摘要
扩展有限元法(XFEM)是一种在常规有限元的框架内仿真不连续问题的新型数值方法。首先给出了扩展有限元法仿真裂纹问题的基本原理,即采用Heaviside函数加强裂尖后面的裂纹,采用渐近裂尖位移场加强裂尖附近。接着给出了基于残值法的扩展有限元后验误差估计,算例表明可以通过后验误差估计确定优的裂尖加强范围。其次,给出了扩展有限元仿真裂纹扩展的过程。最后,仿真了单一裂纹扩展和多裂纹扩展。仿真结果表明,基于扩展有限元后验误差确定优的裂尖加强范围是可行的,采用扩展有限元仿真裂纹扩展是有效的。
The extended finite element method（XFEM） is a new numerical method for simulating discontinuities within a standard finite element framework.The principle of simulating crack growth with XFEM,i.e.enriching the basis of the classical finite element method by some singular functions around the crack tip and by a step function along the crack line,was first proposed.Based on the residual method,a posteriori error estimation in the XFEM was developed and deduced.Examples show that the optimal enriched domain around the crack tip can be determined by the posteriori error.The procedure of simulating crack growth with XFEM was proposed.Finally,single crack growth and multi-cracks growth were simulated by XFEM.The simulated results show that it is feasible that determination of the optimal enriched domain around the crack tip by the posteriori error,and it is effective that simulation of crack growth with XFEM.
出处
《系统仿真学报》
CAS
CSCD
北大核心
2009年第6期1756-1759,共4页
Journal of System Simulation
基金
国家自然科学基金(50539030和50609004)
关键词
扩展有限元法
后验误差估计
优的裂尖加强范围
仿真
裂纹扩展
XFEM
posteriori error estimation
optimal enriched domain around crack tip
simulation
crack growth.
作者简介
余天堂（1971-），男，湖北洪湖人，博士，副教授，研究方向为计算力学与工程仿真。
