https://oldena.lpnu.ua/handle/ntb/52527| Title: | Mathematical Modeling of Two-Dimensional Deformation-Relaxation Processes in Environments with Fractal Structure |
| Authors: | Sokolovskyy, Yaroslav Levkovych, Maryana Mokrytska, Olha Atamanyuk, Vitalij |
| Affiliation: | Ukrainian National Forestry University Hetman Petro Sahaidachnyi National Army Academy |
| Bibliographic description (Ukraine): | Mathematical Modeling of Two-Dimensional Deformation-Relaxation Processes in Environments with Fractal Structure / Yaroslav Sokolovskyy, Maryana Levkovych, Olha Mokrytska, Vitalij Atamanyuk // Data stream mining and processing : proceedings of the IEEE second international conference, 21-25 August 2018, Lviv. — Львів : Lviv Politechnic Publishing House, 2018. — P. 375–380. — (Hybrid Systems of Computational Intelligence). |
| Bibliographic description (International): | Mathematical Modeling of Two-Dimensional Deformation-Relaxation Processes in Environments with Fractal Structure / Yaroslav Sokolovskyy, Maryana Levkovych, Olha Mokrytska, Vitalij Atamanyuk // Data stream mining and processing : proceedings of the IEEE second international conference, 21-25 August 2018, Lviv. — Lviv Politechnic Publishing House, 2018. — P. 375–380. — (Hybrid Systems of Computational Intelligence). |
| Is part of: | Data stream mining and processing : proceedings of the IEEE second international conference, 2018 |
| Conference/Event: | IEEE second international conference "Data stream mining and processing" |
| Issue Date: | 28-Feb-2018 |
| Publisher: | Lviv Politechnic Publishing House |
| Place of the edition/event: | Львів |
| Temporal Coverage: | 21-25 August 2018, Lviv |
| Keywords: | two-dimensional mathematical model derivative of fractional order deformation-relaxation processes numerical method statistical criterion |
| Number of pages: | 6 |
| Page range: | 375-380 |
| Start page: | 375 |
| End page: | 380 |
| Abstract: | In the work, the general mathematical model of two-dimensional viscoelastic deformation using the fractional integro-differential apparatus is constructed. The relations in the differential and integral forms are given to present twodimensional Kelvin’s and Voigt’s rheological models. The algorithm of a numerical method for solving the problem, based on the use of finite-difference schemes, was developed. The analytical expressions to describe deformations of onedimensional fractal models are given, and on the basis of which the identification of fractional-differential parameters is carried out. The influence of fractal parameters on the dynamics of deformation and stress variation for different rheological models is investigated. |
| URI: | https://ena.lpnu.ua/handle/ntb/52527 |
| ISBN: | © Національний університет „Львівська політехніка“, 2018 © Національний університет „Львівська політехніка“, 2018 |
| Copyright owner: | © Національний університет “Львівська політехніка”, 2018 |
| References (Ukraine): | [1] J. Sokolovskyy, V. Shymanskyi, M. Levkovych, and V. Yarkun, “Mathematical and Software providing of research of deformation and relaxation processes in environments with fractal structure,” XII international scientific and technical conference “Computer science and informational technologies” CSIT 2017, Lviv, Ukraine, pp. 24-2705-08 September, 2017. [2] Ya. I. Sokolovsky, and M. V. Levkovych, “Numerical method for the study of nonisothermic moisture transfer in the environments with fractal structure,” Bulletin of the National University "Lviv Polytechnic" Computer Science and Information Technologies, no. 843, pp. 288-296, 2015. (in Ukrainian) [3] L. Livi, A. Sadeghian, and A. Di Ieva, Fractal Geometry Meets Computational Intelligence: Future Perspectives. In: Di Ieva A. (eds) The Fractal Geometry of the Brain. Springer Series in Computational Neuroscience. Springer, New York, NY, 2016 [4] V. V. Vasilyev, amd L. A. “Simak Fractional calculus and approximation methods in the modeling of dynamic systems,” Scientific publication Kiev, National Academy of Sciences of Ukraine, p.256, 2008 [5] V. Uchajkin, Method of fractional derivatives. Ulyanovsk: Publishing house «Artishok», 2008. [6] I. Podlubny, Fractional Differential Equations, vol. 198. Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999. [7] Liu Tong, “Creep of wood under a large span of loads in constant and varying environments,” Pt.1: Experimental observations and analysis, Holz als Roh- und Werkstoff, vol. 51, pp. 400-405, 1993. [8] Е. Ogorodnikov, V. Radchenko, and L. Ugarova, “Mathematical modeling of hereditary deformational elastic body on the basis of structural models and of vehicle of fractional integro-differentiation Riman-Liuvil”, Vest. Sam. Gos. Techn. Un-ty. Series. Phys.-math. sciences, vol. 20, no. 1, pp. 167-194, 2016. [9] O. Riznik, I. Yurchak, E. Vdovenko, and A. Korchagina, “Model of stegosystem images on basis of pseudonoise codes”, VIth International Conference on Perspective Technologies and Methods in MEMS Design, Lviv, pp. 51-52, 2010. |
| References (International): | [1] J. Sokolovskyy, V. Shymanskyi, M. Levkovych, and V. Yarkun, "Mathematical and Software providing of research of deformation and relaxation processes in environments with fractal structure," XII international scientific and technical conference "Computer science and informational technologies" CSIT 2017, Lviv, Ukraine, pp. 24-2705-08 September, 2017. [2] Ya. I. Sokolovsky, and M. V. Levkovych, "Numerical method for the study of nonisothermic moisture transfer in the environments with fractal structure," Bulletin of the National University "Lviv Polytechnic" Computer Science and Information Technologies, no. 843, pp. 288-296, 2015. (in Ukrainian) [3] L. Livi, A. Sadeghian, and A. Di Ieva, Fractal Geometry Meets Computational Intelligence: Future Perspectives. In: Di Ieva A. (eds) The Fractal Geometry of the Brain. Springer Series in Computational Neuroscience. Springer, New York, NY, 2016 [4] V. V. Vasilyev, amd L. A. "Simak Fractional calculus and approximation methods in the modeling of dynamic systems," Scientific publication Kiev, National Academy of Sciences of Ukraine, p.256, 2008 [5] V. Uchajkin, Method of fractional derivatives. Ulyanovsk: Publishing house "Artishok", 2008. [6] I. Podlubny, Fractional Differential Equations, vol. 198. Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999. [7] Liu Tong, "Creep of wood under a large span of loads in constant and varying environments," Pt.1: Experimental observations and analysis, Holz als Roh- und Werkstoff, vol. 51, pp. 400-405, 1993. [8] E. Ogorodnikov, V. Radchenko, and L. Ugarova, "Mathematical modeling of hereditary deformational elastic body on the basis of structural models and of vehicle of fractional integro-differentiation Riman-Liuvil", Vest. Sam. Gos. Techn. Un-ty. Series. Phys.-math. sciences, vol. 20, no. 1, pp. 167-194, 2016. [9] O. Riznik, I. Yurchak, E. Vdovenko, and A. Korchagina, "Model of stegosystem images on basis of pseudonoise codes", VIth International Conference on Perspective Technologies and Methods in MEMS Design, Lviv, pp. 51-52, 2010. |
| Content type: | Conference Abstract |
| Appears in Collections: | Data stream mining and processing : proceedings of the IEEE second international conference |
| File | Description | Size | Format | |
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| 2018_Sokolovskyy_Y-Mathematical_Modeling_375-380.pdf | 420.86 kB | Adobe PDF | View/Open | |
| 2018_Sokolovskyy_Y-Mathematical_Modeling_375-380__COVER.png | 442.64 kB | image/png | View/Open |
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