Crack tip enrichment in the XFEM using a cutoff function
Crack tip enrichment in the XFEM using a cutoff function
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DOI：
10.1002/nme.2265
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发表时间：
2008-08
影响因子：
2.9
通讯作者：
E. Chahine;P. Laborde;Y. Renard
中科院分区：
文献类型：
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作者：
E. Chahine;P. Laborde;Y. Renard
我们考虑扩展有限元法 (XFEM) 的一种变体，其中使用截止函数来定位奇异富集表面。该变体的目标是在数值上获得最佳收敛速率，同时降低具有固定富集区域的经典 XFEM 的计算成本。我们给出了准最优误差估计的数学结果。本文的重点之一是证明奇异富集和不连续富集之间耦合的最优性。最后，我们提出了一些验证理论结果的数值计算。这些计算与经典 XFEM 和非丰富方法的计算进行了比较。版权所有 © 2008 约翰·威利父子有限公司
We consider a variant of the eXtended Finite Element Method (XFEM) in which a cutoff function is used to localize the singular enrichment surface. The goal of this variant is to obtain numerically an optimal convergence rate while reducing the computational cost of the classical XFEM with a fixed enrichment area. We give a mathematical result of quasi‐optimal error estimate. One of the key points of this paper is to prove the optimality of the coupling between the singular and the discontinuous enrichments. Finally, we present some numerical computations validating the theoretical result. These computations are compared with those of the classical XFEM and a non‐enriched method. Copyright © 2008 John Wiley & Sons, Ltd.