A novel virtual node method for polygonal elements

  • Xu-hai Tang (唐旭海)Email author
  • Sheng-chuan Wu (吴圣川)
  • Chao Zheng (郑超)
  • Jian-hai Zhang (张建海)


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 

Chinese Library Classification


2000 Mathematics Subject Classification



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Copyright information

© Shanghai University and Springer Berlin Heidelberg 2009

Authors and Affiliations

  • Xu-hai Tang (唐旭海)
    • 1
    Email author
  • Sheng-chuan Wu (吴圣川)
    • 2
    • 3
  • Chao Zheng (郑超)
    • 1
  • Jian-hai Zhang (张建海)
    • 1
  1. 1.State Key Lab of Hydraulics and Mountain River EngineeringSichuan UniversityChengduP. R. China
  2. 2.Centre for Advanced Materials Joining and Computations (AMJC), School of Materials Science and EngineeringHefei University of TechnologyHefeiP. R. China
  3. 3.Centre for Advanced Computations in Engineering Science (ACES), Department of Mechanical EngineeringNational University of SingaporeSingaporeSingapore

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