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hp-adaptive finite element method for linear elasticity using higher-order virtual node method

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Abstract

Higher-order polygonal finite elements are developed for adaptive analyses of linear elastic problem. These elements are constructed using virtual node method based on partition of unity coupled with polynomial enrichment functions. Because the element shape functions are polynomials, the stiffness matrix is computed precisely with standard Gauss quadrature rules. Several numerical examples of linear elasticity are presented to validate the accuracy and convergence of the proposed elements. One of the advantages of the proposed elements is that they can be used as transition elements with hanging nodes on higher-order approximation meshes. Building on this advantage, h- and hp-adaptive finite element analyses of numerical examples with local singularities are performed on triangular quadtree meshes in order to demonstrate the performance of the adaptive strategies using the proposed elements.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, 373-1, Daejeon, 305-701, Korea

    Hyeon Cheol Oh & Byung Chai Lee

Authors
  1. Hyeon Cheol Oh
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  2. Byung Chai Lee
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Correspondence to Byung Chai Lee.

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Recommended by Associate Editor Gang-Won Jang

Byung Chai Lee received B.S. degree (1977) of mechanical engineering from Seoul National University, Korea and Ph. D. (1984) of mechanical engineering from Korea Advanced Institute of Science and Technology (KAIST), Korea. He is currently a professor at the department of mechanical engineering in KAIST. His areas of interest are finite element method and structural optimization.

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Oh, H.C., Lee, B.C. hp-adaptive finite element method for linear elasticity using higher-order virtual node method. J Mech Sci Technol 29, 4299–4312 (2015). https://doi.org/10.1007/s12206-015-0927-y

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  • DOI: https://doi.org/10.1007/s12206-015-0927-y

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