An adaptive polytree approach to the scaled boundary boundary finite element method

Abstract

In this paper, a h-adaptive methodology based on the polytopal meshes is proposed for capturing high stress gradients at the materials corners and the stress singularities at the vicinity of a crack tip. The adaptive refinement is based on the error indicator directly computed from the displacement solutions of the scaled boundary finite element method. Based on the error indicator, a polygon of n-sides which has an error exceeding a specified tolerance is subdivided recursively into \((n+1)\) child polygons. The salient features of the proposed framework are: (a) circumvents a need for post-processing techniques for error estimation; (b) elements with hanging nodes are treated as polygons without a need for special treatment and (c) stress gradients and stress singularities are accurately captured due to the semi-analytical formulation. The robustness and the convergence properties of the proposed framework is demonstrated with three benchmark examples.

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Correspondence to L. N. Pramod Aladurthi.

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Aladurthi, L.N.P., Kamdi, K., Hung, NX. et al. An adaptive polytree approach to the scaled boundary boundary finite element method. Int J Adv Eng Sci Appl Math 12, 171–182 (2020). https://doi.org/10.1007/s12572-020-00280-8

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Keywords

  • Adaptive refinement
  • Hanging nodes
  • Scaled boundary finite element method
  • Error indicator
  • Polytree meshes