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Approximate impedance of a planar thin layer in couple stress elasticity

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Abstract

We consider the transmission problem of couple stress elasticity in a fixed domain \(\Omega _{-}\) juxtaposed with a thin layer \(\Omega _{+}^{\delta }\). Our aim is to model the effect of the thin layer \(\Omega _{+}^{\delta }\) on the fixed domain \(\Omega _{-}\) by an impedance boundary condition. For that we use the techniques of asymptotic expansion to approximate the transmission problem by an impedance problem set in the fixed domain \(\Omega _{-}\), and we prove an error estimate between the solution of the transmission problem in \(\Omega _{-}\) and the solution of the approximate impedance problem.

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Acknowledgements

The authors thank the reviewers for their helpful comments. We acknowledge with thanks the support of the General Direction of Scientific Research and Technological Development (Algeria) (DGRSDT).

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Authors and Affiliations

  1. Laboratoire de Mathématiques et Physique Appliquées, École Normale Supérieure de Bou Saâda, 28001, Bou Saâda, M’Sila, Algeria

    A. Abdallaoui

  2. Faculté des Mathematiques et Informatique, Université Mohamed El Bachir El Ibrahimi, Al-Anasser, 34030, Bordj Bou Arréridj, Algeria

    A. Berkani

  3. Faculté des Sciences et de la Technologie, Université Djilali Bounâama, Soufay, 44225, Khemis Miliana, Algeria

    A. Kelleche

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  1. A. Abdallaoui
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  2. A. Berkani
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  3. A. Kelleche
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Correspondence to A. Abdallaoui.

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Abdallaoui, A., Berkani, A. & Kelleche, A. Approximate impedance of a planar thin layer in couple stress elasticity. Z. Angew. Math. Phys. 72, 150 (2021). https://doi.org/10.1007/s00033-021-01581-z

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  • DOI: https://doi.org/10.1007/s00033-021-01581-z

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