计算力学学报2016，Vol.33Issue(4)：469-477,9.DOI:10.7511/jslx201604007
改进型XFE M进展
Recent progresses on improved XFEM
摘要
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 enrich-ment 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.关键词
XFEM/扩展有限元法/广义有限元/线性依赖/质量集中/动态裂纹扩展Key words
XFEM/extra-dof/crack/mass lumping/dynamic fracture/iXFEM/partition of unity分类
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田荣,龙飞..改进型XFE M进展[J].计算力学学报,2016,33(4):469-477,9.基金项目
国家自然科学基金(11472274)资助项目 （11472274）
