Comparison of displacement and stress fields upon diffraction of elastic waves at different defects: Cracks and thin rigid intrusions

Попов, В. Г.

doi:10.1007/bf02432987

Cited by 1 publication

(3 citation statements)

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“…The problems of determination of the stress state in infinite bodies containing defects in the form of thin inclusions or cracks and subjected to dynamic (in particular, harmonic) loads can be regarded as fairly well investigated. Note that, as shown in [10,13,17,18,20], this is true for both two-dimensional and three-dimensional problems of the theory of elasticity. One of the approaches to the solution of these problems is connected with the application of direct numerical methods (difference and finite-element methods) [19,21].…”

mentioning

confidence: 66%

“…To solve the posed problem, we first construct in the system x 1 O 1 y 1 a discontinuous solution of the Helmholtz equation [9,10] with jump χ 2 (x 1 ) determined by equality (5):…”

Section: Solution Of the Problem In The Case Of A Crackmentioning

confidence: 99%

“…To solve the problem in the case of inclusions, in the coordinate system x 1 O 1 y 1 we also construct a discontinuous solution of the Helmholtz equation ( 1) with jump χ 1 (x 1 ) determined by relation ( 7) [9,10]:…”

Section: Solution Of the Problem In The Case Of Inclusionsmentioning

confidence: 99%

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Stress state in an infinite cylinder of any cross section with tunnel defect under harmonic oscillations of longitudinal shear

Kyrylova

Попов

2013

J Math Sci

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We solve the problems of finding the stress state near through defects (cracks or thin rigid inclusions) in an infinite cylinder of any cross section under the conditions of oscillations of longitudinal shear. We propose an approach that enables one to separately satisfy the conditions imposed on the surfaces of the defects and on the boundary of the body. Approximate relations for the stress intensity factors are obtained and the influence of the frequencies of oscillations, type of the defects, and their location on the values of the stress intensity factors are investigated by using the indicated relations,.

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mentioning

confidence: 66%

“…To solve the posed problem, we first construct in the system x 1 O 1 y 1 a discontinuous solution of the Helmholtz equation [9,10] with jump χ 2 (x 1 ) determined by equality (5):…”

Section: Solution Of the Problem In The Case Of A Crackmentioning

confidence: 99%