Determination of enrichment type of node in extended finite element method

YU Tian-tang; GONG Zhi-wei

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Determination of enrichment type of node in extended finite element method

更新时间：2026-06-25

- Determination of enrichment type of node in extended finite element method
- Vol. 34, Issue 11, (2013)
- 作者机构：
  
  河海大学力学与材料学院工程力学系,南京,210098
- 作者简介：
- 基金信息：
- DOI：
  CLC： O242.2
- Online First：11 November 2013，
  
  Published：2013
- 稿件说明：
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YU Tian-tang, GONG Zhi-wei. Determination of enrichment type of node in extended finite element method[J]. 2013, 34(11).
DOI：

YU Tian-tang, GONG Zhi-wei. Determination of enrichment type of node in extended finite element method[J]. 2013, 34(11). DOI：

摘要

扩展有限元法的网格剖分不需要考虑裂纹的位置，但计算时需根据计算网格和裂纹位置关系确定加强节点和加强类型。一般根据加强单元类型确定加强节点和加强类型。确定加强单元类型，不仅要考虑裂纹位置，还要考虑单元形状。指出现有文献中只考虑裂纹位置根据节点水平集值判别加强单元类型的不足，提出相应的改进方法。对于复杂形状裂纹，采用水平集法确定加强单元类型并不方便；给出了一种确定加强单元类型、加强节点和加强类型的有效方法，即根据裂纹与单元边界交点数和裂纹拐点位置确定加强单元类型，然后根据加强单元类型确定加强节点及加强类型；给出了该方法详细的执行过程。算例分析表明了本文方法的正确性。

Abstract

Meshes are generated without taking account of existence of cracks in the extended finite element method. However

the enriched nodes and their enrichment types are determined by the interaction between the computational mesh and the locations of cracks. In general

the enriched nodes and their enrichment types are determined according to the enriched element types. To determine the enriched element types

the locations of cracks and the shapes of elements must be considered. The limitations judging the enriched element types with the nodal level set values only considering the locations of cracks are pointed out; and the improved method is proposed. For complex cracks

it is inconvenient to determine the enriched element types with the level set method. An effective method is proposed to determine the enriched element types

enriched nodes and their enrichment types

i.e. according to the intersection number between the cracks and element boundaries and the locations of crack inflection points

the enriched element types are determined; then the enriched nodes and their enrichment types are determined by the enriched element types. The detailed procedure of the method is presented. The case studies of numerical simulation show the correctness of the proposed method.

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