Geodesic
On existence of solutions of nonlinear equilibrium problems on shallow inhomogeneous anisotropic shells of the Timoshenko type
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2019), pp. 45-61

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We prove the existence of solutions to geometrically nonlinear boundary value problem for an elastic inhomogeneous anisotropic shallow shells with rigidly clamped edges under shear model S.P. Timoshenko. The boundary value problem is reduced to one nonlinear operator equation, the solvability of which is established using the principle of compressed maps. The investigation method is based on integral representations for generalized displacements containing arbitrary holomorphic functions determined by boundary conditions involving the theory of Cauchy type integrals with real densities.
Mots-clés : Timoshenko type shell
Keywords: equilibrium equations system, boundary problem, generalized shifts, generalized problem solution, integral images, singular integral equation, existence theorem. 
S. N. Timergaliev. On existence of solutions of nonlinear equilibrium problems on shallow inhomogeneous anisotropic shells of the Timoshenko type. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2019), pp. 45-61. http://geodesic.mathdoc.fr/item/IVM_2019_8_a4/
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     title = {On existence of solutions of nonlinear equilibrium problems on shallow inhomogeneous anisotropic shells of the {Timoshenko} type},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {45--61},
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     number = {8},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2019_8_a4/}
}
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[1] Vorovich I. I., Matematicheskie problemy nelineinoi teorii pologikh obolochek, Nauka, M., 1989

[2] Morozov N. F., Izbrannye dvumernye zadachi teorii uprugosti, LGU, L., 1978

[3] Karchevskii M. M., “Nelineinye zadachi teorii plastin i obolochek i ikh setochnye approksimatsii”, Izv.vuzov. Matem., 1985, no. 10, 17–30

[4] Karchevskii M. M., Paimushin V. N., “O variatsionnykh zadachakh teorii trekhsloinykh pologikh obolochek”, Differents. uravneniya, 30:7 (1994), 1217–1221 | MR

[5] Timergaliev S. N., Teoremy suschestvovaniya v nelineinoi teorii tonkikh uprugikh obolochek, Izd-vo Kazan. un-ta, Kazan, 2011

[6] Badriev I. B., Makarov M. V., Paimushin V. N., “Solvability of a physically and geometrically nonlinear problem of the theory of sandwich plates with transversal-soft core”, Russian Math. (Iz. Vuz.), 59:10 (2015), 57–60 | DOI | MR | Zbl

[7] Timergaliev S. N., “O razreshimosti geometricheski nelineinykh kraevykh zadach dlya anizotropnykh obolochek tipa Timoshenko s zhestko zadelannymi krayami”, Izv. vuzov. Matem., 2011, no. 8, 56–68 | Zbl

[8] Timergaliev S. N., “Dokazatelstvo suschestvovaniya resheniya sistemy differentsialnykh uravnenii s chastnymi proizvodnymi nelineinoi teorii pologikh obolochek tipa Timoshenko”, Differents. uravneniya, 48:3 (2012), 450–454 | Zbl

[9] Timergaliev S. N., “O suschestvovanii reshenii geometricheski nelineinykh zadach dlya pologikh obolochek tipa Timoshenko so svobodnymi krayami”, Izv. vuzov. Matem., 2014, no. 3, 40–56 | Zbl

[10] Timergaliev S. N., Differents. uravneniya, 51:3 (2015), K voprosu o suschestvovanii reshenii nelineinoi kraevoi zadachi dlya sistemy differentsialnykh uravnenii s chastnymi proizvodnymi teorii pologikh obolochek tipa Timoshenko so svobodnymi krayami | DOI

[11] Timergaliev S. N., Kharasova L. S., “Issledovanie razreshimosti odnoi kraevoi zadachi dlya sistemy nelineinykh differentsialnykh uravnenii teorii pologikh obolochek tipa Timoshenko”, Differents. uravneniya, 53:5 (2016), 651–664 | DOI

[12] Timergaliev S. N., “Metod integralnykh uravnenii v nelineinykh kraevykh zadachakh dlya pologikh obolochek tipa Timoshenko so svobodnymi krayami”, Izv. vuzov. Matem., 2017, no. 4, 59–75 | Zbl

[13] Timergaliev S. N., “K probleme razreshimosti nelineinykh zadach ravnovesiya pologikh obolochek tipa Timoshenko”, PMM, 82:1 (2018), 98–113

[14] Galimov K. Z., Osnovy nelineinoi teorii tonkikh obolochek, Izd-vo Kazansk. un-ta, Kazan, 1975

[15] Vekua I. N., Obobschennye analiticheskie funktsii, Nauka, M., 1988

[16] Muskhelishvili N. I., Singulyarnye integralnye uravneniya, Fizmatgiz, M., 1962

[17] Vekua I. N., Novye metody resheniya ellipticheskikh uravnenii, Gostekhizdat, M., 1948 | MR

[18] Gakhov F. D., Kraevye zadachi, 2-e izd., Fizmatgiz, M., 1963

[19] Mikhailov V. P., Differentsialnye uravneniya v chastnykh proizvodnykh, Nauka, M., 1976

[20] Krasnoselskii M. A., Topologicheskie metody v teorii nelineinykh integralnykh uravnenii, Gostekhizdat, M., 1956