Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed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

A peer-reviewed article of this Preprint also exists.

Rudoy, E. Asymptotic Justification of Models of Plates Containing Inside Hard Thin Inclusions. Technologies 2020, 8, 59. Rudoy, E. Asymptotic Justification of Models of Plates Containing Inside Hard Thin Inclusions. Technologies 2020, 8, 59.

Journal reference: Technologies 2020, 8, 59
DOI: 10.3390/technologies8040059

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 $N\in (-1,1)$.

Keywords

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

Subject

MATHEMATICS & COMPUTER SCIENCE, Algebra & Number Theory

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