Asymptotic Justification of Models of Plates Containing Inside Hard Thin Inclusions

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 the width of the inclusion ε as εN with N<1. The passage to the limit as the parameter ε 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∈(−1,1).