Asymptotic solution of three-dimensional problems of the theory of elasticity of extended plane separation cracks
type: Item
instance of: scholarly article
title: Asymptotic solution of three-dimensional problems of the theory of elasticity of extended plane separation cracks
zbMATH Open document ID: 0585.73168
DOI: 10.1016/0021-8928(84)90071-6
author: R. V. Gol'dshtejn
author: A. V. Kaptsov
author: L. B. Korel'shtejn
published in: Journal of Applied Mathematics and Mechanics
publication date: 1984-01-01T00:00:00Z
review text: A solution of three-dimensional elasticity theory problems for separation cracks occupying a plane domain with one characteristic dimension much smaller than the other is constructed by the method of matched asymptotic expansions (cracks that are extended along a certain plane curve). The appropriate terms of the expansion of the solution in a small parameter characterizing the extent of the crack are constructed using an integro- differential equation in the displacement of points of the crack surface. For cracks that are extended along a line, the representation of the integro-differential equation in terms of a two-dimensional Fourier transform is used, which substantially simplifies the calculation. In the general case, the expansion is executed directly in the equation written in x-space. The asymptotic expansion constructed is valid in the middle part of the crack, outside of certain small neighbourhoods of the ends of the curve along which the crack is drawn. The accuracy of the solution obtained is analysed, and formulas are presented for the crack aperture and the distribution of the stress intensity factors for specific kinds of cracks.
Mathematics Subject Classification ID: 74R05
zbMATH DE Number: 3938800
zbMATH Keywords: cracks of elliptical planform
zbMATH Keywords: ring
zbMATH Keywords: ring sector
zbMATH Keywords: crescents
zbMATH Keywords: bounded by parabolic arcs
zbMATH Keywords: narrow crescent domains
zbMATH Keywords: extended along
zbMATH Keywords: a parabolic arc
zbMATH Keywords: three-dimensional elasticity theory problems
zbMATH Keywords: separation cracks
zbMATH Keywords: plane domain
zbMATH Keywords: method of matched asymptotic expansions
zbMATH Keywords: integro-differential equation in the displacement of points of
zbMATH Keywords: the crack surface
zbMATH Keywords: two- dimensional Fourier transform
zbMATH Keywords: accuracy
zbMATH Keywords: distribution of the stress intensity factors
zbMATH Keywords: integro-differential equation in the displacement of points of the crack surface
MaRDI profile type: Publication
full work available at URL: 0021-8928(84)90071-6
OpenAlex ID: W1969599230
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description: scientific article; zbMATH DE number 3938800