非连续问题中单元分割的模板方法

王理想; 文龙飞; 肖桂仲; 田荣

doi:10.6052/0459-1879-20-360

非连续问题中单元分割的模板方法

doi: 10.6052/0459-1879-20-360

王理想^*,†,
文龙飞^*,†,
肖桂仲^*,†,**,
田荣^*,†,2), ,

^*中物院高性能数值模拟软件中心, 北京 100088
^††北京应用物理与计算数学研究所, 北京100088
^**南京理工大学, 南京 210094

基金项目: 1) 国家重点研发计划(2016YFB0201002);国家重点研发计划(2016YFB0201004);科学挑战专题(TZ2018002)

详细信息

作者简介:
2) 田荣, 研究员, 主要研究方向: 计算力学与高性能计算. E-mail: tian_rong@iapcm.ac.cn

通讯作者:
田荣

中图分类号: TB115,O346.1
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出版历程
- 收稿日期: 2020-10-20
- 刊出日期: 2021-03-10

A TEMPLATED METHOD FOR PARTITIONING OF SOLID ELEMENTS IN DISCONTINUOUS PROBLEMS

Wang Lixiang^*,†,
Wen Longfei^*,†,
Xiao Guizhong^*,†,**,
Tian Rong^{*,†,2)
, ,}

^*CAEP Software Center for High Performance Numerical Simulation$,$ Beijing $100088$$,$ China
^††Institute of Applied Physics and Computational Mathematics$,$ Beijing $100088$$,$ China
^**Nanjing University of Science and Technology$,$ Nanjing $210094$$,$ China

摘要

摘要: 扩展有限元法 (extended finite element method, XFEM) 因具有裂纹几何独立于模拟网格、裂纹扩展时无需网格重分重映、计算精度高等优点,成为裂纹分析的主流数值方法之一. 但该方法在工程实践中存在单元被裂纹分割的几何困难 —— 现有精确几何分割方法实现复杂、计算量大、鲁棒性差. 为克服这一困难, 本文提出一种基于单元水平集的模板分割方法, 用于非连续单元子剖分和数值积分. 首先, 遍历单元水平集值所有形态并建立标准单元分割模板库; 然后, 根据单元水平集值, 对非标准单元进行形态查询和模板插值; 最后, 套用标准单元分割模板实现单元高效分割和子剖分. 将该方法与常规XFEM、改进型XFEM进行结合,从而应用于孔洞、夹杂、裂纹等非连续问题分析中. 算例分析表明, 本文提出的模板分割方法具有较高计算精度. 由于不引入复杂几何操作, 该模板分割方法同时具有较高计算效率和鲁棒性, 故可为XFEM类方法在实际工程应用中提供有效支撑.
- 子剖分 /
- 水平集 /
- 非连续性 /
- 裂纹扩展 /
- 常规XFEM /
- 改进型XFEM
Abstract: The extended finite element method (XFEM) has been one of the privileged tools for crack analysis due to its significant advantages: (1) Independence of crack geometry on the simulation mesh; (2) no necessity of remeshing when a crack grows; and (3) high accuracy. However, the method is hindered in engineering practices by the partitioning difficulty of discontinuous elements, i.e. the geometric interaction between discontinuous interfaces and solid elements. Though current partitioning algorithms are geometrically exact, they are cumbersome to implement, computationally expensive, and insufficiently robust. To overcome these issues, a templated partitioning algorithm is proposed based on element level sets for subdivision and numerical integration of discontinuous elements. Firstly, a templated partitioning library for standard discontinuous elements is established by enumerating all the patterns of element level set values. Secondly, the pattern of a non-standard element to be partitioned is looked up and the sub-coordinates are interpolated based on the element level set values. Lastly, the non-standard element is efficiently partitioned into sub-triangles based on the standard element template. The algorithm is incorporated into the conventional XFEM and the improved XFEM for analysis of discontinuous problems, i.e. the problems with holes, inclusions, cracks and so forth. Numerical examples indicate that the proposed algorithm achieves favorable accuracy. Without cumbersome geometrical operations, the templated partitioning algorithm is also efficient and robust, thereby enabling itself to support the extended finite element methods in practical engineering problems.
- subdivision /
- level set /
- discontinuity /
- crack propagation /
- conventional XFEM /
- improved XFEM

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