Efficient three-dimensional shell model for fiber study of stress-strain state of irregular cylindrical shells

V. N. Bakulin

Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2024), pp. 64-70

Résumé

An approach to obtaining approximations and constructing a three-dimensional shell model of a filler layer based on the use of effective approximating functions used in two-dimensional models of bearing layers in the general case of irregular three-layer cylindrical shells, including those weakened by rectangular cutouts, is presented. The effective approximating functions of the displacements of the bearing layers are based on the initial approximation of deformations. As an example, studies of the influence of the angular dimension of rectangular cutouts on the stress and strain state of sandwich cylindrical shells are carried out for the first time.

Bibliographie

[1] Vasilev V.V., Mekhanika konstruktsii iz kompozitsionnykh materialov, Mashinostroenie, M., 1988

[2] Bakulin V.N., Obraztsov I.F., Potopakhin V.A., Dinamicheskie zadachi nelineinoi teorii mnogosloinykh obolochek. Deistvie intensivnykh termosilovykh nagruzok, kontsentrirovannykh potokov energii, Nauka, M., 1998

[3] Bakulin V.N., “Trekhsloinye obolochki — effektivnye elementy konstruktsii sovremennykh letatelnykh apparatov. Modeli prochnostnogo analiza”, Mat-ly KhIKh Mezhdunar. konf. po prikladnoi matematike i mekhanike v aerokosmicheskoi otrasli, AMMAI'2022 (5–12 sentyabrya 2022 g.), Izd-vo MAI, M., 2022, 270–272

[4] Solomonov Yu.S., Lipanov A.M., Aliev A.V. i dr., Tverdotoplivnye reguliruemye dvigatelnye ustanovki, eds. A.M. Lipanov, Yu.S. Solomonov, Mashinostroenie, M., 2011

[5] Bakulin V.N., “Primenenie trekhsloinykh obolochek. Kratkii obzor rabot po raschetu napryazhenno-deformirovannogo sostoyaniya trekhsloinykh obolochek s pryamougolnymi v plane vyrezami”, Voprosy oboronnoi tekhniki: Nauchno-tekhnicheskii sb. Ser. 15: Kompozitsionnye nemetallicheskie materialy v mashinostroenii, 2023, no. 3 (208), 17–24

[6] Avdeev V.S., Tsentralnyi nauchno-issledovatelskii institut spetsialnogo mashinostroeniya. Put dlinoi v polveka, Khotkovo, 2015

[7] Bakulin V.N., “Layer-by-layer study of the stress and strain state of sandwich conical aircraft compartments with rectangular cutouts”, Rus. Aeronautics, 65:4 (2022), 668–676 | DOI

[8] Pelekh B.L., Syaskii A.A., Raspredelenie napryazhenii vozle otverstii v podatlivykh na sdvig anizotropnykh obolochkakh, Naukova dumka, Kiev, 1975

[9] Bakulin V.N., Revenko V.P., “Analytical and numerical method of finite bodies for calculation of cylindrical orthotropic shell with rectangular hole”, Rus. Math., 60:6 (2016), 1–11 | DOI | MR | Zbl

[10] Bakulin V.N., “Layer-by-layer analysis of the stress-strain state of three-layer shells with cutouts”, Mech. Solids, 54:3 (2019), 448–460 | DOI

[11] Revenko V.P., Bakulin V.N., “Method of Finite Bodies for Mathematical Modeling of the Stress-strain State of Cylindrical Orthotropic Shell with the Reinforced Rectangular Hole”, Proc. IV Int. Conf. “Supercomputer Technologies of Mathematical Modeling (SCTeMM'19)” (Steklov Mathematical Institute of the Russian Academy of Sciences in cooperation with Ammosov North-Eastern Federal University, Ivannikov Institute for System Programming of the Russian Academy of Sciences and Bauman Moscow State Technical University, 2019), J. Phys.: Conference Series, 1392, 2019, 012021 | DOI

[12] Sheshenin S.V., Demidovich P.N., “Primenenie metoda osredneniya dlya postroeniya sloistogo konechnogo elementa”, Uprugost i neuprugost, Mat-ly Mezhdunar. nauch. simp. po problemam mekhaniki deformiruemykh tel, posvyaschennogo 95-letiyu so dnya rozhdeniya A.A. Ilyushina (Moskva, 19–20 yanvarya 2006 g.), LENAND, M., 2006, 432–437

[13] Rikards R.B., Metod konechnykh elementov v teorii obolochek i plastin, Zinatne, Riga, 1988 | MR

[14] Bakulin V.N., “Posloinyi analiz napryazhenno-deformirovannogo sostoyaniya neregulyarnykh trekhsloinykh obolochek vrascheniya nenulevoi gaussovoi krivizny”, Prikl. matem. i mekhan., 85:1 (2021), 90–106

[15] Babeshko V.A., Evdokimova O.V., Babeshko O.M., “Blochnye elementy i analiticheskie resheniya granichnykh zadach dlya sistem differentsialnykh uravnenii”, Dokl. RAN, 454:2 (2014), 163–167 | DOI | MR

[16] Balabukh L.I., Kolesnikov K.S., Zarubin V.S. i dr., Osnovy stroitelnoi mekhaniki raket, Vysshaya shkola, M., 1969

[17] Bakulin V.N., “Effective model of load-bearing layers for layer-by-layer analysis of the stress-strain state of three-layer cylindrical irregular shells of revolution”, Mech. Solids, 55:3 (2020), 557–565 | DOI

[18] Bakulin V.N., Krivtsov V.S., Rassokha A.A., “Algoritm polucheniya matritsy zhestkosti konechnogo elementa anizotropnoi obolochki”, Izv. vuzov. Aviats. tekhnika, 1983, no. 4, 14–18

[19] Bakulin V.N., Rassokha A.A., Metod konechnykh elementov i golograficheskaya interferometriya v mekhanike kompozitov, Mashinostroenie, M., 1987