一维六方准晶的两类周期接触问题  

2 Kinds of Periodic Contact Problems of 1D Hexagonal Quasicrystals

作　　者：马小丹[1] 李星[1] 

机构地区：[1]宁夏大学数学计算机学院,银川750021

出　　处：《应用数学和力学》2016年第7期699-709,共11页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11362018;11261045;11261041);高等学校博士学科点专项科研基金(20116401110002)~~

摘　　要：利用复变函数方法讨论了一维六方准晶非周期平面的两类周期接触问题,即无摩擦周期接触以及半平面粘结周期接触问题.利用Hilbert核积分公式,得到了两类周期接触问题封闭形式的解.对于无摩擦周期接触问题,给出了3种常见压头(周期直水平基底、周期直倾斜基底、周期圆基底)作用下接触应力的显式表达式;对于半平面粘结周期接触问题,给出了实际工程中常见的边界上有尖劈形周期位移情况下应力的解析表达式.当忽略相位子场的贡献时,结果与正交各向异性材料周期接触问题的相应结果一致.With the complex variable method,2 kinds of periodic contact problems（ the frictionless and the adhesive periodic contact problems） of 1D hexagonal quasicrystals in the aperiodic plane were discussed.Based on the Hilbert kernel integral formula,the closed-form solutions were obtained to the 2kinds of periodic contact problems. In the frictionless case,the explicit solutions of contact stresses were given under the actions of 3 common basal punches（ the straight horizontal,the straight inclined and the circular basal punches）. In the adhesive case,the analytic solutions of contact stresses were given with the wedge-shaped periodic displacement at the contact boundary. If the effect of the phason field is neglected,the obtained results will match well with the corresponding solutions to the periodic contact problems of orthogonal anisotropic materials.

关 键 词：一维六方准晶 非周期平面 周期接触问题 复变函数方法 Hilbert核积分公式 

分 类 号：O343[理学—固体力学]