# Main publications

**Siasiev, A.V. and Siasieva A.A.,**Mathematical simulation of building up the shells of heated bodies of revolutio.*Topical areas of fundamental and applied research V. Proceedings of the Conference. North Charleston, USA, 22-23.12.2014. ‒ CreateSpace, 2015. ‒ Vol. 1. ‒ P. 131-133.*

**Abstract**

The development of new technologies related to production of pipes and other bodies of revolution by building up the thickness of their shells requires the introduction of new methods of calculations, which represents more fully the properties of the used material. It is known, in particular, that the polymers and some metals (at high temperatures), which are widely used for manufacturing the pipes by centrifugal casting, have the clearly expressed creep property. It leads to redistribution of stresses within the material during the process of building up the thickness at the shell as well as to the change of its geometry after manufacturing, loading and heating. The use of viscoelasticity and thermal conductivity theories allows to perform the theoretical evaluation of these factors and develop the technology in accordance with the requirements which are related to manufactured product.

**Сясев, А.В., Макаренков, Е.А., Матяш, М.В.,**Об одной задаче определения оптимальной формы наращиваемой колонны.*Topical areas of fundamental and applied research V. Proceedings of the Conference. North Charleston, USA, 22-23.12.2014. ‒ CreateSpace, 2015. ‒ Vol. 1. ‒ P. 126-130.*

**Abstract**

В данной работе представлены результаты решения задачи об определении оптимальной формы армированной колонны произвольного поперечного сечения, которая возводится из неоднородно-стареющего вязкоупругого материала с постоянной скоростью в случае зависимости коэффициента армирования от длины колонны. Поскольку постоянство коэффициента армирования упрощает технологию возведения колонн, то в качестве примера рассмотрена колонна с постоянным коэффициентом армирования. Исследовано влияние скорости наращивание и коэффициента армирования на оптимальную форму и напряженно-деформированное состояние колонны.

**Siasiev A.V. and Vlasiuk K.V.,**Variational methods in the construction of a mathematical model of the process of deposition of thin coatings.*Матеріали Міжнародної науково-практичної конференції: «IV осінні наукові читання», м. Київ. – К.: Центр наукових публікацій «ВЕЛЕС», 2015. – С. 6 – 8.*

**Abstract**

In this paper, a mathematical model is proposed for the application of thin polymer coatings on a flexible basis. The variational method, which is an extension of the principle of the least action of Hamilton, was used in its construction. As a result, the problem of minimizing functional is reduced to the solution of the boundary value problem for a differential equation of Euler.

**Siasiev A.V. and Melnyk A.L.,**On optimization of parameters of winding bodies and winding mechanisms designing.*Materials of International scientific and practical conference «PERSPECTIVE TRENDS IN SCIENTIFIC RESEARCH – 2015», October, 17 – 22, Bratislava, Slovak Republic – K.: Вид-во «Центр навчальної літератури», 2015. – Vol. 2. – P. 138 – 140.*

**Abstract**

The report is a review of one of the optimal problems winding bodies forming within the given distribution of stresses, namely, the task of winding, characterized by the constancy of the radius of the winding body of residual tension in coils of threads. To solve this problem the collocation method was used. Based on numerical calculation some features and general patterns considered optimal implementation of tasks can be noted: the higher the required level of residual stress in the coils of thread, the greater rigidity should be for the mandrel; it is possible to obtain the exact solution (the subject to further personal research) of the optimal problem for a wide class of options, but any universal law of management of winding thread tension can be specified, abstracting the specific values of these parameters; in the final phase of forming the component the law winding tension always goes down; interlayer pressure distribution in the body winding under the optimal problem implementing is usually uneven.

**Siasiev A.V. and Zelenskaya T.S.,**Lengthwise movement dynamic boundary-value problem for trailing boundary ropes.*Metallurgical and Mining Industry, 2015, No. 3, pp. 283 – 287.*

**Abstract**

The statement and solution of mathematical physics initial boundary value problem of elastic wave motion in variable-length ropes as applied to the machines, which perform the load hoisting and lowering by using ropes, were considered. The primal problem boundary conditions accurately consider the state equation integration domain boundary changes of rope-load interaction character. The dynamic stress field amplitude value for steel-wire rope section was obtained and also maximum and minimum stress values throughout hoisting unit operating period were determined. The modified continuation method applying showed that the wave motion character in variable length environments has specific features and significantly differ from the wave motion character in fixed boundary environment.

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