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Upper-bound limit analysis based on the natural element method

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Abstract

The natural element method (NEM) is a newly-developed numerical method based on Voronoi diagram and Delaunay triangulation of scattered points, which adopts natural neighbour interpolation to construct trial functions in the framework of Galerkin method. Owing to its distinctive advantages, the NEM is used widely in many problems of computational mechanics. Utilizing the NEM, this paper deals with numerical limit analysis of structures made up of perfectly rigid-plastic material. According to kinematic theorem of plastic limit analysis, a mathematical programming natural element formulation is established for determining the upper bound multiplier of plane problems, and a direct iteration algorithm is proposed accordingly to solve it. In this algorithm, the plastic incompressibility condition is handled by two different treatments, and the nonlinearity and nonsmoothness of the goal function are overcome by distinguishing the rigid zones from the plastic zones at each iteration. The procedure implementation of iterative process is quite simple and effective because each iteration is equivalent to solving an associated elastic problem. The obtained limit load multiplier is proved to monotonically converge to the upper bound of true solution. Several benchmark examples are investigated to validate the significant performance of the NEM in the application field of limit analysis.

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Authors and Affiliations

  1. Department of Engineering Mechanics, AML, Tsinghua University, 100084, Beijing, China

    Shu-Tao Zhou & Ying-Hua Liu

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  1. Shu-Tao Zhou
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  2. Ying-Hua Liu
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Correspondence to Ying-Hua Liu.

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The project was supported by the National Foundation for Excellent Doctoral Thesis of China (200025), the Program for New Century Excellent Talents in University (NCET-04-0075) and the National Natural Science Foundation of China (19902007).

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Zhou, ST., Liu, YH. Upper-bound limit analysis based on the natural element method. Acta Mech Sin 28, 1398–1415 (2012). https://doi.org/10.1007/s10409-012-0149-9

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  • DOI: https://doi.org/10.1007/s10409-012-0149-9

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