摘要
结合广义有限元法(GFEM)和扩展有限元法(XFEM)的特点,提出了一种新的数值方法——广义扩展有限元法(GXFEM).阐述了广义扩展有限元法的基本原理,对相关公式进行推导,探讨数值实现中需注意的重要问题,给出利用广义扩展有限元法进行断裂分析时应力强度因子的计算方法,编写了广义扩展有限元法程序.通过算例进行了应力强度因子的计算,模拟了结构裂纹的扩展过程.算例结果表明,利用广义扩展有限元法计算交叉裂纹扩展问题,不需要进行过密的网格划分,且网格在裂纹扩展后无需重新剖分,具有相当高的计算精度.
A new numerical method-generalized extended finite element method （GXFEM） is proposed in this paper by combining the generalized finite element method （GFEM） and the extended finite element method （XFEM）. The basic principles of GXFEM are presented in detail and relevant formula is derived. Some important problems in numerical realization are discussed. Then, a method of calculating stress intensity factors （S1F） in the analysis of fracture problems is given by using GXFEM. The GXFEM program to analyze fracture process is compiled. The numerical examples are applied to calculate the SIF and to simulate the crack propagation. The results show that it is not necessary to set frequent grids, or to re-mesh when cracks propagate. In addition, the results are provided with very high accuracy.
出处
《中国科学：物理学、力学、天文学》
CSCD
北大核心
2014年第5期539-546,共8页
Scientia Sinica Physica,Mechanica & Astronomica
基金
国家自然科学基金资助项目(批准号:51179064
11132003
11372099)
关键词
广义扩展有限元法
应力强度因子
裂纹扩展
数值模拟
断裂力学
generalized extended finite element method, stress intensity factors, crack propagation, numerical simulation,fracture mechanics
