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A 2D model for a highly heterogeneous plate

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Abstract

In this paper we investigate the 2d-model for a thin plate \( \Omega _\varepsilon :=\omega \times \varepsilon {\mathrm I}\) of \(\mathbb R^3\) having two components: a circular stiff layer \(F_\varepsilon \) and its complement the soft matrix \(M_\varepsilon \) with \(\frac{1}{\varepsilon ^2}\) as a ratio between their respective elasticity coefficients. We prove that the limit model is associated to a nonlocal system involving Kirchoff-Love displacements in the layer and we exhibit a corrector for the displacements in the initial cylindrical structure of \(\mathbb R^3\).

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Authors and Affiliations

  1. Institut Supérieur d’Informatique et de Mathématiques de Monastir, Analyse et Contrôle des EDP, UR 13ES64, Université de Monastir, 5019, Monastir, Tunisia

    Ahmed Boughammoura

  2. Laboratoire de mathématiques pures et appliquées, Mouloud Mammeri University of Tizi-Ouzou, Tizi-Ouzou, Algeria

    Leila Rahmani

  3. Institut de Mathématiques de Marseille (I2M) UMR 7373, Aix-Marseille Université, CNRS, CMI, 39 rue F. Joliot-Curie, 13453, Marseille cedex 13, France

    Ali Sili

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  1. Ahmed Boughammoura
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  2. Leila Rahmani
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  3. Ali Sili
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Correspondence to Ali Sili.

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Boughammoura, A., Rahmani, L. & Sili, A. A 2D model for a highly heterogeneous plate. Ricerche mat (2021). https://doi.org/10.1007/s11587-021-00671-4

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  • DOI: https://doi.org/10.1007/s11587-021-00671-4

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