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Applied Mathematics and Mechanics (English Edition) ›› 2009, Vol. 30 ›› Issue (10): 1233-1246.doi: https://doi.org/10.1007/s10483-009-1003-3

• Articles • 上一篇    下一篇

A novel virtual node method for polygonal elements

唐旭海1 吴圣川2,3 郑超1 张建海1   

  1. 1. State Key Lab of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu 610065, P. R. China;
    2. Centre for Advanced Materials Joining and Computations (AMJC), School of Materials Science and Engineering, Hefei University of Technology, Hefei 230009, P. R. China;
    3. Centre for Advanced Computations in Engineering Science (ACES), Department of Mechanical Engineering, National University of Singapore, 117576, Singapore
  • 收稿日期:2008-12-22 修回日期:2009-09-07 出版日期:2009-10-01 发布日期:2009-10-01

A novel virtual node method for polygonal elements

TANG Xu-Hai1, WU Sheng-Chuan2,3, ZHENG Chao1, ZHANG Jian-Hai1   

  1. 1. State Key Lab of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu 610065, P. R. China;
    2. Centre for Advanced Materials Joining and Computations (AMJC), School of Materials Science and Engineering, Hefei University of Technology, Hefei 230009, P. R. China;
    3. Centre for Advanced Computations in Engineering Science (ACES), Department of Mechanical Engineering, National University of Singapore, 117576, Singapore
  • Received:2008-12-22 Revised:2009-09-07 Online:2009-10-01 Published:2009-10-01

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摘要： A novel polygonal finite element method (PFEM) based on partition of unity is proposed, termed the virtual node method (VNM). To test the performance of the present method, numerical examples are given for solid mechanics problems. With a polynomial form, the VNM achieves better results than those of traditional PFEMs, including the Wachspress method and the mean value method in standard patch tests. Compared with the standard triangular FEM, the VNM can achieve better accuracy. With the ability to construct shape functions on polygonal elements, the VNM provides greater flexibility in mesh generation. Therefore, several fracture problems are studied to demonstrate the potential implementation. With the advantage of the VNM, the convenient refinement and remeshing strategy are applied.

关键词: virtual node method, polygonal finite element method, partition of unity, crack propagation

Abstract: A novel polygonal finite element method (PFEM) based on partition of unity is proposed, termed the virtual node method (VNM). To test the performance of the present method, numerical examples are given for solid mechanics problems. With a polynomial form, the VNM achieves better results than those of traditional PFEMs, including the Wachspress method and the mean value method in standard patch tests. Compared with the standard triangular FEM, the VNM can achieve better accuracy. With the ability to construct shape functions on polygonal elements, the VNM provides greater flexibility in mesh generation. Therefore, several fracture problems are studied to demonstrate the potential implementation. With the advantage of the VNM, the convenient refinement and remeshing strategy are applied.

Key words: virtual node method, polygonal finite element method, partition of unity, crack propagation

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