×

Method of averaging in the problems of stability of elastic plates possessing fine periodic structure. (English. Russian original) Zbl 0515.73052

J. Appl. Math. Mech. 46, 513-519 (1983); translation from Prikl. Mat. Mekh. 46, 647-654 (1982).

MSC:

74G60 Bifurcation and buckling
74K20 Plates
49R50 Variational methods for eigenvalues of operators (MSC2000)
74H55 Stability of dynamical problems in solid mechanics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Lur’e, A. I., Nonlinear Theory of Elasticity (1980), NAUKA: NAUKA Moscow · Zbl 0506.73018
[2] Zubov, L. M., Variational principles of the nonlinear theory of elasticity. Case of superposition of a small deformation on a finite deformation, PMM, Vol.35, No.5 (1971) · Zbl 0255.73052
[3] Bogoliubov, N. N.; Mitropol’skii, Iu. M., Asymptotic Methods in the Theory of Nonlinear Oscillations (1964), Gordon & Breach: Gordon & Breach New York
[4] Bakhvalov, N. S., Averaged characteristics of the bodies with periodic structure, Dokl. Akad. Nauk SSSR, Vol.218, No.5 (1974)
[5] Bakhvalov, N. S.; Zlotnik, A. A., Coefficient instability of differential equations and averaging the equations with random coefficients, Dokl. Akad. Nauk SSSR, Vol.242, No.4 (1978) · Zbl 0417.35078
[6] Berdichevskii, V. L., Spatial averaging of periodic structures, Dokl. Akad. Nauk SSSR, Vol.222, No.3 (1975) · Zbl 0158.46505
[7] Bartenev, G. M.; Khazanovich, T. N., On the law governing highly elastic deformations of crosslinked polymers, Vysokomolekul. soedineniia, Vol.2, No.1 (1960)
[8] Zubov, L. M., On the Jaumann derivative for second rand tensors, Izv. Sev.—Kavkaz. Nauchn. tsentra vyssh. shkoly. Estestv. n., No.2 (1976)
[9] Zubov, L. M., Theory of small deformations of prestressed thin shells, PMM, Vol.40, No.1 (1976) · Zbl 0352.73072
[10] Timoshenko, S. P., Stability of Elastic Systems (1955), GOSTEKHIZDAT: GOSTEKHIZDAT Moscow
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.