扩展有限元方法及应用综述  

A Review of the Extended Finite Element Method and its Applications

作　　者：郭历伦[1] 陈忠富[1] 罗景润[1] 陈刚[1] 

机构地区：[1]中国工程物理研究院总体工程研究所,四川绵阳621900

出　　处：《力学季刊》2011年第4期612-625,共14页Chinese Quarterly of Mechanics

基　　金：中国工程物理研究院科学技术发展基金(2010B021024)

摘　　要：扩展有限元(XFEM)是在标准有限元方法的框架下,提出来的一种用于解决裂纹、孔洞、夹杂等间断问题的数值方法。在有限元的近似函数中,增加能反映待求问题间断特性的附加函数项,采用水平集方法(LSM)描述间断面的几何特性及其移动规律。扩展有限元方法与标准有限元方法相比,具有计算精度高、勿需网格重构等特点。本文综述了扩展有限元的理论基础及近年来的研究进展和应用情况。第1～4节论述了扩展有限元方法所涉及的理论基础;第5节对制约扩展有限元发展的两个问题及其修正方法进行了讨论;第6节和第7节分别介绍了扩展有限元程序实现及其在各领域的应用情况;最后,第8节对可进一步开展的研究工作进行了展望。The extended finite element method（XFEM） is a numerical method for modeling discontinuity such as cracks,holes,inclusions etc within a standard finite element framework.In the XFEM,special functions which can reflect the problem＇s solution characteristics are added to the finite element approximation using the framework of partition of unity.The geometry and extended process of discontinuous interface is described by level sets method（LSM）.Compared to the standard finite element method,it can obtain more accuracy without remeshing.An overview and recent progress of the extended finite element method are presented.The theory basis of XFEM is introduced from section 1 to 4.Tow critical problems in XFEM are discussed in section 5.The implementation and application of XFEM are outlined in Section 6 and Section 7,and finally some recommendations of future work are presented in section 8.

关 键 词：扩展有限元 单位分解 水平集方法 快速推进法 富集函数 

分 类 号：O242.21[理学—计算数学]