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| Recent progresses on improved XFEM |
| Received:May 13, 2016 Revised:June 15, 2016 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx201604007 |
| KeyWord:XFEM extra-dof crack mass lumping dynamic fracture iXFEM partition of unity |
| Author | Institution |
| 田荣 |
北京应用物理与计算数学研究所 中物院高性能数值模拟软件中心, 北京 |
| 文龙飞 |
中国科学院 计算技术研究所, 北京 |
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| Abstract: |
| As an unprecedentedly successful tool for crack analysis XFEM gains broad attention in both academy and industries.However,there are still two daunting issues hindering the practical applications of the method.One is the linear dependence issue reflected by the ill-conditioning of global matrices in steady problems.The other is the issue of generalized mass terms associated with the extra dofs in time-dependent problems.The paper presents an improved XFEM,which features:(1) crack tip enrichment without introducing extra dofs; (2) being free of linear dependence and avoiding the singularity of (global) stiffness matrices; (3) well-conditioned.The condition number of the stiffness matrix increases as h-2,which is the same as the standard FEM,whereas the standard XFEM increases as h-6 in our tests; (4) overcoming the mass lumping issue of generalized mass and energy inconsistency issue asso-ciated with extra dofs in dynamic analyses.Recent progresses of the new method are summarized in this short paper.The method is tested using selected numerical examples in both static and dynamic problems.It is shown that the new method is the same accuracy as the existing XFEM,but it offers additionally excellent conditioning stability,good computationally efficiency,and implemtnational straifht-forwardness in dynamic problems. |
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