平面裂纹应力强度因子的半解析有限元法  

SEMI-ANALYTICAL FINITE ELEMENT METHOD FOR PLANE CRACK STRESS INTENSITY FACTOR

作　　者：王承强[1] 郑长良[1] 

机构地区：[1]大连理工大学工程力学系工业装备结构分析国家重点实验室,辽宁大连116023

出　　处：《工程力学》2005年第1期33-37,共5页Engineering Mechanics

基　　金：国家教育部博士点专项基金资助项目(20010141024);教育部留学回国人员科研启动基金(教外司留[2001]498);辽宁省博士启动基金(2001102093);国家自然科学基金资助项目(10172021);2001年国家高科技研究发展计划(2001AA412220)

摘　　要：利用弹性平面扇形域哈密顿体系的方程,通过分离变量法及共轭辛本征函数向量展开法,推导了一个圆形奇异解析单元列式,该单元能准确地描述平面裂纹尖端场。将该解析元与有限元相结合,构成半解析的有限元法,可求解任意几何形状和载荷的平面裂纹应力强度因子及扩展问题。对典型算例的计算结果表明本文方法简单有效,具有令人满意的精度。Based on the Hamiltonian governing equations of plane elasticity for sectorial domain, the variable separation and eigenfunction expansion techniques are employed to formulate a circular singular analytical element. The analytical element gives a precise description of the displacement and stress fields in the vicinity of plane crack tip for the plane crack problem. The new analytical element can be implemented into FEM program systems to solve for stress intensity factor and deal with crack propagation problems for plane cracks with arbitrary shapes and loads. Numerical results for typical problems show that the method is simple, efficient and accurate.

关 键 词：平面裂纹 应力强度因子 哈密顿体系 网格 半解析有限元法 

分 类 号：O346.1[理学—固体力学]