduced to the solutions of the frictional contact problem in one-dimensional tetragonal and hexagonal quasicrystals. If the friction coefficient is equal to 0, the results can be degenerated into the solutions of frictionless contact problem in one-dimensional orthorhombic quasicrystals.

关 键 词：一维正方准晶 非周期平面问题 有限摩擦接触问题 RIEMANN-HILBERT边值问题 

分 类 号：O343.8[理学—固体力学]