On singular models of a thin inclusion in a homogeneous elastic medium
type: Item
instance of: scholarly article
title: On singular models of a thin inclusion in a homogeneous elastic medium
zbMATH Open document ID: 0566.73013
DOI: 10.1016/0021-8928(84)90106-0
author: S. K. Kanaun
published in: Journal of Applied Mathematics and Mechanics
publication date: 1985-01-01T00:00:00Z
review text: The equilibrium of an unbounded homogeneous and anisotropic elastic medium containing an inclusion, one of whose characteristic dimensions is much less than the other two is considered. It is assumed that the elastic moduli of the medium and the inclusion differ substantially. The principal terms of the expansion of the elastic fields in the neighbourhood of the thin inclusion are constructed in asymptotic series in small parameters of the problem: the ratio of the characteristic linear dimensions of the inclusion and the ratio of the characteristic values of the elastic moduli of the medium and the inclusion. The problem of constructing the principal terms of these expansions reduces to solving two-dimensional pseudo-differential equations derived by using the procedure of matching the external and internal asymptotic expansions [e.g. \textit{A. H. Nayfeh}, Perturbation methods (1973; Zbl 0265.35002)]. The results obtained enable two singular models of thin inclusions to be formulated for the cases when their elastic moduli are substantially greater and substantially less than the elastic modulus of the medium. It is shown that one of these models is equivalent to the model of a thin inclusion proposed e.g. in \textit{O. V. Sotkilava}, \textit{G. P. Cherepanov}, Prikl. Mat. Mekh. 38, 539-550 (1974; Zbl 0312.73115).
Mathematics Subject Classification ID: 74E05
Mathematics Subject Classification ID: 74E10
Mathematics Subject Classification ID: 74C15
Mathematics Subject Classification ID: 74C20
Mathematics Subject Classification ID: 74A99
zbMATH DE Number: 3904051
zbMATH Keywords: equilibrium
zbMATH Keywords: unbounded homogeneous
zbMATH Keywords: one of whose characteristic dimensions is much less than the other two
zbMATH Keywords: elastic moduli
zbMATH Keywords: medium
zbMATH Keywords: inclusion differ substantially
zbMATH Keywords: principal terms of the expansion of the elastic fields
zbMATH Keywords: asymptotic series in small parameters
zbMATH Keywords: two-dimensional pseudo-differential equations
zbMATH Keywords: matching the external and internal asymptotic expansions
zbMATH Keywords: two singular models of thin inclusions
zbMATH Keywords: moduli are substantially greater
zbMATH Keywords: substantially less than the elastic modulus of the medium
MaRDI profile type: Publication
full work available at URL: 0021-8928(84)90106-0
OpenAlex ID: W1970717726
cites work: Q5509552
cites work: Perturbation methods and non-linear hyperbolic waves
cites work: Some problems of the nonhomogeneous elasticity theory
cites work: Q5642088
cites work: Q4043492
cites work: Q3956025
cites work: Q5635076
cites work: On the problem of a three-dimensional crack in an anisotropic elastic medium
cites work: Stress concentration on an ellipsoidal inhomogeneity in an anisotropic elastic medium
description: scientific article; zbMATH DE number 3904051