Research

Current research
Analytical methods for solving boundary value problems based on constructed versions of the mathematical theory of linearly and nonlinearly elastic homogeneous and layered plates and shallow shells of arbitrary constant thickness. Generalization of newly developed methods for reducing systems of inhomogeneous differential equations with high-order partial derivatives to homogeneous and inhomogeneous differential equations with second-order partial derivatives. Development of new conceptual approaches to the design and construction of structures, residential buildings, shelters, airfields, tanks with a high level of protection against destruction as a result of missile and bomb strikes.
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Past research
Research of the stress-strain state of linearly and nonlinearly elastic homogeneous and layered plates and shallow shells of arbitrary constant thickness based on constructed variants of the mathematical theory.
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Expertise Summary

Calculations of thin and non-thin plates and shells according to mathematical theory. Development of new conceptual approaches to the design and construction of structures, residential buildings, shelters, airfields, tanks with a high level of protection against destruction as a result of missile and bomb strikes. Design calculations of the specified objects with a high level of life support.

Publications

1. A. G. Zelensky, Fundamental solutions of the defining system of differential equations of the mathematical theory of plates. Bulletin of Zaporizhzhya National University. Mathematical modeling and applied mechanics. Physical and mathematical sciences. Zaporizhzhia (Ukraine). 2018. No. 1. P. 13–29. ( Index COPERNICUS, ICV 2017: 80.00, CiteFactor, ResearchBib, Journal Factor). DOI: 10.26661/2413-6549-2018-1-1-02.

2. Zelensky A. G. Mathematical Theory of Transversally Isotropic Shells of Arbitrary Thickness at Static Load. Materials Science Forum. Actual problems of engineering mechanics. Switzerland: Trans Tech Publications Ltd, 2019. V. 968. P. 496–510. Scopus. ISSN: 1662–9752, doi: 10.4028/www.scientific.net/MSF.968.496.
3. Zelensky A. G. The Method of Successive Approximations in the Mathematical the-orv of Shallow Shells of Arbitrary Thickness. World Science, Multidisciplinary Scientific Edition, Physics and Mathematics. RS Global Sp. z O.O.: Warsaw, 2019. V. 1, №11(51). P. 31–39. (RS Global, Google Scholar, Index Copernicus, Academia.edu, Library.ru, Biblioteka Narodowa, CiteFactor). ISSN 2413–1032; DOI:https://doi.org/10.31435/rsglobal_ws/30112019/6764; http://ws-conference.com/.
4. Zelensky A. G. Analytical and Practical Development of Variant of Mathematical Theory of Shells of Small Curvature of Arbitrary Thickness. New Stages of Development of Modern Scince in Ukraine and eu Countries. Chapter “Physical and Mathematical Sciences”. Monograph. Riga, Latvia: “Baltija Publishing”, 2019. P. 308–328. ISBN:978-9934-588-15-0, DOI:https://doi.org/10.30525/978-9934-588-15-0-63.
5. Zelensky A. G. Some theorems of Variant of Mathematical Theory of Plates and Shallow Shells of Arbitrary Thickness. Proceedings of the XX1 International Scientific and Practical Conference. International Trends in Science and Technology. Multidisciplinary Scientific Edition. Physics and Mathematics. RS Global Sp. z O.O., Warsaw, Poland, January 31,2020. P. 3–11. ISBN 978-83-956628-1-2. Indexed by: RS Global, Academia.edu, Google Scholar.
6. Zelensky Anatoly, Privarnikov Arkady. The method of integrating systems of high-order equi-librium equations of the mathematical theory of thick plates under intermittent loads (part 1). Innovative scientific researches: european development trends and regional aspect. Chapter “Physical and Mathematical Sciences”. Collective monograph, Riga, Latvia: “Baltija Publishing”, 2020. P. 221–255. ISBN: 978-9934-588-38-9, DOI: https://doi.org/10.30525/978-9934-588-38-9-6.
7. Zelensky A. G. Development of aVariant of Mathematical Theory of Thick Transversal-isotropic Plates, International periodic scientific journal. Modern engineering and innovative technologies. Karlsruhe, 2020. Issue № 11. Part 1. P. 27–41. ISSN 2567-5273, DOI: 10.30890/2567-5273.2020-11-01-041. Indexed in Index COPERNICUS high impact factor (ICV:84.35). http://www.moderntechno.de/index.php/meit/article/view/meit11-01-041.
8. Zelensky A.G., Demianenko A.G. A method for Solving Boundary Value Problems of Mathematical Theory of Thick Transversely Isotropic Plates. APEM 2021, IOP Publishing. IOP Conf. Series: Materials Science and Engineering. 1164 (2021) 012091. doi:10.1088/1757-899X/1164/1/012091. P.1-11. (Web of Science, in the process of indexing).
9. Kliushnyk D., Demianenko A., Zelensky A. Some features of oscillations and stability of reinforced cylindrical shells under action of movable inertial loading. APEM 2021, IOP Publishing. IOP Conf. Series: Materials Science and Engineering. 1164 (2021) 012032. doi:10.1088/1757-899X/1164/1/012032. P.1-8. (Web of Science, in the process of indexing).
10. Zelensky A. G. Monographic series “European Science”. SWordl Germany. Heritage of European Science Engineering, Informatics, Physics and Mathematics, Medicsne. Karlsruhe, 2022. Book 9. Part 1. Kapitel 4. General solutions of systems of inhomogeneous equations of high orders of the variant of mathematical theory of non-thin plates. ISBN 978-3-949059-50-6. DOI: 10.30890/2709-2313.2022-09-01-014.