一维正方准晶垂直于准周期方向具有不对称共线裂纹的圆形孔口问题  

The Problem of a Circular Hole with Asymmetry Collinear Cracks Perpendicular to Quasic-periodic Direction in One-dimensional Orthorhombic Quasicrystals

作　　者：刘莹[1] 刘官厅[1] 

机构地区：[1]内蒙古师范大学数学科学学院,内蒙古呼和浩特010022

出　　处：《数学的实践与认识》2012年第4期124-132,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(10761005);内蒙古自然科学基金(2009MS0102)

摘　　要：利用复变函数方法,通过构造广义保角映射,研究了一维正方准晶垂直于准周期方向具有不对称共线裂纹的圆形孔口问题,给出了各应力分量在象平面的复表示,并得到该裂纹尖端的应力强度因子.在极限情形下,给出一维正方准晶中具有对称共线裂纹的圆形孔口,带单裂纹的圆形孔口和Griffith裂纹在裂纹尖端的应力强度因子.By proposing a generalized conformal mapping and using the complex variable function method, the problem about a circular hole with asymmetry collinear cracks perpendicular to quasic-periodic direction in one-dimensional orthorhombic quasicrystals was considered. Complex representation of stress was derived in mathematical plane,and the solutions of the SIFs at the crack tip were obtained. Under the conditions of limitation, the solutions of the SIFs at the crack tip of a circular hole with symmetrical collinear cracks, a circular hole with one crack and the Griffith crack were found out.

关 键 词：一维正方准晶 具有不对称共线裂纹的圆形孔口 应力强度因子 

分 类 号：O753.3[理学—晶体学]