employee
Makeevka, Ukraine
The work is devoted to carrying out multidimensional interpolation and approximation methods for the numerical solution of differential equations and computer model development of the stress-strain state of metal structures. The core of the work is a fundamental computational algorithm for the numerical solution of differential equations using geometric interpolants on regular and irregular networks. On its basis, computational experiments are carried out on numerical simulation of the stress-strain state of operated reservoirs for storing petroleum products, which form a software package implemented in the Maple interpreter. At the same time, the differential equation for modelling the stress-strain state of an elastic cylindrical shell under axisymmetric loading is improved for the numerical analysis of the stress-strain state of a cylindrical reservoir with geometric imperfections. Also a new approach is proposed to take into consideration the initial conditions of the differential equation, which consists of parallel transfer of the numerical solution to the point, its coordinates correspond to the initial conditions. The advantage of the proposed approach for the numerical solution of differential equations using geometric interpolants is that it eliminates the need to coordinate geometric information in the process of interaction between CAD and FEA systems, by analogy with the isogeometric method.
computer model, geometric interpolant, differential equation, numerical solution, stress-strain state, metal structures
1. Israfilova A.I., Kutrunov V., Garcia M., Kaliske M. Isogeometric Analysis as an Alternative to the Standard Finite Element Method. Construction of Unique Buildings and Structures. 2019;9(84):7-21. doi:https://doi.org/10.18720/CUBS.84.1.
2. An efficient isogeometric solid-shell formulation for geometrically nonlinear analysis of elastic shells / L. Leonetti, F. Liguori, D. Magisano, G. Garcea // Computer Methods in Applied Mechanics and Engineering, 2018. Vol. 331. pp. 159-183. DOI:https://doi.org/10.1016/j.cma.2017.11.025.
3. Li W., Nguyen-Thanh N., Zhou K. Geometrically nonlinear analysis of thin-shell structures based on an isogeometric-meshfree coupling approach // Computer Methods in Applied Mechanics and Engineering. 2018. Vol. 336. pp. 111-134. DOI:https://doi.org/10.1016/j.cma.2018.02.018.
4. Tornabene F., Fantuzzi N., Bacciocchi M. A new doubly-curved shell element for the free vibrations of arbitrarily shaped laminated structures based on weak formulation isogeometric analysis // Composite Structures. 2017. Vol. 171. pp. 429-461. DOI:https://doi.org/10.1016/j.compstruct.2017.03.055.
5. Konopatsky EV. Solving Differential Equations Using Geometric Modelling Methods. In: Proceedings of the 28th International Conference on Computer Graphics and Machine Vision: GraphiCon; 2018 Sep 24-27; Tomsk: TPU: 2018. p. 358-361.
6. About one method of numeral decision of differential equalizations in partials using geometric interpolants / E.V. Konopatskiy, O.S. Voronova, O.A. Shevchuk, A.A. Bezditnyi. - CEUR Workshop Proceedings. 2020. Vol. 2763. pp. 213-219. DOI:https://doi.org/10.30987/conferencearticle_5fce27708eb353.92843700.
7. Konopatskiy E.V., Bezditnyi A.A., Shevchuk O.A. Modeling geometric varieties with given differential characteristics and its application // CEUR Workshop Proceedings. 2020. Vol. 2744. DOI:https://doi.org/10.51130/graphicon-2020-2-4-31.
8. Konopatsky E.V. Geometric Theory of Multidimensional Interpolation. Automation and Modelling in Design and Management. 2020;1(07): 9-16. doi:https://doi.org/10.30987/2658-6436-2020-1-9-16
9. Konopatsky EV. Principles of Construction of Computer Models of Multifactor Processes and Phenomena by the Method of Multidimensional Interpolation. In: Proceedings of the 2d International Scientific and Practical Conference: Software Engineering: Methods and Technologies for the Development of Information and Computing Systems (PIIVS-2018); 2018 Nov 14-15; Donetsk: Donetsk National Technical University: 2018. p. 309-318.9. Novikov D.A. The Theory of Management of Organizational Systems: an Introductory Course. Available at: http://window.edu.ru/catalog/pdf2txt/747/47747/23705 / (Accesses: the 2nd of January 2022).
10. Konopatskiy E.V., Bezditnyi A.A. Geometric modeling of multifactor processes and phenomena by the multidimensional parabolic interpolation method // IoP conference series: Journal of Physics: Conf. Series 1441 (2020) 012063. DOI:https://doi.org/10.1088/1742-6596/1441/1/012063.
11. Introduction to the mathematical apparatus of BN calculus / A.I. Paper, E.V. Konopatsky, A.A. Krysko, O.A. Chernysheva // Problems of quality of graphic training of students in a technical university: traditions and innovations. 2017. Vol. 1. pp. 76-82..
12. Balyuba I.G., Konopatsky E.V., Paper A.I. Point calculus. Makeyevka: DONNASA. 2020. 244 p.
13. Baliuba IG, Konopatsky EV. Point Calculus. Historical Background and Fundamental Definitions. In: Proceedings of the 8th International Scientific Conference: Physical and Technical Informatics; 2020 Nov 09-13; Nizhny Novgorod: 2020. Part 2. p. 321-327. doi:https://doi.org/10.30987/conferencearticle_5fd755c0adb1d9.27038265.
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19. Shevchuk O.A. Using Geometric Interpolants for the Numerical Solution of The Laplace Equation in a Rectangle. Informatics and Cybernetics. 2021;1-2 (23-24):74-79.
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22. An approach to comparing multidimensional geometric objects / I.V. Seleznev, E.V. Konopatskiy, O.S. Voronova, O.A. Shevchuk, A.A. Bezditnyi // CEUR Workshop Proceedings. Proceedings of the 31st International Conference on Computer Graphics and Vision (GraphiCon 2021) Nizhny Novgorod. September 27-30. 2021. Vol. 3027. pp. 682-688. DOI:https://doi.org/10.20948/graphicon-2021-3027-682-688.
23. Konopatsky E.V., Krysko A.A., Bumaga A.I. Computational Algorithms for Modelling of One-Dimensional Contours through k in Advance Given Points. Geometry and Graphics. Moscow: Infra-M. 2018;3:20-32. doi:https://doi.org/10.12737/article_5bc457ece18491.72807735
