Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Asymptotic Justification of Models of Plates Containing Inside Hard Thin Inclusions

Version 1 : Received: 1 October 2020 / Approved: 2 October 2020 / Online: 2 October 2020 (10:38:58 CEST)

How to cite: Rudoy, E. Asymptotic Justification of Models of Plates Containing Inside Hard Thin Inclusions. Preprints 2020, 2020100038 (doi: 10.20944/preprints202010.0038.v1). Rudoy, E. Asymptotic Justification of Models of Plates Containing Inside Hard Thin Inclusions. Preprints 2020, 2020100038 (doi: 10.20944/preprints202010.0038.v1).

Abstract

An equilibrium problem of the Kirchhoff-Love plate containing a nonhomogeneous inclusion is considered. It is assumed that elastic properties of the inclusion depend on a small parameter characterizing width of the inclusion $\varepsilon$ as $\varepsilon^N$ with $N<1$. The passage to the limit as the parameter $\varepsilon$ tends to zero is justified, and an asymptotic model of a plate containing a thin inhomogeneous hard inclusion is constructed. It is shown that there exists two types of thin inclusions: rigid inclusion ($N<-1$) and elastic inclusion ($N=-1$). The inhomogeneity disappears in the case of $N\in (-1,1)$.

Subject Areas

Kirchhoff-Love plate; Composite material; Thin inclusion; Asymptotic analysis

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