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The asymptotic method in problems of the linear and nonlinear elasticity theory

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Category: Geotechnical and mining mechanical engineering, machine building

Last Updated on 30 October 2015

Published on 30 October 2015

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Authors:

T.S. Kagadiy, Dr. Sci. (Phys.–Math.), Associate Professor, State Higher Educational Institution “National Mining University”, Professor of the Department of Higher Mathematics, Dnipropetrovsk, Ukrainе.

A.H. Shporta, State Higher Educational Institution “National Mining University”, Assistant Lecturer of the Department of Higher Mathematics, Dnipropetrovsk, Ukrainе.

Abstract:

Purpose. To develop analytical method for complex properties constructions calculations. To study viscoelasticity influence on construction stress-strain state and the possibility of considering final deformations.

Methodology. The mathematical model of tree-dimensional problem on load transfer from supporting element to the viscoelastic massif was constructed.

Findings. The circle of analytical solutions for nonlinear elasticity and linear viscoelasticity theory problems was extended by means of elaborating perturbation method.

Originality. The asymptotic method for three-dimensional linear viscoelasticity of orthotropic bodies problems solutions or for nonlinear problems was elaborated. Analytical solutions of new problems on load transfer through supporting element to the viscoelastic material massif in spatial statement were received.

Practical value. The method suggested allows passing from the solution of the complex mixed tasks of mechanics to the consecutive solution of potential theory problems, which is the most developed section of mathematical physics. The solutions of a range of new complex challenges received due to the offered approach provide an opportunity to analyse stress-strain state of bodies with supporting elements. These results can be used in engineering calculations of piles foundations and substructures.

References:

1. Manevych, L.I. and Pavlenko, A.V. (1991), Asimptoticheskii metod v mikromekhanike kompozitsionnykh materialov [The Asymptotic Method in Micromechanics of Composite Materials], Vyscha Shkola, Kiev, Ukraine.

Маневич Л.И. Асимптотический метод в микромеханике композиционных материалов / Маневич Л.И., Павленко А.В. – К.: Вища шк., 1991. – 131 с.

2. Aleksandrov, V.M. and Chebakov, M.I. (2004), Analiticheskie metody v kontaktnykh zadachakh teorii uprugosti [The Analytical Methods in Elasticity Theory Contact Problems], FIZMATLIT, Moscow, Russia.

Александров В.М. Аналитические методы в контактных задачах теории упругости / Александров В.М., Чебаков М.И. – М.: ФИЗМАТЛИТ, 2004. – 302 с.

3. Kagadiy, T.S. (1998), Metod vozmushcheniy v mekhanike uprugikh (viazkouprugikh) anizotropnykh i kompozi-tsionnykh materialov [Method of Indignations in Mechanics of Elastic (Viscoelastic) Anisotropic and Composite Materials], RYK NGA Ukrainy, Dnipropetrovsk, Ukraine.

Кагадий Т.С. Метод возмущений в механике упругих (вязкоупругих) анизотропных и композиционных материалов / Кагадій Т.С. – Дніпропетровськ: РИК НГА України,1998. – 260 с.

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