一维六方准晶非周期半平面的第一周期基本问题  

The First Periodic Fundamental Problem for a Semi-infinite Aperiodical Plane in the One-dimensional Hexagonal Quasicrystals

作　　者：时朋朋[1,2] 崔江彦[1] 李星[1] 

机构地区：[1]宁夏大学数学计算机学院,银川750021 [2]西安电子科技大学机电工程学院,西安710071

出　　处：《工程数学学报》2014年第4期545-556,共12页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11362018;41204041;11261045);中央高校基本科研业务费专项资金(JB142001-2);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一维六方准晶非周期半无限平面的第一周期基本问题,周期问题是指非周期半无限平面内的应力、应变和边界条件关于垂直于准周期方向的轴是周期的,并且假定应力是有界的,应用Hilbert核积分公式得到问题封闭形式的解.最后给出实际工程常见的周期均匀压载作用和剪切载荷作用下应力函数的解析表达式.当忽略相位子场的贡献,本文结果退化为各向异性材料已有的相关结果.Based on the complex variable method, the first periodic fundamental problem for a semi-infinite aperiodical plane in the one-dimensional hexagonal quasicrystals is discussed in this paper. The periodic problem means that the stresses, the displacements and the boundary conditions in the aperiodical plane are assumed to be periodic for the axis which is perpendicular to the quasiaperiodical direction, and furthermore, the stresses are assumed to be bounded at infinity. By using the Hilbert kernel integral formula, the solutions are expressed in closed forms. Finally, two cases of this problem which are common in engineering construction are studied. By ignoring the contribution of the phanon field, the results can be degenerated into the well-known results for the anisotropic materials.

关 键 词：一维六方准晶 非周期平面 周期载荷 复变函数法 唯一可解性 

分 类 号：O343.1[理学—固体力学]