1维正方准晶的2类接触问题  

Two Kinds of Contact Problem in One-Dimensional Orthorhombic Quasicrystals

作　　者：赵雪芬[1,2] 

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：《江西师范大学学报（自然科学版）》2017年第4期379-384,共6页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11362018);宁夏高等学校科学技术研究课题(NGY2015182);宁夏大学新华学院科学研究基金(16XHKY01)资助项目

摘　　要：利用广义复变函数方法研究了1维正方准晶的2类接触问题,即有限摩擦接触和半平面粘结接触问题,得到了刚性平底压头作用下压头下方接触应力及接触位移的显式表达式.结果表明:(i)对于有限摩擦接触问题,接触应力在压头边缘呈现-1/2±θ阶奇异性,其中θ由准晶的弹性常数和摩擦系数确定;对于半平面粘结接触问题,接触应力在压头的边缘显现出-1/2±iε阶奇异性,其中ε由准晶的弹性常数确定;(ii)由数值算例可知,对于2类接触问题,接触应力在压头下方分布规律相似;接触位移与声子场作用力之间成正比例关系;接触应力在接触区边缘变化非常剧烈,且产生了应力集中现象.在一定条件下可得到1维4方和6方准晶2类接触问题的解.By using generalized complex variable method,two kinds of contact problems in one-dimensional orthorhombic quasicrystals are discussed. One kind of contact problem is the frictional one,the other is the adhesive one.Under the action of a flat rigid punch,the explicit expressions of contact stresses and contact displacements are obtained. The results show that contact stresses exhibit the singularities-1/2 ± θ for the frictional contact problem with θ determined by the elastic constants of the quasicrystal and the frictional factor,contact stresses exhibit the singularities-1/2 ± iε at the edge of the contact zone for the adhesive contact problem,where ε determine by the elastic constants of the quasicrystal. Numerical examples indicate that for two kinds of problems,the distribution regulations of the contact stress under the punch are similar,and the contact displacement is proportion to the applied force. It can be also obtained that the magnitude of the contact stress changes quickly and stress concentration phenomenon emerges in the edge of contact zone. As special cases,the conclusions can reduce to the solutions of two kinds of contact problems in one-dimensional tetragonal and hexagonal quasicrystals,respectively.

关 键 词：1维正方准晶 有限摩擦接触问题 半平面粘结接触 广义复变函数方法 

分 类 号：O346.3[理学—固体力学]