Doubly Periodic Cracks in the Anisotropic Medium with the Account of Contact of Their Faces

Maksymovych, О. V.; Pasternak, Iaroslav; Sulym, Heorhiy; Kutsyk, Serhiy

doi:10.2478/ama-2014-0029

Cited by 10 publications

(10 citation statements)

References 5 publications

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“…Let us write a general solution of the problem based on [12,15] through the Lekhnitskii potentials in the form…”

Section: Integral Equations For Anisotropic Bounded Plate With Holes mentioning

confidence: 99%

“…Let us substitute the potentials (6) into the formulas (4) for projections of stress vectors determined at the boundaries path L and Γ. Using Plemelj-Sokhotski formula, we obtain a system of integral equations [12,15]:…”

Section: Integral Equations For Anisotropic Bounded Plate With Holes mentioning

confidence: 99%

“…Let us replace the integrals with Lobatto-type quadrature formulas [15], and the integrals at the boundaries of the holes replaced by the quadrature of a rectangle, which, for periodic functions, are Gauss quadrature-type formulas [12]. Then we obtain the system of equations:…”

Section: Integral Equations For Anisotropic Bounded Plate With Holes mentioning

confidence: 99%

“…In [12,13], the simple dependencies between the Lekhnitskii complex potentials and stress and strain are obtained. In a simple form based on them and the Cauchy theorem, the integral equations are written for anisotropic plates with holes [12,13] and cracks [14][15][16]. We will use the established dependencies for the construction and regularization of integral equations for anisotropic plates with holes and cracks.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Determination of Stresses in Composite Plates with Holes and Cracks Based on Singular Integral Equations

Maksymovych¹,

Podhorecki²

2020

Dynamical Systems Theory

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The problems of determination of stresses at crack in bounded plates with holes of different shapes under the action of concentrated forces or distributed forces at its boundary are considered. The study is performed by the singular integral equation method. They were determined based on the established interdependences between the Lekhnitskii potentials and the stress and strain. The numerical method for solving integral equations is developed based on the quadrature method for the systems of holes and cracks. The eigen solutions of the problem were taken into account in this method. The research of stresses at cracks in samples which are used in experimental studies of crack fracture resistance was performed.

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“…Let us write a general solution of the problem based on [12,15] through the Lekhnitskii potentials in the form…”

Section: Integral Equations For Anisotropic Bounded Plate With Holes mentioning

confidence: 99%

Section: Integral Equations For Anisotropic Bounded Plate With Holes mentioning

confidence: 99%

Section: Integral Equations For Anisotropic Bounded Plate With Holes mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Determination of Stresses in Composite Plates with Holes and Cracks Based on Singular Integral Equations

Maksymovych¹,

Podhorecki²

2020

Dynamical Systems Theory

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“…In publications [4], [6]- [7], the interdependencies between the potentials of Lehnitskiy and the stresses and displacements have been determined. Based on these interdependencies and on the Cauchy theorem, the modified singular integral equations for anisotropic plates with holes are written in the simplified form.…”

Section: Introduction and Review Of Modern Information Sourcesmentioning

confidence: 99%

Determination of Stresses and Ultimate Loads for Composite Plates with Elastic Inclusions

Jaroszewicz¹,

Maksymovych²,

Dzyubyk³

et al. 2017

Ukr. j. mech. eng. mater. sci.

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In the article, the algorithm for determination of stresses in anisotropic plates with elastic inclusions of another anisotropic material was developed on the basis of complex singular integral equations. The solving of integral equations has been carried out numerically using the method of mechanical quadratures. The strength analysis (calculation of strength) of composite plates with inclusions has been performed using the Hoffman criterion.

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Crack tip fields in anisotropic planes: a review

2021

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This paper reviews crack tip asymptotic fields in generic plane anisotropic media, rigorously categorising about 400 studies devoted to the determination of the asymptote coefficients, also referred to as crack tip parameters. These studies cover a broad spectrum of methodologies focused on determining crack tip parameters in anisotropic materials, from analytical, numerical and experimental perspectives, conducted over the last six decades. Brief descriptions are given for a selected number of approaches to shed light on their general concepts and their methodology to characterise crack tip parameters. Lastly, the influence of higher order coefficients in the crack tip stress field is demonstrated by a representative example from the literature.

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Doubly Periodic Cracks in the Anisotropic Medium with the Account of Contact of Their Faces

Cited by 10 publications

References 5 publications

Determination of Stresses in Composite Plates with Holes and Cracks Based on Singular Integral Equations

Determination of Stresses in Composite Plates with Holes and Cracks Based on Singular Integral Equations

Determination of Stresses and Ultimate Loads for Composite Plates with Elastic Inclusions

Crack tip fields in anisotropic planes: a review

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