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Upper Bound Shakedown Analysis of Plates Utilizing the C\(^{1}\) Natural Element Method

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Abstract

This paper proposes a numerical solution method for upper bound shakedown analysis of perfectly elasto-plastic thin plates by employing the C\(^{1}\) natural element method. Based on the Koiter’s theorem and von Mises yield criterion, the nonlinear mathematical programming formulation for upper bound shakedown analysis of thin plates is established. In this formulation, the trail function of residual displacement increment is approximated by using the C\(^{1}\) shape functions, the plastic incompressibility condition is satisfied by introducing a constant matrix in the objective function, and the time integration is resolved by using the König’s technique. Meanwhile, the objective function is linearized by distinguishing the non-plastic integral points from the plastic integral points and revising the objective function and associated equality constraints at each iteration. Finally, the upper bound shakedown load multipliers of thin plates are obtained by direct iterative and monotone convergence processes. Several benchmark examples verify the good precision and fast convergence of this proposed method.

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Acknowledgements

S. Zhou is supported by the Chinese Postdoctoral Science Foundation (2013M540934). Y. Liu is supported by the National Key Research and Development Program of China (2016YFC0801905, 2017YFF0210704).

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Authors and Affiliations

  1. Beijing Institute of Structure and Environment Engineering, Beijing, 100076, China

    Shutao Zhou, Binjie Ma, Chuantao Hou, Yatang Ju, Bing Wu & Kelin Rong

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

    Yinghua Liu

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  1. Shutao Zhou
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  2. Yinghua Liu
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Correspondence to Shutao Zhou.

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Zhou, S., Liu, Y., Ma, B. et al. Upper Bound Shakedown Analysis of Plates Utilizing the C\(^{1}\) Natural Element Method. Acta Mech. Solida Sin. 34, 221–236 (2021). https://doi.org/10.1007/s10338-020-00193-w

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  • DOI: https://doi.org/10.1007/s10338-020-00193-w

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