Geodesic
Inverse problem of pure beam bending in creep conditions
Sibirskij žurnal industrialʹnoj matematiki, Tome 26 (2023) no. 2, pp. 37-52.

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The algorithm was proposed for solving the inverse problem of forming structural elements under creep conditions using the Nelder-Mead algorithm. The initial task of finding the forces that must be applied to obtain the required curvature of the part is reduced to a sequence of auxiliary direct problems of modeling the stress-strain state of pure bending of rectangular beams. This model, which takes into account the difference in the properties of the material in tension and compression, as well as the presence of accumulated damage in the material during creep, was verified by numerical methods and implemented in finite element program MSC Marc.
Keywords: rectangular beam, inverse problem, bending, creep, damage parameter, resistance to tension and compression.
Mots-clés : fracture 
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S. V. Boyko; A. Yu. Larichkin. Inverse problem of pure beam bending in creep conditions. Sibirskij žurnal industrialʹnoj matematiki, Tome 26 (2023) no. 2, pp. 37-52. http://geodesic.mathdoc.fr/item/SJIM_2023_26_2_a3/

[1] F. C. Ribeiro, E. P. Marinho, D. J. Inforzato, P. R. Costa, G. F. Batalha, “Creep age forming: a short review of fundaments and applications”, J. Achiev. Mater. Manufactur. Engrg., 43:1 (2010), 353–361

[2] H. Luo, W. Li, Ch. Li, M. Wan, “Investigation of creep-age forming of aluminum lithium alloy stiffened panel with complex structures and variable curvature”, J. Adv. Manufactur. Technol., 91:912 (2017), 3265–3271 | DOI

[3] A. C.L. Lam, Zh. Shi, H. Yang, W. Li, C. M. Davies, J. Lin, Sh. Zhou, “Creep-age forming AA2219 plates with different stiffener designs and pre-form age conditions: experimental and finite element studies”, J. Mater. Process Technol., 219 (2015), 155–163 | DOI

[4] Bormotin K.S., Belykh S.V., Vin Aung, “Matematicheskoe modelirovanie obratnykh zadach mnogotochechnogo formoobrazovaniya v rezhime polzuchesti s pomoschyu rekonfiguriruemogo ustroistva”, Vychisl. metody i programmirovanie, 17 (2016), 258–267 | DOI

[5] Gorev B.V., Panamarev V.A., “Metod integralnykh kharakteristik dlya rascheta izgiba elementov konstruktsii”, Nauchno-tekhn. vedomosti SPb. gos. politekh. un-ta. Fiz.-mat. nauki, 2013, no. 177, 201–211

[6] Annin B.D., Oleinikov A.I., Bormotin K.S., “Modelirovanie protsessov formoobrazovaniya panelei kryla samoleta”, Prikl. matematika i tekhn. fizika, 51:4 (2010), 155–165 | Zbl

[7] A. Zolochevsky, S. Sklepus, T. H. Hyde, A. A. Becker, S. Peravali, “Numerical modeling of creep and creep damage in thin plates of arbitrary shape from materials with different behavior in tension and compression under plane stress conditions”, J. Numer. Meth. Engrg., 80:11 (2009), 1406–1436 | DOI | Zbl

[8] K. Naumenko, H. Altenbach, Modeling High Temperature Materials Behavior for Structural Analysis, v. I, Continuum Mechanics Foundations and Constitutive Models, Springer-Verl, London, 2016 | MR | Zbl

[9] Agapov V.P., “Modelirovanie sterzhnei tavrovogo secheniya v raschetakh stroitelnykh konstruktsii metodom konechnykh elementov”, Stroit. mekhanika inzhenernykh konstruktsii i sooruzhenii, 2016, no. 2, 55–59

[10] Rabotnov Yu.N., Polzuchest elementov konstruktsii, Nauka, M., 1966

[11] Nikitenko A.F., Polzuchest i dlitelnaya prochnost metallicheskikh materialov, izd. IGiL SO RAN, Novosibirsk, 1997

[12] Sosnin O.V., Gorev B.V., Nikitenko A.F., Energeticheskii variant teorii polzuchesti, izd. IGiL SO RAN, Novosibirsk, 1986

[13] Volegov P.S., Gribov D.S., Trusov P.V., “Povrezhdennost i razrushenie: klassicheskie kontinualnye teorii”, Fiz. mezomekhanika, 18:4 (2015), 68–87

[14] Lokoschenko A.M., Polzuchest i dlitelnaya prochnost metallov, Fizmatlit, M., 2016

[15] Radchenko V.P., Kichaev P.E., Energeticheskaya kontseptsiya polzuchesti i vibropolzuchesti metallov, izd. Samar. gos. tekhn. un-ta, Samara, 2011

[16] M. Ya. Brovman, “Creep deformation of beams under compression and bending stresses”, Mech. Solids, 52:1 (2017), 75–80 | DOI

[17] Gorev B.V, Lyubashevskaya I.V., Panamarev V.A., Iyavoinen S.V., “Opisanie protsessa polzuchesti i razrusheniya sovremennykh konstruktsionnykh materialov s ispolzovaniem kineticheskikh uravnenii v energeticheskoi forme”, Prikl. matematika i tekhn. fizika, 55:6 (2014), 132–144

[18] Kuznetsov E.B., Leonov S.S., “Matematicheskoe modelirovanie chistogo izgiba balki iz raznomodulnogo aviatsionnogo materiala v usloviyakh polzuchesti”, Vestn. RUDN. Ser. Inzh. issledovaniya, 2015, no. 1, 111–122

[19] Korobeinikov S.N., Oleinikov A.I., Gorev B.V., Bormotin K.S., “Matematicheskoe modelirovanie protsessov polzuchesti metallicheskikh izdelii iz materialov, imeyuschikh raznye svoistva pri rastyazhenii i szhatii”, Vychisl. metody i programmirovanie, 9 (2008), 346–365

[20] Lokoschenko A.M., Agakhi K.A., Fomin L.V., “Chistyi izgib balki v usloviyakh polzuchesti iz raznosoprotivlyayuschegosya materiala”, Vestn. Samar. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 2012, no. 1(26), 66–73 | DOI

[21] M. Sitar, F. Kosel, M. Brojan, “Numerical and experimental analysis of elasticplastic pure bending and spring back of beams of asymmetric cross-sections”, J. Mech. Sci., 90 (2015), 77–88 | DOI

[22] R. H. Merson, “An operational methods for integration processes”, Proc. Symp. on Data Processing, Weapons Research Establishment, Salisbur, 1957, 239–240

[23] Mudrov A.E., Chislennye metody dlya PEVM na yazykakh Beisik, Fortran i Paskal, RASKO, Tomsk, 1991

[24] Gorev B.V., “K raschetu na neustanovivshuyusya polzuchest izgibaemogo brusa iz materiala s raznymi kharakteristikami na rastyazhenie i szhatie”, Dinamika sploshnoi sredy, 1973, no. 14, 44–51

[25] MSC. Marc Vol. A: Theory and User Information, MSC.Software Corporation, 2014 http://www.mscsoftware.com/product/marc

[26] K. J. Bathe, Finite Element Procedures in Engineering Analysis, Prentice-Hall, N.Y., 1982 | MR

[27] Bormotin K.S., Iteratsionnye chislennye metody kompyuternogo modelirovaniya optimalnoi formovki i klepki tonkostennykh panelei, Dis. ...d-ra fiz.-mat. nauk, Komsomolsk-na-Amure, 2014

[28] MSC. Marc Vol. D: User Subroutines and Special Routines, MSC.Software Corporation, 2014 http://www.mscsoftware.com/product/marc

[29] Korobeinikov S.N., Nelineinoe deformirovanie tverdykh tel, Izd-vo SO RAN, Novosibirsk, 2000

[30] Rudakov K.N., UGS Femap 10.2.0. Geometricheskoe i konechno-elementnoe modelirovanie konstruktsii, KPI, Kiev, 2011

[31] Sosnin O.V., Gorev B.V., Rubanov V.V., “Kruchenie kvadratnoi plastinki iz materiala, raznosoprotivlyayuschegosya rastyazheniyu i szhatiyu pri polzuchesti”, Raschety prochnosti sudovykh konstruktsii i mekhanizmov, 117 (1976), 78–88

[32] J. A. Nelder, R. Mead, “A simplex for function minimization”, Comput. J., 7:4 (1965), 308–313 | DOI | MR | Zbl

[33] Gorodetskii S.Yu., Grishagin V.A., Nelineinoe programmirovanie i mnogoekstremalnaya optimizatsiya, Izd-vo NNGU, N. Novgorod, 2007