Yaroslav Sokolovskyy

Work place: Ukrainian National Forestry University, UNFU /Department of Information Technologies, Lviv, 79057, UKRAINE

E-mail: sokolowskyy@ukr.net


Research Interests: Computer systems and computational processes, Computer Architecture and Organization, Parallel Computing, Data Structures and Algorithms, Analysis of Algorithms, Mathematics of Computing, Models of Computation


Yaroslav Sokolovskyy, Professor, Doctor of Technical Sciences, Ya. I. Sokolovskyy is the Head of the Department of Information Technologies at the Ukrainian National Forestry University. He graduated from the Faculty of Mechanics and Mathematics and completed postgraduate study at the T. Shevchenko Kiev national university. The author of many scientific papers and textbooks. Head of a number of promising research and development projects. Area of scientific interests: mathematical modeling of interconnected deformation and heat-mass-exchange processes in complex environments, in particular, with fractal structure; Information technologies for the design of technological processes and systems (CAD / CAM / CAE); parallel computing technology.

Author Articles
Two-Dimensional Mathematical Models of Visco-Elastic Deformation Using a Fractional Differentiation Apparatus

By Yaroslav Sokolovskyy Maryana Levkovych

DOI: https://doi.org/10.5815/ijmecs.2018.04.01, Pub. Date: 8 Apr. 2018

In this paper, using fractional differential and integral operators, constructed are two-dimensional mathematical models of viscoelastic deformation, which are characterized by memory effects, spatial non-locality, and self-organization. The fractal rheological models by Maxwell, Kelvin and Voigt, their structural properties and the influence of the fractional integro-differential operator on the process of viscoelasticity are investigated.
Using the Laplace transform method and taking into account the properties of the fractional differential apparatus, analytical relations are obtained in the integral form for describing the stresses of generalized two-dimensional fractional-differential rheological models by Maxwell, Kelvin, and Voigt. Since the fractional-differential parameters of fractal models allow describing deformation-relaxation processes more perfectly than traditional methods, algorithmic aspects of identification of structural and fractal parameters of models are presented in the work.
Explicit expressions have been obtained to describe the deformation process for one-dimensional fractional-differential models by Voigt, Kelvin, and Maxwell. The results of identification of structural and fractal parameters of the Maxwell and Voigt models are presented. The estimates of the accuracy of the obtained identification results were found using the statistical criterion based on the correlation coefficient. The influence of fractional-differential parameters on deformation-relaxation processes is investigated.

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