On particularities of identification the inhomogeneous characteristics of prestressed thermoelastic cylinder

Authors

  • Vatulyan A.O. South Federal University, Rostov-on-Don, Russian Federation
  • Nesterov S.A. Southern Federal University, Rostov-on-Don, Russian Federation

UDC

539.3

Abstract

Functionally graded and pre-strained materials find wide application in various engineering fields with large thermo-mechanical loads. Knowing the exact laws heterogeneity of materials after fabrication requires the solution of coefficient inverse problems of thermoelasticity. In this work we present the formulation of the inverse problems of thermoelasticity for pre-stressed functionally graded cylinder. The direct problem is solved on the basis of the method of adjustment in transform by Laplace and use handling procedures implemented in accordance with the method of Durbin. As additional information when solving the inverse problem is the measured displacement at the external border. For the solution of nonlinear inverse problems based on the method of linearization was built by an iterative process. Thermomechanical characteristics were recovered in two stages. The first stage was an initial approximation. In the second stage of the amendment to the restoring characteristics were determined from the solution of the Fredholm integral equations of the 1st kind. The results of computational experiments are presented. The influence of prestressed term on the results of reconstruction of thermoelastic characteristics is considered.

Keywords:

coefficient inverse problem, thermoelasticity, pre-stressing, functionally graded cylinder, integral equations

Funding information

Работа выполнена при поддержке гранта РФФИ (13-01-00196-а), проекта Министерства образования и науки РФ (9.665.2014/K) на выполнение научно-исследовательской работы в рамках проектной части государственного задания в сфере научной деятельности и проекта "Математическое моделирование неоднородных и многофазных структур" (в рамках Программы фундаментальных исследований по стратегическим направлениям развития науки Президиума РАН №1 "Фундаментальные проблемы математического моделирования").

Author info

  • Aleksandr O. Vatulyan

    д-р физ.-мат. наук, профессор, заведующий кафедрой теории упругости Института математики, механики и компьютерных наук им. И.И. Воровича Южного федерального университета; заведующий отделом дифференциальных уравнений Южного математического института Владикавказского научного центра РАН и Правительства Республики Северная Осетия-Алания

  • Sergey A. Nesterov

    канд. физ.-мат. наук, научный сотрудник кафедры теории упругости Института математики, механики и компьютерных наук им. И.И. Воровича Южного федерального университета

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Issue

No. 1 (2015)

Pages

34-40

Section

Article

Dates

Submitted

February 24, 2015

Accepted

March 5, 2015

Published

March 26, 2015

How to Cite

[1]
Vatulyan, A.O., Nesterov, S.A., On particularities of identification the inhomogeneous characteristics of prestressed thermoelastic cylinder. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2015, № 1, pp. 34–40.

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Copyright (c) 2015 Ватульян А.О., Нестеров С.А.

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