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Title: A theoretical approach to the problem of the most dangerous initial deflection shape in stability type structural problems (English)
Author: Sadovský, Zoltán
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 23
Issue: 4
Year: 1978
Pages: 248-266
Summary lang: English
Summary lang: Slovak
Summary lang: Russian
Category: math
Summary: The author introduces a global measure of initial deflection given by the energy norm. Solving the formulated minimization problem with a subsidiary condition the most dangerous initial deflection shape is obtained. The theoretical results include a wide range of stability type structural problems. (English)
Keyword: dangerous initial diflection shape
Keyword: thin elastic plate
Keyword: Foeppl-Karman-Marguerre
Keyword: Sobolev’s space
Keyword: real separable Hilbert space
Keyword: potential energy
Keyword: variational inequalities
MSC: 00A89
MSC: 73H99
MSC: 73K99
MSC: 74B20
MSC: 74G60
MSC: 74K20
idZBL: Zbl 0402.73063
idMR: MR0495428
DOI: 10.21136/AM.1978.103751
Date available: 2008-05-20T18:09:45Z
Last updated: 2020-07-28
Stable URL:
Reference: [1] Bauer L., Reiss E. L.: Nonlinear buckling of rectangular plates.J. Soc. Ind. Appl. Math., 13 (1965), 3, 603-625. 10.1137/0113039
Reference: [2] Sadovský Z.: Rectangular thin plate in shear - theoretical solution.(in Slovak). Staveb. Čas., 25 (1977), 3, 197-228.
Reference: [3] Hlaváček I.: Einfluss der Form der Anfangskrümmung auf das Ausbeulen der gedrückten rechteckigen Platte.Acta Technica ČSAV, 7 (1962), 2, 174-206.
Reference: [4] Sadovský Z.: Influence of initial imperfections and boundary conditions on stability of shallow shells and thin plates.(in Slovak). Research rep., ÚSTARCH SAV, Bratislava Dec. 1975.
Reference: [5] Berger M. S.: On von Kármán's equations and the buckling of a thin elastic plate, I. The clamped plate.Comm. Pure Appl. Math., 20 (1967), 687-719. MR 0221808, 10.1002/cpa.3160200405
Reference: [6] Berger M. S., Fife P. C.: Von Kármán's equations and the buckling of a thin elastic plate, II. Plate with general edge conditions.Comm. Pure Appl. Math., 21 (1968), 227-241. Zbl 0162.56501, MR 0229978, 10.1002/cpa.3160210303
Reference: [7] Vainberg M. M.: Variational methods for the study of nonlinear operators.(in Russian). Gostechizdat, Moscow 1956.


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