V. V. Struzhanov

ON ONE PROBLEM OF DETERMINING THE OPTIMAL RESIDUAL STRESS FIELD

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.

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).

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