摘要
在扩展有限元法(extended finite element methods,XFEM)的理论框架下,重点研究了动荷载作用下稳定裂纹尖端动态应力强度因子(dynamic stress intensity factors,DSIFs)的求解方法。根据XFEM的位移模式,推导了动力XFEM的支配方程,采用Newmark隐式算法进行时间积分。同时,提出一种XFEM质量矩阵的集中策略,给出了求解DSIFs的相互作用积分方法,与静态问题的相互作用积分方法相比,增加了惯性项的贡献。最后,若干典型算例的计算结果表明:XFEM可以准确评价稳定裂纹尖端的DSIFs,建议的质量矩阵集中策略是有效的,为得到正确的DSIFs,惯性项的贡献不可忽略。
In the framework of the extended finite element methods （ XFEM）, the extraction of dynamic stress intensity factors （DSIFs） for stationary cracks being subjected to dynamic loads was detally studied. Having constructed the approximation of dynamic XFEM, the derivation of governing equation for dynamic XFEM was presented. The Newmark implicit algorithm was used for time integration. Meanwhile, a mass lumping strategy for XFEM implicit dynamics was proposed. In addition, the interaction integral method was given for evaluating DSIFs. Com- pared with the interaction integral method for evaluating stress intensity factors （SIFs） of cracks under static conditions, the contril^ution of inertial effects was added to the interaction integral method for evaluating DSIFs. The numerical illustrations show that the XFEM can eval- uate accurately DSIFs and the proposed mass lumping strategy is also quite effective. To obtain DSIFs correctly, the inertial effects on interaction integral cannot be ignored.
出处
《应用数学和力学》
CSCD
北大核心
2013年第6期586-597,共12页
Applied Mathematics and Mechanics
基金
国家自然科学基金资助项目(11132003)
中国博士后科学基金资助项目(2013M530233)
关键词
扩展有限元法
动载
裂纹
动应力强度因子
相互作用积分
extended finite element methods
dynamic loads
cracks
dynamic stress intensityfactors
interaction integral
