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Shakedown Analysis of Reissner-Mindlin Plates Using the Edge-Based Smoothed Finite Element Method

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Direct Methods for Limit States in Structures and Materials

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Abstract

This paper concerns the development of a primal-dual algorithm for limit and shakedown analysis of Reissner-Mindlin plates made of von Mises material. At each optimization iteration, the lower bound of the shakedown load multiplier is calculated simultaneously with the upper bound using the duality theory. An edge-based smoothed finite element method (ES-FEM) combined with the discrete shear gap (DSG) technique is used to improve the accuracy of the solutions and to avoid the transverse shear locking behaviour. The method not only possesses all inherent features of convergence and accuracy from ES-FEM, but also ensures that the total number of variables in the optimization problem is kept to a minimum compared with the standard finite element formulation. Numerical examples are presented to demonstrate the effectiveness of the present method.

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Authors and Affiliations

  1. Institute for Bioengineering, Biomechanics Lab., Aachen University of Applied Sciences, Heinrich-Mußmann-Str. 1, Jülich Campus, 52428, Jülich, Germany

    Thanh Ngọc Trần & M. Staat

  2. Chair of Mechanics and Robotics, University of Duisburg-Essen, Lotharstr. 1, 47057, Duisburg, Germany

    Thanh Ngọc Trần

Authors
  1. Thanh Ngọc Trần
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  2. M. Staat
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Correspondence to M. Staat .

Editor information

Editors and Affiliations

  1. Department of Structural Engineering, National Technical University of Athens School of Civil Engineering, Athens, Greece

    Konstantinos Spiliopoulos

  2. Institute of General Mechanics, RWTH-Aachen University, Aachen, Germany

    Dieter Weichert

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Trần, T.N., Staat, M. (2014). Shakedown Analysis of Reissner-Mindlin Plates Using the Edge-Based Smoothed Finite Element Method. In: Spiliopoulos, K., Weichert, D. (eds) Direct Methods for Limit States in Structures and Materials. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6827-7_5

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  • DOI: https://doi.org/10.1007/978-94-007-6827-7_5

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-6826-0

  • Online ISBN: 978-94-007-6827-7

  • eBook Packages: EngineeringEngineering (R0)

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