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

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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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Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology Bombay, Mumbai, India

    L. N. Pramod Aladurthi

  2. Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai, India

    Krishna Kamdi & S. Natarajan

  3. CIRTech Institute, Ho Chi Minh City University of Technology (HUTECH), Ho Chi Minh City, Viet Nam

    Nguyen-Xuan Hung

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  2. Krishna Kamdi
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  3. Nguyen-Xuan Hung
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  4. S. Natarajan
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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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