Article
MSC:
00A89,
73H99,
73K99,
74B20,
74G60,
74K20 | MR 0495428 | Zbl 0402.73063 | DOI: 10.21136/AM.1978.103751
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Keywords:
dangerous initial diflection shape; thin elastic plate; Foeppl-Karman-Marguerre; Sobolev’s space; real separable Hilbert space; potential energy; variational inequalities
dangerous initial diflection shape; thin elastic plate; Foeppl-Karman-Marguerre; Sobolev’s space; real separable Hilbert space; potential energy; variational inequalities
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.
References:
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[2] Sadovský Z.: Rectangular thin plate in shear - theoretical solution. (in Slovak). Staveb. Čas., 25 (1977), 3, 197-228.
[3] Hlaváček I.: Einfluss der Form der Anfangskrümmung auf das Ausbeulen der gedrückten rechteckigen Platte. Acta Technica ČSAV, 7 (1962), 2, 174-206.
[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.
[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. DOI 10.1002/cpa.3160200405 | MR 0221808
[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. DOI 10.1002/cpa.3160210303 | MR 0229978 | Zbl 0162.56501
[7] Vainberg M. M.: Variational methods for the study of nonlinear operators. (in Russian). Gostechizdat, Moscow 1956.
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