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Analysis of numeric results for analogue of Galin’s problem in curvilinear coordinates

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Authors:


A.H.Shporta*, orcid.org/0000-0002-1260-7358, Dnipro University of Technology, Dnipro, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

T.S.Kagadii, orcid.org/0000-0001-6116-4971, Dnipro University of Technology, Dnipro, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

V.B.Govorukha, orcid.org/0000-0002-0936-9272, Dnipro State Agrarian and Economic University, Dnipro, Ukraine,  e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

O.D.Onopriienko, orcid.org/0000-0002-3127-4616, Dnipro State Agrarian and Economic University, Dnipro, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Shuo Zhao, orcid.org/0000-0002-7216-4317, Hebei University of Science and Technology, School of Mechanical Engineering, Shijiazhuang, the People’s Republic of China, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

* Corresponding author e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.


повний текст / full article



Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu. 2023, (1): 142 - 148

https://doi.org/10.33271/nvngu/2023-1/142



Abstract:



Purpose.
Studying the results obtained when applying the perturbation method to the individual contact problems solution. Considering the influence of non-ideal material properties of interaction bodies. Considering the contact area’s complex geometry influence.


Methodology.
Mathematical models of the interaction of an elastic plate with cylindrical anisotropy in the form of a curvilinear sector problems have been constructed and considered. In the process of interaction between the stamp and the plate, areas of slippage and adhesion occur. The original complex problems of the theory of elasticity in the process of applying the perturbation method are reduced to the sequential solution of the potential theory problems.


Findings.
An analytical solution to the interaction of an elastic anisotropic plate in the form of a curvilinear sector and a rigid stamp problem was obtained considering the existence of slippage and adhesion areas in the contact area. Laws of stress distribution under the stamp were found, as well as dependence of this distribution on the dimensions of the contact area.


Originality.
The perturbation method is convenient and expedient to use when solving mining mechanics problems.

The study on the stress-strain state of an elastic anisotropic plate for the analogue of Galin’s problem was carried out, and the corresponding analytical solutions were obtained. The dependence of the coupling area size on the dimensions of the stamp and the opening angle of the sector, physical properties of the material is analyzed. Possible boundary transitions have been completed.


Practical value.
The proposed approach makes it possible to obtain analytical solutions to practically important problems in mining, to evaluate the stress-strain state of thick-walled structures with reinforcing elements, stamps, overlays. The results can be useful when designing mine workings.



Keywords:
stress distribution, adhesion, anisotropy, sliding, curvilinear sector, asymptotic method

References.


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ISSN (print) 2071-2227,
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Journal was registered by Ministry of Justice of Ukraine.
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