非对称Ⅲ型裂纹表面受运动载荷的动态扩展问题  

Dynamic Propagation Problems Concerning the Surfaces of Asymmetrical Mode Ⅲ Crack Subjected to Moving Loads

作　　者：吕念春[1] 程云虹[2] 李新刚[3] 程靳[3] 

机构地区：[1]沈阳理工大学材料科学与工程学院,沈阳110168 [2]东北大学土木工程系,沈阳110006 [3]哈尔滨工业大学航天工程与力学系,哈尔滨150001

出　　处：《应用数学和力学》2008年第10期1161-1171,共11页Applied Mathematics and Mechanics

基　　金：the Post-Doctoral Science Foundation of China(No.2005038199);the Natural Science Foundation of Heilongjiang Province of China(No.ZJG04-08)

摘　　要：通过复变函数论的方法,对非对称Ⅲ型裂纹表面受运动载荷的动态扩展问题进行了研究.采用自相似函数的方法可以获得解析解的一般表达式.应用该法可以迅速地将所讨论的问题转化为Riemann-Hilbert问题,并求得了非对称扩展裂纹表面分别受到常数运动载荷、阶跃运动载荷作用下的应力、位移和动态应力强度因子解析解.利用这些解并采用叠加原理,就可以求得任意复杂问题的解.By the measures of the theory of complex functions, dynamic propagation problems conceming the surfaces of asymmetrical mode Ⅲ crack subjected to moving loads were investigated. General representations of analytical solutions were obtained by the approaches of serf-similar functions. The problems dealt with can be facilely transformed into Riemarm-Hilbert problems by this technique, and analytical solutions of the stress, the displacement and dynamic stress intensity factor under the action of constant moving loads and unit-step moving loads situated at the surfaces of asymmetrical extension crack, respectively, are acquired, By application of those solutions gained and superposition principle, the solutions of discretionarily intricate problems can be attained.

关 键 词：复变函数 非对称Ⅲ型裂纹 动态扩展 自相似函数 解析解 

分 类 号：O346.1[理学—固体力学]