圆形孔口裂纹的反平面剪切问题的解析解  

Analytic Solutions of the Anti-plane Problems about a Circular Hole with a Crack

作　　者：杨娟[1,2] 李星[1] 

机构地区：[1]宁夏大学数学计算机学院,宁夏银川750021 [2]宁夏大学民族预科教育学院,宁夏银川750002

出　　处：《数学的实践与认识》2014年第21期245-249,共5页Mathematics in Practice and Theory

基　　金：国家自然科学基金(10962008;51061015);高等学校博士学科点专项基金资助课题(博导类;20116401110002)

摘　　要：利用复变函数方法,通过构造保角映射,研究了带裂纹的圆形孔口的反平面剪切问题,给出了Ⅲ型裂纹问题的应力强度因子.在极限情形下,求得Griffith裂纹在裂纹尖端处应力强度因子,这与已有的结果完全一致.最后数值算例给出了半经和裂纹长度对应力强度因子的影响.By means of the complex variable function method and using the technique of conformal mapping, the anti-plane shear problem about a circular hole with a straight crack is investigated and the solution of the stress intensity factors （SIFs） of mode III is found ＂out. Under the condition of limitation, the solutions of the Griffith crack at the crack tip is obtained, which matchs with the classical result. The numerical results demon strate the effect of the radius and crack length on the stress intensity factor.

关 键 词：圆孔裂纹 保角变换 反平面剪切 应力强度因子 复变函数方法 

分 类 号：O346.1[理学—固体力学]