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A novel virtual node method for polygonal elements

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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.

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Authors and Affiliations

  1. State Key Lab of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu, 610065, P. R. China

    Xu-hai Tang  (唐旭海), Chao Zheng  (郑超) & Jian-hai Zhang  (张建海)

  2. Centre for Advanced Materials Joining and Computations (AMJC), School of Materials Science and Engineering, Hefei University of Technology, Hefei, 230009, P. R. China

    Sheng-chuan Wu  (吴圣川)

  3. Centre for Advanced Computations in Engineering Science (ACES), Department of Mechanical Engineering, National University of Singapore, Singapore, 117576, Singapore

    Sheng-chuan Wu  (吴圣川)

Authors
  1. Xu-hai Tang  (唐旭海)
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  2. Sheng-chuan Wu  (吴圣川)
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  3. Chao Zheng  (郑超)
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  4. Jian-hai Zhang  (张建海)
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Correspondence to Xu-hai Tang  (唐旭海).

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Communicated by Xing-ming GUO

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Tang, Xh., Wu, Sc., Zheng, C. et al. A novel virtual node method for polygonal elements. Appl. Math. Mech.-Engl. Ed. 30, 1233–1246 (2009). https://doi.org/10.1007/s10483-009-1003-3

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  • DOI: https://doi.org/10.1007/s10483-009-1003-3

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