含裂纹多材料反平面分析的解析奇异单元  

A singular finite element of multi-material crack problems under elastic antiplane shear deformation

作　　者：姚伟岸[1] 李翔[1] 胡小飞[1] 张兆军[1] YAO WeiAn LI Xiang HU XiaoFei ZHANG ZhaoJun(State Key Laboratory of Structural Analysis for Industial Equipment, Dalian University of Technology, Dalian 116024, China)

机构地区：[1]大连理工大学工业装备结构分析国家重点实验室,大连116024

出　　处：《中国科学：技术科学》2016年第12期1225-1231,共7页Scientia Sinica(Technologica)

基　　金：国家自然科学基金(编号:11372065)资助项目

摘　　要：含裂纹多材料反平面问题是一个典型的III型断裂问题,已有的文献给出了其极坐标辛体系下的辛本征解,并讨论了其裂纹尖端的应力奇异性阶次.本文在此基础上,首先补充给出界面有外力作用时其非齐次边界条件所对应的特解,然后利用辛本征解和特解构造出相关问题分析的一类解析奇异单元.将所提出的奇异单元与外部的常规单元相结合,就可用于多材料III型断裂问题的分析,并直接给出应力强度因子的数值结果.数值算例表明,本方法具有很好的求解精度,是相关问题分析的一个非常有效的数值方法.Multi-material antiplane crack problem is a typical mode III crack problem, of which the symplectic eigen-solutions under polar coordinate system and the stress singularity order at the crack tip have been reported in existing literatures. Based on the existing works, the special solution corresponding to the non-homogeneous boundary condition on crack surfaces is derived in this study, and then a symplectic analytical singular element（SASE） is constructed using the symplectic eigen-solutions and the special solution to deal with the related problems. Combining the proposed SASE with conventional finite elements, the multi-material mode III crack problems can be solved and the numerical results of stress intensity factors（SIF） can be calculated directly. Numerical examples show that the proposed method possesses high solving accuracy as well as high efficiency for the analysis of the discussed problem.

关 键 词：辛弹性力学 奇异单元 反平面问题 多材料裂纹 应力强度因子 

分 类 号：O346.1[理学—固体力学]