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Asymptotic Analysis of Shell-like Inclusions with High Rigidity

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Abstract

We study the problem of an elastic shell-like inclusion with high rigidity in a three-dimensional domain by means of the asymptotic expansion method. The analysis is carried out in a general framework of curvilinear coordinates. After defining a small real adimensional parameter ε, we characterize the limit problems when the rigidity of the inclusion has order of magnitude \(\frac{1}{\varepsilon }\) and \(\frac{1}{\varepsilon^{3}}\) with respect to the rigidities of the surrounding bodies. Moreover, we prove the strong convergence of the solution of the initial three-dimensional problem towards the solution of the simplified limit problem.

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Authors and Affiliations

  1. Institut de Mathématiques de Toulon, EA-CNRS 2134, Université de Toulon et du Var, Avenue de l’Université, BP 132, 83957, La Garde Cedex, France

    Anne-Laure Bessoud

  2. Institut de Mathématiques et de Modélisation de Montpellier, UMR-CNRS 5149, Université Montpellier 2, Case courier 051, Place Eugène Bataillon, 34095, Montpellier Cedex 5, France

    Françoise Krasucki

  3. Dipartimento di Architettura, Costruzioni e Strutture, Università Politecnica delle Marche, via Brecce Bianche, 60131, Ancona, Italy

    Michele Serpilli

Authors
  1. Anne-Laure Bessoud
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  2. Françoise Krasucki
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  3. Michele Serpilli
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Corresponding author

Correspondence to Françoise Krasucki.

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Bessoud, AL., Krasucki, F. & Serpilli, M. Asymptotic Analysis of Shell-like Inclusions with High Rigidity. J Elast 103, 153–172 (2011). https://doi.org/10.1007/s10659-010-9278-1

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  • DOI: https://doi.org/10.1007/s10659-010-9278-1

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