The plane mixed problem for an elastic semi-strip under different load types at its short edge

Menshykov, Oleksandr; Reut, Olena; Reut, V. V.; Vaysfeld, Natalya; Zhuravlova, Zinaida

doi:10.1016/j.ijmecsci.2018.05.049

Cited by 8 publications

(3 citation statements)

References 31 publications

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“…The first singular integral equation in system (24) is the partial case of the equation with two fixed singularities. [39] The transcendental equation for the definition of the singularity indicator of the solution̂( ) was constructed. It is congruent to the transcendental equation presented in [40] for the problem of a wedge with the angle of openness ∕2.…”

Section: Casementioning

confidence: 99%

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The investigation of semi‐strip's stress state with a longitudinal crack

Vaysfeld

Zhuravlova

2020

Z Angew Math Mech

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The article is dedicated to the investigation of the stress state of a semi-strip weakened by a longitudinal crack. Two statements of the problem are considered. The integral Fourier transform is applied directly to the initial problem. The discontinuous boundary problem which is formulated in vector form is solved with the help of the matrix differential calculation and the Green's matrix-function's discontinuous properties. The solving of the problem is reduced to the solving of the system of three singular integral equations (SSIE). This system is solved by two methods regarding to the conditions at the semi-strip's short edge. The orthogonal polynomials method is used when the semi-strip is loaded at the center of its short edge, and the special generalized scheme, which allows consideration of fixed singularities, this is applied when the whole semi-strip's short edge is loaded. The stress intensity factors (SIF) are investigated for the two cases. K E Y W O R D Sfixed singularity, Green's function, longitudinal crack, semi-strip, singular integral equations INTRODUCTIONThe elasticity problem for a semi-strip with a longitudinal crack is a model problem. Its solving is important both for the development of theoretical methods and for the practical demand of engineering problems.The problems of elastic strips and semi-strips weakened by cracks have been solved by many methods: with the help of harmonic functions, simple and double layer potentials, integral transformations, asymptotic methods and others.The mixed elasticity problems were solved in [1]. Elastodynamic analysis of multiple crack problem in 3-D bi-materials was made in [2]. A new type of cracks adding to Griffith-Irwin cracks was investigated in [3]. In the case of the new type of cracks, fracture occurs due to an increase in the stress concentrations up to singular concentrations. A finite elastic wedge-shaped thick plate was considered in [4].The problem about determining the thermal stress in a thermoelastic strip with a collinear array of cracks which are parallel to the strip's sides was considered in [5]. The solving of the Duhamel-Neumann equation was constructed with the help of harmonic functions. The solving of the problem for the infinite strip with a semi-infinite crack was reduced to solving of singular integral equation by the use of simple layer and double layer potentials in [6]. The method for the elastic strip which is weakened by cracks and holes was proposed in [7]. The solution of this problem was reduced to singular integral equation with the help of complex potentials.The plane problem about the interfacial crack between the elastic strip and the elastic semi-plane from another material was solved in [8]. The regular asymptotic method was applied for the solving of the system of integral equations for the displacements' jumps. This method is efficient when the crack is sufficiently narrow. Two configurations of modeling of an interfacial crack with parallel free boundaries were investigated in [9]: a crack in the semi-plane...

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Section: Casementioning

confidence: 99%

“…The first singular integral equation in system is the partial case of the equation with two fixed singularities . The transcendental equation for the definition of the singularity indicator of the solution

\hat{χ} false(ξ false)

was constructed.…”

Section: The Solving Of the Ssiementioning

confidence: 99%

The investigation of semi‐strip's stress state with a longitudinal crack

Vaysfeld

Zhuravlova

2020

Z Angew Math Mech

Self Cite

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“…The boundary value problem in the theory of elasticity (and the theory of plate bending) for a half-strip or a rectangle, two opposite sides of which are firmly clamped and stresses are specified at the ends, has been the subject of numerous studies, especially in the period of 1960s to 1980s. Reviews can be found, for example, in previous studies [1][2][3][4][5][6]. Researchers were interested in the question of the singularity for stresses at the corner points of the regions under consideration, which are simultaneously the points of change in the type of boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Exact solutions of the theory of elasticity for a clamped rectangle

Коваленко

Menshova

Kerzhaev

et al. 2022

Mathematics and Mechanics of Solids

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We present the formulas that describe the exact solutions of the boundary value problems in the theory of elasticity for a half-strip and a rectangle in which the horizontal sides are firmly clamped, while normal and tangential stresses are specified on the vertical ones. We consider only an even-symmetric deformation of the half-strip and the rectangle relative to the horizontal axis of symmetry as well as even-symmetric and odd-symmetric deformations relative to the vertical axis of symmetry for the rectangle. This paper is based on the previously obtained solutions for a free half-strip and a free rectangle.

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Dynamic Mixed Problem of Elasticity for a Rectangular Domain

Pozhylenkov¹,

Vaysfeld²

2022

Mechanisms and Machine Science

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The plane mixed problem for an elastic semi-strip under different load types at its short edge

Cited by 8 publications

References 31 publications

The investigation of semi‐strip's stress state with a longitudinal crack

The investigation of semi‐strip's stress state with a longitudinal crack

Exact solutions of the theory of elasticity for a clamped rectangle

Dynamic Mixed Problem of Elasticity for a Rectangular Domain

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