On solving physically nonlinear equilibrium problems for sandwich plates with a transversely soft filler
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 157 (2015) no. 1, pp. 15-24 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The generalized statement for the problem of determining the stress-strain state of sandwich plates with a transversely soft filler in the presence of constraints is given. Its correctness is discussed. This statement is formulated in the form of finding a saddle point of some functional. The existence and uniqueness theorems are proved. An iterative method for solving the problem is proposed. Its convergence is investigated.
Keywords: sandwich plate, transversely soft filler, saddle point, existence theorem, uniqueness theorem, iterative method.
@article{UZKU_2015_157_1_a1,
     author = {I. B. Badriev and G. Z. Garipova and M. V. Makarov and V. N. Paimushin and R. F. Chabibullin},
     title = {On solving physically nonlinear equilibrium problems for sandwich plates with a~transversely soft filler},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {15--24},
     year = {2015},
     volume = {157},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2015_157_1_a1/}
}
TY  - JOUR
AU  - I. B. Badriev
AU  - G. Z. Garipova
AU  - M. V. Makarov
AU  - V. N. Paimushin
AU  - R. F. Chabibullin
TI  - On solving physically nonlinear equilibrium problems for sandwich plates with a transversely soft filler
JO  - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
PY  - 2015
SP  - 15
EP  - 24
VL  - 157
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/UZKU_2015_157_1_a1/
LA  - ru
ID  - UZKU_2015_157_1_a1
ER  - 
%0 Journal Article
%A I. B. Badriev
%A G. Z. Garipova
%A M. V. Makarov
%A V. N. Paimushin
%A R. F. Chabibullin
%T On solving physically nonlinear equilibrium problems for sandwich plates with a transversely soft filler
%J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
%D 2015
%P 15-24
%V 157
%N 1
%U http://geodesic.mathdoc.fr/item/UZKU_2015_157_1_a1/
%G ru
%F UZKU_2015_157_1_a1
I. B. Badriev; G. Z. Garipova; M. V. Makarov; V. N. Paimushin; R. F. Chabibullin. On solving physically nonlinear equilibrium problems for sandwich plates with a transversely soft filler. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 157 (2015) no. 1, pp. 15-24. http://geodesic.mathdoc.fr/item/UZKU_2015_157_1_a1/

[1] Ugrimov S. V., “Raschet trekhsloinykh plastin s kompozitnymi obshivkami”, Voprosy proektirovaniya i proizvodstva konstruktsii letatelnykh apparatov, Sb. nauch. tr. Nats. aerokosm. un-ta im. N. E. Zhukovskogo “Kharkovskii aviatsionnyi institut”, 3(79), Kharkov, 2014, 47–56

[2] Badriev I. B., Makarov M. V., Paimushin V. N., “On the interaction of composite plate having a vibration-absorbing covering with incident acoustic wave”, Russ. Math., 59:3 (2015), 66–71 | DOI

[3] Ekeland I., Temam R., Convex Analysis and Variational Problems, North-Holland, Amsterdam, 1976, 402 pp. | MR | Zbl

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

[5] Badriev I. B., Zheltukhin V. S., Makarov M. V., Paimushin V. N., “Chislennoe reshenie zadachi o ravnovesii trekhsloinoi plastiny s transversalno-myagkim zapolnitelem v geometricheski nelineinoi postanovke”, Vestn. Kazan. tekhnol. un-ta, 17:23 (2014), 393–396

[6] Badriev I. B., Banderov V. V., “Iterative Methods for Solving Variational Inequalities of the Theory of Soft Shells”, Lobachevskii J. Math., 35:4 (2014), 354–365 | DOI | MR

[7] Badriev I. B., Banderov V. V., “Numerical method for solving variation problems in mathematical physics”, Appl. Mech. Mater., 668–669 (2014), 1094–1097 | DOI

[8] Badriev I. B., Banderov V. V., Zadvornov O. A., “On the solving of equilibrium problem for the soft network shell with a load concentrated at the point”, PNRPU Mechanics Bulletin, 2013, no. 3, 17–35

[9] Badriev I. B., Shagidullin R. R., “A study of the convergence of a recursive process for solving a stationary problem of the theory of soft shells”, J. Math. Sci., 73:5 (1995), 519–525 | DOI | MR

[10] Paimushin V. N., “Nonlinear theory of the central bending of three-layer shells with defects in the form of sections of bonding failure”, Soviet Appl. Mechanics, 23:11 (1987), 1038–1043 | DOI

[11] Paimushin V. N., Bobrov S. N., “Refined geometric nonlinear theory of sandwich shells with a transversely soft core of medium thickness for investigation of mixed buckling forms”, Mech. Composite Mater., 36:1 (2000), 59–66 | DOI

[12] Paimushin V. N., “K variatsionnym metodam resheniya nelineinykh prostranstvennykh zadach sopryazheniya deformiruemykh tel”, Dokl. AN SSSR, 273:5 (1983), 1083–1086 | MR

[13] Paimushin V. N., “Obobschennyi variatsionnyi printsip Reissnera v nelineinoi mekhanike prostranstvennykh sostavnykh tel s prilozheniyami k teorii mnogosloinykh obolochek”, Izv. AN SSSR. Mekhanika tverdogo tela, 1987, no. 2, 171–180

[14] Natanson I. P., Teoriya funktsii veschestvennoi peremennoi, Nauka, M., 1974, 480 pp. | MR

[15] Badriev I. B., Zadvornov O. A., Iteratsionnye metody resheniya variatsionnykh neravenstv v gilbertovykh prostranstvakh, Kazan. gos. un-t, Kazan, 2007, 152 pp.

[16] Badriev I. B., Karchevskii M. M., “Convergence of the iterative Uzawa method for the solution of the stationary problem of seepage theory with a limit gradient”, J. Sov. Math., 45:4 (1989), 1302–1309 | DOI | MR

[17] Opial Z., “Weak convergence of the sequence of successive approximations for nonexpansive mappings”, Bull. Am. Math. Soc., 73:4 (1967), 591–597 | DOI | MR | Zbl