Approximation of Dirichlet-to-Neumann operator for a planar thin layer and stabilization in the framework of couple stress elasticity with voids

Article type: Research Article

Authors: Abdallaoui, Athmane^{a; *} | Kelleche, Abdelkarim^b

Affiliations: [a] Laboratoire de Mathématiques et Physique Appliquées, École Normale Supérieure de Bou Saâda, 28001 Bou Saâda, Algeria | [b] Faculté des Sciences et de la Technologie, Université Djilali Bounaâma, Soufay 44225, Khemis Miliana, Algeria

Correspondence: [*] Corresponding author. E-mails: a.abdallaoui18@gmail.com, abdallaoui.athmane@ens-bousaada.dz.

Abstract: In this paper, we start from a two dimensional transmission model problem in the framework of couple stress elasticity with voids which is defined in a fixed domain Ω− juxtaposed with a planar thin layer Ω+δ. We first derive a first approximation of Dirichlet-to-Neumann operator for the thin layer Ω+δ by using the techniques of asymptotic expansion with scaling, which allows us to approximate the transmission problem by a boundary value problem doesn’t take into account any more the thin layer Ω+δ, called approximate impedance problem; after that, we prove an error estimate between the solution of the transmission problem and the solution of the approximate impedance problem.

Keywords: Couple stress elasticity with voids, porous micropolar layer, Dirichlet-to-Neumann operator, impedance operator, asymptotic expansion

DOI: 10.3233/ASY-231886

Journal: Asymptotic Analysis, vol. 137, no. 3-4, pp. 245-265, 2024