On particularities of identification the inhomogeneous characteristics of prestressed thermoelastic cylinder

Authors

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

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

Acknowledgement

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 Infos

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

e-mail: vatulyan@math.rsu.ru

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

e-mail: 1079@list.ru

References

  1. Wetherhold R.C., Seelman S., Wang J. The use of functionally graded materials to eliminated or control thermal deformation. Composites Science and Technology, 1996, no. 56, pp. 1099-1104.
  2. Lee W.Y., Stinton D.P., Bernardt C.C., Erdogan F, Lee Y.D., Mutasin Z. Concept of functionally graded materials for advanced thermal barrier coatings applications. Journal of American Ceramic Society, 1996, vol. 19, pp. 3003-3012.
  3. Alifanov O.M., Artyukhin E.A., Rumyantsev S.V. Ekstremal`nye metody resheniya nekorrektnykh zadach [Extreme methods for solving ill-posed problems]. Moscow, Nauka Publ., 1988, 288 p. (In Russian)
  4. Lukasievicz S.A., Babaei R., Qian R.E. Detection of material properties in a layered body by means of thermal effects. Journal of Thermal Stresses, 2003, vol. 26, no. 1, pp. 13-23.
  5. Lomazov V.A. Zadachi diagnostiki neodnorodnykh termouprugikh sred [The problems of identification inhomogeneous thermoelastic bodies]. Orel, OrelSTU Publ., 2002, 168 p. (In Russian)
  6. Vatulyan A.O. Obratnye zadachi v mekhanike deformiruemogo tverdogo tela [Inverse problems in mechanics of deformable solids]. Moscow, Fizmatlit Publ., 2007, 224 p. (In Russian)
  7. Vatulyan A.O. O variatsionnoy postanovke obratnykh koeffitsientnykh zadach dlya uprugikh [On the variation formulation of the inverse coefficient problems for elastic bodies]. Doklady RAN [Reports of the Russian Academy of Sciences], 2008, vol. 422, no. 2, pp. 182-184. (In Russian)
  8. Vatulyan A.O., Nesterov S.A. Ob odnom sposobe identifikatsii termouprugikh kharakteristik dlya neodnorodnykh tel [About one method of identification of thermoelastic characteristics for inhomogeneous bodies]. Inzhenero-fizicheskiy zhurnal [Journal of engineering physics], 2014, vol. 87, no. 1, pp. 217-224.
  9. Nedin R., Nesterov S., Vatulyan A. On an inverse problem for inhomogeneous thermoelastic rod. International Journal of Solids and Structures, 2014, vol. 51, no. 3, pp. 767-773.
  10. Vatulyan A.O., Nesterov S.A. Ob osobennostyakh identifikatsii termomekhanicheskikh kharakteristik funktsional'no-gradientnykh materialov [About the specifics of identification thermomechanical characteristics of functionally graded materials]. Izvestiya Saratovskogo universitrta. Novaya seriya. Seriya matematika. Mekhanika. Informatika [Proceedings of the Saratov University. The new series. Series Mathematics. The mechanics. Computer science], 2014, vol. 14, iss. 3, pp. 329-335. (In Russian)
  11. Vatulyan A.O., Nesterov S.A. Ob osobennostyakh identifikatsii neodnorodnykh kharakteristik predvaritel'no-napryazhennykh termouprugikh tel [About the specifics of identification the inhomogeneous characteristics of prestressed thermoelastic solids]. Ekologicheskiy vestnik nauchnykh tsentrov Chernomorskogo ekonomicheskogo sotrudnichestva [Ecological Bulletin of the scientific centers of the black sea economic cooperation], 2014, no. 1, pp. 18-24. (In Russian)
  12. Guz A.N. Elastic waves in bodies with initial (residual) stresses. International Applied Mechanics, 2005, no. 38, pp. 23-59.
  13. Vatulyan A.O., Nesterov S.A. Koeffitsientnye obratnye zadachi termouprugosti dlya funktsional'no-gradientnykh materialov [Coefficient inverse problems of thermoelasticity for functionally-graded materials]. Problemy prochnosti i plastichnosty [The problems of toughness and plasticity], 2014, vol. 76, no. 4, pp. 335-342. (In Russian)
  14. Durbin F. Numerical inversion of Laplace transforms: an efficient improvement to Dubner and Abate's method. The Computer Journal, 1974, vol. 17, pp. 371-376.
  15. Tikhonov A.N., Goncharsky A.V., Stepanov V.V., Yagola A.G. Chislennye metody resheniya nekorrektnykh zadach [Numerical methods for solving ill-posed problems]. Moscow: Nauka Publ., 1990, 230 p. (In Russian)

Downloads

Issue

2015. No. 1

Pages

34-40

Submitted

2015-02-24

Published

2015-03-26

How to Cite

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, no. 1, pp. 34-40. (In Russian)

Copyright (c) 2015 Vatulyan A.O., Nesterov S.A.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.