﻿ Main publications | Кафедра Диференціальніх Рівнянь - Part 6

# Main publications

1. Syasev, A., Vesselovskiy, V., Mamuzić, I., Kochubey, A., Syasev, V. and Klim, V., The nonlinear shaping of the thermomechanical status of two-phases. AMATERIALI IN TEHNOLOGIJE 37 (2003) 3-4, pp. 137 — 134.
Abstract

The method and the algorithm for the calculation of the thermomechanical status of bodies are proposed which connect the mechanical behavior of a material at the interchange of heat with the environment. The nonlinear problem of the thermomechanical status of heating of two-phase bodies is solved. The laws of motion of the phase boundary, the temperature field and of the strained state in the rod are given. The outcomes are presented as a relation, of both, temperature and strain upon time and location.

1. Siasiev, A.V. and Stcherbina, I.V., Mathematic modelling of circular cylinder deformation under inner grouwth. Вісник Дніпропетровського університету. – 2009. – Т. 17, вип. 1. – С. 116-125. DOI: 10.15421/140910
Abstract

A task on the intensive deformed state (IDS) of a viscoelastic declivous cylinder, which is grown under the action of inner pressure, is considered. The process of continuous increase takes a place on an internal radius so, that a radius and pressure change on set to the given law. The special case of linear law of creeping is considered, and also numeral results are presented as the graphs of temporal dependence of tensions and moving for different points of cylinder.

1. Zelenskaya, Т.S. and Siasiev, А.V., INITIAL-BOUNDARY PROBLEM OF DETERMINATION OF DYNAMIC STRESS IN MINE LIFTING GEARS WITH BALANCED HEAD ROPE. Вісник Дніпропетровського університету. – 2013. – Т. 21, вип. 5. – С. 118-129. DOI: 10.15421/141309
Abstract

Initial boundary value problem definition for a steel rope of lifting installation is considered in the article.The solution of initial-boundary problem for elastic filament as the area with mobile border is found.Program realization of results of influence of the reflected waves on stress in rope sections is presented.

1. Zelenskaya, Т.S. and Siasiev, А.V., MATHEMATICAL MODELING OF DYNAMICS OF HOISTING ROPES WITH ACCOUNT OF LONGITUDINAL MOVEMENT. Вісник Дніпропетровського університету. – 2014. – Т. 22, вип. 6. – С. 150-158. DOI: 10.15421/141409
Abstract

Constructed and substantiated refined mathematical model of multiple-rope hoist. The dynamic processes that occur in the main rope, with the aim to improve the strength and durability of lifting and balancing ropes. The results of calculations.

1. Siasiev, А.V., Kostashchuk, М.V., Simulation of the crystallization process of the rod with regard to the mutual influence of thermal and mechanical fields. Вісник Дніпропетровського університету. – 2015. – Т. 23, вип. 7. – С. 9-28. DOI: 10.15421/141502
Abstract

The problem of defining the law of motion of crystallization front and the thermo-mechanical state of the two-phase rod in case of mutual influence of thermal and me­chanical fields is solved. To meet the challenge the approximate analytical method is used, in the aggregate of the method of the sequential intervals and variational prin­ciple of Gibbs (which should indicate that it is ”profitable” for nature under specified external effects to change the temperature of a fixed element of the body or to transfer the element from one aggregate state to another). Correlations to determine the law of motion of the boundary of phases of the temperature field and stress-deformed state in the rod are gained. The results are presented in the form of charts of dependency based on temperature and stress of time and coordinates. The analysis of the gained results indicates that a change of the conditions of heat exchange with the environment and geometrical sizes have determinative influence on the solidification process and therefore on thermal and mechanical fields. The main result is the following: an approximate analytical method and algorithm to solve the problem of thermo-viscosity for growing bodies in the presence of phase transfer, taking into account the heat exchange with the environment is developed; the law of motion of the boundary of phases division, the temperature field and stress-deformed state are determined by the decisions of the so-called associated problem of thermo-viscosity on the basis of the developed method; approximate analytical solutions that allow to simulate different technological processes are obtained.

Страницы: 1 2 3 4 5 6 7 8 9 10

### Journal of Optimization, Differential Equations and their Applications

The "Journal of Optimization, Differential Equations and their Applications” (shortly JODEA) publishes original research articles related with the recent developments both in theory and applications of ordinary differential equations, partial differential equations, integral equations, functional differential equations, stochastic differential equations, optimal control theory, scalar and vector optimization, and other related topics. The journal will also accept papers from some related fields such as functional analysis, probability theory, stochastic analysis, inverse problems, numerical computation, mathematical finance, game theory, system theory, etc., provided that they have some intrinsic connections with control theory and differential equations. Papers employing differential equations as tools serving the cause of interdisciplinary areas such as physical, biological, environmental and health sciences, mechanics and engineering are encouraged. The goal is to provide a complete and reliable source of mathematical methods and results in these fields.

The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools. To be published in this journal, an original paper must be correct, new, nontrivial and of interesting to readers.

JODEA is issued two times per year. It is edited by a group of international leading experts in mathematical control theory, differential equations and related fields. The journal is essential reading for scientists and researchers who wish to keep abreast of the latest developments in the field of differential equations and their applications. The journal is founded in 2018 by Oles Honchar Dnipro National Universuty for researchers and PhD-students who are working in the field of mathematics and applied mathematics. JODEA is printed according to the decision of the Academic council of the Oles Honchar Dnipro National University and is continuation of the journal "Bulletin of the Dnipropetrovsk University. Series: Modeling" (2009 – 2017, ISSN (Print): 2312-4547, ISSN (Online): 2415-7325) and a series of releases of the collection of scientific works "Differential equations and their applications" which were annually printed during the period from 1968 to 2008.

JODEA is not a peer-reviewed journal without any donations and payment for publications.