Electronic Scientific Journal
 
Diagnostics, Resource and Mechanics 
         of materials and structures
Рус/Eng  

 

advanced search

IssuesAbout the JournalAuthorContactsNewsRegistration

2021 Issue 1

All Issues
 
2024 Issue 2
 
2024 Issue 1
 
2023 Issue 6
 
2023 Issue 5
 
2023 Issue 4
 
2023 Issue 3
 
2023 Issue 2
 
2023 Issue 1
 
2022 Issue 6
 
2022 Issue 5
 
2022 Issue 4
 
2022 Issue 3
 
2022 Issue 2
 
2022 Issue 1
 
2021 Issue 6
 
2021 Issue 5
 
2021 Issue 4
 
2021 Issue 3
 
2021 Issue 2
 
2021 Issue 1
 
2020 Issue 6
 
2020 Issue 5
 
2020 Issue 4
 
2020 Issue 3
 
2020 Issue 2
 
2020 Issue 1
 
2019 Issue 6
 
2019 Issue 5
 
2019 Issue 4
 
2019 Issue 3
 
2019 Issue 2
 
2019 Issue 1
 
2018 Issue 6
 
2018 Issue 5
 
2018 Issue 4
 
2018 Issue 3
 
2018 Issue 2
 
2018 Issue 1
 
2017 Issue 6
 
2017 Issue 5
 
2017 Issue 4
 
2017 Issue 3
 
2017 Issue 2
 
2017 Issue 1
 
2016 Issue 6
 
2016 Issue 5
 
2016 Issue 4
 
2016 Issue 3
 
2016 Issue 2
 
2016 Issue 1
 
2015 Issue 6
 
2015 Issue 5
 
2015 Issue 4
 
2015 Issue 3
 
2015 Issue 2
 
2015 Issue 1

 

 

 

 

 

V. V. Struzhanov

ON ONE PROBLEM OF DETERMINING THE OPTIMAL RESIDUAL STRESS FIELD

DOI: 10.17804/2410-9908.2021.1.055-063

An operator equation is obtained, the solution of which is an intrinsic (residual) stress tensor reducing the stress level to zero in a predetermined region of a rigidly loaded elastic body. It is shown that the operator of this equation is a contraction operator and, therefore, this equation can be solved by the method of successive approximations. An example is given.

Keywords: residual stresses, energy Hilbert space, orthogonal subspaces, operator equation, contraction operator, successive approximations

References:

  1. Birger I.A. Ostatochnye napryazheniya [Residual Stresses]. Moscow, Mashgiz Publ., 1963, 262 p. (In Russian).
  2. Pozdeev A.A., Nyashin Yu.I., Trusov P.V. Ostatochnye napryazheniya: teoriya i prilozheniya [Residual Stresses: Theory and Applications]. Moscow, Nauka Publ., 1982, 111 p. (In Russian).
  3. Pavlov V.F., Kirpichev V.A., and Ivanov V.B. Ostatochnye napryazheniya i soprotivlenie ustalosti uprochnennykh detalei s kontsentratorami napryazhenii [Residual Stresses and Fatigue Resistance of the Reinforced Components with Stresses Concentration]. Samara, SNTs RAN Publ., 2008. (In Russian).
  4. Abramov V.V. Ostatochnye napryazheniya i deformatsii v metallakh [Residual Stresses and Strains in Metals]. Moscow, Mashgiz Publ., 1963, 355 p. (In Russian).
  5. Korolev A.V., Mazina A.A., Yakovishin A.S., Shalunov A.V. Technological causes of residual stresses. Sovremennye Materialy, Tehnika i Tekhnologii, 2016, vol. 5 (8), pp. 116–119. (In Russian).
  6. Struzhanov V.V. Determination of shrinkage stresses in components of stochastically reinforced composites. Soviet Applied Mechanics, 1982, vol. 18, no. 5, pp. 445–449. DOI: 10.1007/bf00883786.
  7. Shinkin V.N. Residual stresses during expansion of steel pipes. Young Scientist, 2015, No. 20, pp. 88–93. ISSN 072-0297. (In Russian).
  8. Kolmogorov G.L., Kuznecova E.V., Tiunov V.V. Tekhnologicheskie ostatochnye napryazheniya i ikh vliyanie na dolgovechnost i nadezhnost metalloizdeliy [Technological Residual Stresses and their Effect on the Longevity and Reliability of Hardware]. Perm, Izd-vo Permskogo nats. issled. politekhnicheskogo un-ta Publ., 2012, 226 p. (In Russian).
  9. Burkin S.P., Shimov G.V., Andryukova Е.А. Ostatochnye napryazheniya v metalloproduktsii [Residual stresses in metal products: tutorial]. Ekaterinburg, Izdatelstvo Uralskogo gosudarstvennogo universiteta Publ., 2015, 248 p. (In Russian).
  10. Hosford W.F. Mechanical Behavior of Materials. Cambridge, Cambridge University Press, 2005, 421 p.
  11. Kozic D., Gänser H.-P., Brunner R., Kienerb D., Antretterc T., Kolednik O. Grack arrest in thin metallic film stacks due to material and residual stress inhomogeneities. Thin Solid Films, 2018, vol. 668, pp. 14–22. DOI: 10.1016/j.tsf.2018.10.014.
  12. Konovalov D.A., Vichuzhanin D.I., Smirnov S.V. Evaluating the residual stresses by the method of indentation. In: Proceedings of the Second All-Russian Scientific Conference “Matem. Mod. Kraev. Zadachi”, 1–3 June 2005, part 1, Samara State Technical Univ., Samara, 2005, pp. 155–157. (In Russian).
  13. Fishkin A.I. Application of the Tikhonov regularization for residual stresses determination. Stroitelnaya Mekhanika Inzhenernykh Konstruktsij i Sooruzhenij, 2009, No. 4, pp. 48–55.
  14. Kudryavtsev I.V. Vnutrennie napryazheniya kak rezerv prochnosti v mashinostroenii [Internal Stresses as a Strength Reserve in Mechanical Engineering]. Moscow, Mashgiz Publ., 1951, 278 p. (In Russian).
  15. Rozhkov I.I., Mylnikov V.V. Calculation of internal residual stresses arising in hardened parts of machines after chemical-thermal processing. International Journal of Experimental Education, 2014. vol. 1, pp. 114–118. (In Russian).
  16. Sinchurin D.V. The effect of hydraulic shot peening on the increase of the service reliability of parts. Young Scientist, 2015, vol. 21.2 (101.2), pp. 54–57. (In Russian).
  17. Lurie A. I. Teoriya uprugosti [Theory of Elasticity]. Moscow, Nauka Publ., 1970, 940 p. (In Russian).
  18. Sokolov A.G., Struzhanov V.V. A problem of optimizing the stressed state in an elastic solid. Journal of Applied Mathematics and Mechanics, 2001, vol. 65, iss. 2, pp. 311–316. DOI: 10.1016/S0021-8928(01)00035-1.
  19. Mikhlin S.G. Variatsionnye metody v matematicheskoy fizike [Variational Methods in Mathematical Physics]. Moscow, Nauka Publ., 1970, 512 p. (In Russian).
  20. Struzhanov V. V. On the method of orthogonal projections in the theory of elasticity. Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2017, vol. 21, no. 2, pp. 308–325. DOI: 10.14498/vsgtu1542. (In Russian).
  21. Kantorovich A.V., Akilov G.P. Funrtsionalnyi Analiz [Functional Analysis]. Moscow, Nauka Publ., 1977, 744 p. (In Russian).
  22. Konstantinov R.V. Lektsii po funktsionalnomu analizu [Lectures on Functional Analysis]. Moscow, MFTI Publ., 2009, 374 p. (In Russian).


PDF      

Article reference

Struzhanov V. V. On One Problem of Determining the Optimal Residual Stress Field // Diagnostics, Resource and Mechanics of materials and structures. - 2021. - Iss. 1. - P. 55-63. -
DOI: 10.17804/2410-9908.2021.1.055-063. -
URL: http://eng.dream-journal.org/issues/2021-1/2021-1_296.html
(accessed: 06/22/2024).

 

impact factor
RSCI 0.42

 

MRDMS 2024
Google Scholar


NLR

 

Founder:  Institute of Engineering Science, Russian Academy of Sciences (Ural Branch)
Chief Editor:  S.V. Smirnov
When citing, it is obligatory that you refer to the Journal. Reproduction in electronic or other periodicals without permission of the Editorial Board is prohibited. The materials published in the Journal may be used only for non-profit purposes.
Contacts  
 
Home E-mail 0+
 

ISSN 2410-9908 Registration SMI Эл № ФС77-57355 dated March 24, 2014 © IMACH of RAS (UB) 2014-2024, www.imach.uran.ru