带任意裂纹的一维六方准晶弹性半平面第一基本问题  

First Fundamental Problem of One-dimensional Hexagonal Quasicrystals Half-plane with Arbitrary Cracks

作　　者：张炳彩[1] 赵雪芬[1] 张来萍 ZHANG Bing-cai;ZHAO Xue-fen;ZHANG Lai-ping(Xinhua College,Ningxia University,YinChuan 750021,China)

机构地区：[1]宁夏大学新华学院,宁夏银川750021

出　　处：《数学的实践与认识》2022年第4期156-163,共8页Mathematics in Practice and Theory

基　　金：宁夏大学新华学院科学研究基金项目经费资助(19XHKY07)。

摘　　要：研究了周期平面内含任意裂纹的一维六方准晶的弹性半平面第一基本问题.首先借助保角变换将半平面第一基本问题转化为单位圆内带任意裂纹的第一基本问题;再利用复变函数方法将求有界域内的弹性平衡问题转化为奇异积分方程的求解,并证明方程是唯一可解的.该问题的求解为研究工程断裂问题提供了理论方法.The first fundamental problem of elastic half plane of one-dimensional hexagonal quasicrystals with arbitrary cracks in the periodic plane is studied.First,conformal transformation is used to transform the first fundamental problem of a half-plane into the first fundamental problem with arbitrary cracks in the unit circle.Then,complex function method is used to transform elastic equilibrium problem in the bounded domain into the singular integral equation.Furthermore,the unique solvability of the equation is proved.It is provided a theoretical method for studying the engineering fracture problem.

关 键 词：一维六方准晶 裂纹 保角变换 复变函数方法 

分 类 号：O346.1[理学—固体力学] O753.3[理学—力学]