Conformal contact between layered foundations and punches

Kazakov, K. E.; Manzhirov, Alexander V.

doi:10.3103/s0025654408030229

Cited by 14 publications

(8 citation statements)

References 1 publication

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“…In a fairly general case, integral equations arising in plane contact and wear problems for coated base [9,14,15] are reduced to the following dimensionless form:…”

Section: Integral Equation and Orthonormal Basismentioning

confidence: 99%

“…In the works [9,14,15], it is shown that if the functions m(x) and/or g(x) are rapidly changing, then the solution must be constructed in a special way so that these functions are present in it as multipliers and terms. Otherwise, the solution obtained by standard methods will not allow to perform real calculations, since the number of terms of infinite series necessary to be calculated will be large.…”

Section: Integral Equation and Orthonormal Basismentioning

confidence: 99%

“…The paper presents approaches that allow one to calculate decomposition coefficients of kernels on a special system of eigenfunctions for plane problems of contact between a rigid punch and a coated foundation in cases when the coating has complex properties and/or the shapes of the contacting surfaces are described by rapidly changing functions. Such contact problems were considered, for example, in the works [9,14]. Some numerical calculations and graphs are presented in these articles.…”

Section: Introductionmentioning

confidence: 99%

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Calculation of the decomposition coefficients for plane contact problem kernel in the orthonormal basis

Kazakov

2024

ACM

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Analytical solutions of some contact problems are infinite functional series according to the system of basic functions. When constructing such solutions, it becomes necessary to represent the kernels of integral equations describing the process of interaction in the form of two-dimensional series on a given basis. Often the kernels have a rather complex appearance, therefore, the process of finding the decomposition coefficients is a rather complex and labor-intensive process, on which the accuracy and speed of obtaining final results depend. The paper proposes a calculation method that allows calculating the coefficients of decomposition of the kernels of plane contact problems according to a special orthonormal basis that takes into account the features of contacting bodies. Other approximate formulas are also derived for the special case when coating characteristics are constant. Based on the received presentation, conclusions and recommendations are formulated.

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“…In a fairly general case, integral equations arising in plane contact and wear problems for coated base [9,14,15] are reduced to the following dimensionless form:…”

Section: Integral Equation and Orthonormal Basismentioning

confidence: 99%

Section: Integral Equation and Orthonormal Basismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Calculation of the decomposition coefficients for plane contact problem kernel in the orthonormal basis

Kazakov

2024

ACM

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“…47 This work is a continuation of the research that was reflected in previous articles. 45,[48][49][50][51][52][53][54][55][56][57][58][59][60][61] It is devoted to the construction of an analytical solution for the problem of the interaction of a strip with a multilayer nonuniform coating and a system of rigid punches.…”

Section: Introductionmentioning

confidence: 99%

Plane problems of multiple interactions of rigid punches and bodies with complex multilayer coatings

Kazakov

Kurdina

2023

Math Methods in App Sciences

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The article deals with the most general formulation of the problem of the interaction of a system of rigid punches and a viscoelastic aging foundation covered by several different nonuniform thin layers of variable thickness. It is shown that the mathematical model of such a problem is a system of mixed integral equations with additional integral conditions. On the basis of a special approach described in present article, an analytical solution is obtained in series for various versions of the problem statement. It is indicated that the obtained solution representation is effective even in the case when the properties of the coating layers and the shape of the contacting surfaces are described by complex functions.

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“…The study of plane contact problems for bodies with complex coatings began with solving problems for foundations with coatings having a complex shape, consistent with the shape of the acting punch [1] and for bodies with nonuniform coatings [2]. The mathematical model of such problems contained one complex function.…”

Section: Introductionmentioning

confidence: 99%

Contact problem for foundations with multilayer nonuniform coatings of variable thickness

Kazakov

Kurdina

2020

E3S Web Conf.

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The article is devoted to study of the contact problem for a punch with a complex shape and a base with a coating consisting of nonuniform layers of variable thickness. Such a foundations are often found in practice. Coating layers in them can play a role, for example, heat or electric insulators. Such layers can be used as protection against mechanical stress on the main structure. Mathematical model of the problem is constructed. It is a mixed integral equation containing functions that describe the properties and thicknesses of the layers, as well as the shapes of the contacting bodies, and additional integral conditions. Analytical solution of the problem is presented for one of the formulation options. In the resulting solution, the functions associated with the properties and forms of bodies are distinguished by separate terms. This allows one to perform high-quality calculations and analysis of the behavior of the punch on the layer, even if these functions are rapidly changing.

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Conformal contact between layered foundations and punches

Cited by 14 publications

References 1 publication

Calculation of the decomposition coefficients for plane contact problem kernel in the orthonormal basis

Calculation of the decomposition coefficients for plane contact problem kernel in the orthonormal basis

Plane problems of multiple interactions of rigid punches and bodies with complex multilayer coatings

Contact problem for foundations with multilayer nonuniform coatings of variable thickness

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