不同载荷作用下Ⅲ型动态裂纹的解析解  

ANALYTICAL SOLUTIONS OF MODE Ⅲ DYNAMIC CRACK UNDER THE ACTION OF DIFFERENT LOADS

作　　者：吕念春[1,2] 李新刚[2] 程云虹 程靳[4] 

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]哈尔滨工程大学建筑工程学院,哈尔滨150001 [4]哈尔滨工业大学航天工程与力学系,哈尔滨150001

出　　处：《工程力学》2010年第A01期34-38,共5页Engineering Mechanics

基　　金：中国博士后基金项目(2003033378);国家自然科学基金项目(30205035);黑龙江省自然科学基金重点项目(ZJG04-08)

摘　　要：通过复变函数论的方法,对Ⅲ型动态裂纹坐标原点受阶跃载荷、常数载荷作用下的问题分别进行研究。采用自相似函数的方法可以获得应力、位移、应力强度因子、应变能密度因子、应变能释放率和位错分布函数的解析解。应用该法可以迅速地将所讨论的问题转化为Riemann-Hilbert问题,并可以相当简单地得到问题的闭合解。利用这些解并采用叠加原理,就可以很容易地求得任意复杂问题的解。By the theoretical approaches of complex functions,the problems concerning mode Ⅲ dynamic crack under the action of unit-step loads and constant loads located at the origin of the coordinates respectively,are researched.Analytical solutions of stresses,displacements,stress intensity factors,strain energy density factors,strain energy release rates and dislocation distribution functions are acquired by means of self-similar functions.The problems considered can be very readily translated into Riemann-Hilbert problems and their closed solutions are attained rather straightforward in terms of this technique.Utilizing those solutions and superposition theorem,the solutions of arbitrarily complex problems can be attained.

关 键 词：复变函数 Ⅲ型动态裂纹 自相似函数 解析解 闭合解 

分 类 号：O346.1[理学—固体力学]