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An asymptotic strain gradient Reissner-Mindlin plate model

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Abstract

In this paper we derive a strain gradient plate model from the three-dimensional equations of strain gradient linearized elasticity. The deduction is based on the asymptotic analysis with respect of a small real parameter being the thickness of the elastic body we consider. The body is constituted by a second gradient isotropic linearly elastic material. The obtained model is recognized as a strain gradient Reissner-Mindlin plate model. We also provide a mathematical justification of the obtained plate model by means of a variational weak convergence result.

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Authors and Affiliations

  1. Department of Civil and Building Engineering, and Architecture, Università Politecnica delle Marche, via Brecce Bianche, 60131, Ancona, Italy

    Michele Serpilli

  2. Institut de mathématique et de modélisation de Montpellier, UMR-CNRS 5149, Université Montpellier II, CC 051, place Eugène-Bataillon, 34095, Montpellier cedex 5, France

    Françoise Krasucki

  3. Laboratoire de Mécanique des Solides, UMR-CNRS 7649, École Polytechnique, Route de Saclay, 91128, Palaiseau cedex, France

    Giuseppe Geymonat

Authors
  1. Michele Serpilli
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  2. Françoise Krasucki
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  3. Giuseppe Geymonat
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Correspondence to Michele Serpilli.

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Serpilli, M., Krasucki, F. & Geymonat, G. An asymptotic strain gradient Reissner-Mindlin plate model. Meccanica 48, 2007–2018 (2013). https://doi.org/10.1007/s11012-013-9719-6

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  • DOI: https://doi.org/10.1007/s11012-013-9719-6

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