幂函数型曲线裂纹平面问题的一般解  

General Solutions of Plane Problem for Power Function Curved Cracks

作　　者：郭俊宏[1] 袁泽帅[1] 卢子兴[1] 

机构地区：[1]北京航空航天大学固体力学研究所,北京100191

出　　处：《应用数学和力学》2011年第5期533-540,共8页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10932001;11072015;10761005);北京市教育委员会共建项目建设计划资助项目(KZ201010005003);高等学校博士学科点专项科研基金资助项目(201011021100167)

摘　　要：通过构造一个新的、精确的和通用的保角映射,利用Muskhelishvili复势法研究了任意自然数次幂的幂函数型曲线裂纹的平面弹性问题,给出了远处受单向拉伸载荷下裂纹尖端Ⅰ型和Ⅱ型应力强度因子的一般解.当幂次取不同的自然数时,可以退化为若干已有的结果.通过数值算例,讨论了幂函数型曲线裂纹的系数、幂次及在x轴上的投影长度对Ⅰ型和Ⅱ型应力强度因子的影响规律.A new,exact and universal conformal mapping was proposed.Using the Muskhelishvili＇s complex potential method,the plane elasticity problem of power function curved cracks with an arbitrary power of natural number was investigated and the general solutions of stress intensity factors（SIFs） for mode Ⅰ and mode Ⅱ at the crack tip were obtained under the remotely uniform tensile loads.The present results can be reduced to the well-known solutions when the power of power function is prescribed to different natural numbers.Numerical examples are conducted to reveal the effects of opening orientation,opening size,power and projected length along x-axis of the power function curved crack on the SIFs for mode Ⅰ and mode Ⅱ.

关 键 词：幂函数型曲线裂纹 保角映射 复变函数 应力强度因子 平面问题 

分 类 号：O346.1[理学—固体力学]