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

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-12-08 DOI:10.3233/asy-231886

Athmane Abdallaoui, A. Kelleche

引用次数: 0

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.

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平面薄层的 Dirichlet 到 Neumann 算子的近似以及有空隙的耦合应力弹性框架下的稳定化

在本文中，我们从一个在固定域Ω−和一个平面薄层Ω + δ中定义的带空洞的耦合应力弹性框架下的二维传输模型问题开始。我们首先利用带标度的渐近展开技术推导出薄层Ω + δ的Dirichlet-to-Neumann算子的第一个近似，这使得我们可以用边值问题来近似传输问题，不再考虑薄层Ω + δ，称为近似阻抗问题;然后，我们证明了传输问题的解与近似阻抗问题解之间的误差估计。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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