No CrossRef data available.
Article contents
Approximation of the elastic deformation of a thin cylinder
Published online by Cambridge University Press: 26 September 2008
Abstract
The elastic displacement of a thin cylinder subject to given forces is approximated by means of a function constructed from the solutions of certain one-dimensional problems. Estimates are given for the error in terms of a decreasing function of the radius of the cylinder.
- Type
- Research Article
- Information
- Copyright
- Copyright © Cambridge University Press 1995
References
[AcBuPl]Acerbi, E., Buttazzo, G. & Percivale, D. 1988 Thin inclusion in linear elasticity: a variational approach. J. Reine Angew. Math. 386, 99–115.Google Scholar
[AcBuP2]Acerbi, E., Buttazzo, G. & Percivale, D. 1991 Non linear elastic strings. J. Elasticity 25 (2), 137–148.CrossRefGoogle Scholar
[AB]Anzellotti, G. & Baldo, S. 1994 Asymptotic development by Γ-convergence. Appl. Math. Opt. 27, 105–123.CrossRefGoogle Scholar
[ABP]Anzellotti, G., Baldo, S. & Percivale, D. 1994 Dimension reduction in variational problems, asymptotic development in Γ-convergence and thin structures in elasticity. Asymptotic Analysis 9, 61–100.CrossRefGoogle Scholar
[BCGR]Bourquin, F., Ciarlet, P. G., Geymonat, G. & Raoult, A. 1992 Γ-convergence et analyse asymptotique des plaques minces. CR Acad. Sci. Paris Ser I 315, 1017–1024.Google Scholar
[C]Ciarlet, P. G. 1980 A Justification of the von Karman equation. Arch. Rat. Mech. Anal. 73, 349–389.CrossRefGoogle Scholar
[CD]Ciarlet, P. G. & Destuynder, P. 1979 A justification of the two-dimensional linear plate model. J. de Mécanique 18 (2), 315–344.Google Scholar
[CK]Ciarlet, P. G. & Kesavan, S. 1981 Two dimensional approximation of three dimensional eigenvalue problems in plate theory. Comput. Math. Appl. Mech. Eng. 26, 147–172.CrossRefGoogle Scholar
[D]Destuynder, P. 1981 Comparaison entre les modèles tridimensionnels et bidimensionnels de plaques en élasticité. RAIRO Analyse Numérique 15, 331–369.CrossRefGoogle Scholar
[DGF]De Giorgi, E. & Franzoni, T. 1979 Su un tipo di convergenza variazionale. Rend. Sem. Mat. Brescia 3, 63–101.Google Scholar
[ET]Ericksen, J. L. & Truesdell, C. 1979 Exact theory of stress and strain in rods and shells. Arch. Rat. Mech. Anal. 1, 295–323.CrossRefGoogle Scholar
[H]Hay, G. E. 1942 The finite displacement of thin rods. Trans. Am. Math. Soc. 51, 65–102.CrossRefGoogle Scholar
[KV]Kohn, R. V. & Vogelius, M. 1985 A new model for thin plates with rapidly varying thickness, II: a convergence proof. Quart. Appl. Math. 43, 1–22.CrossRefGoogle Scholar
[MS]Morgenstern, D. & Szabo, I. 1961 Vorlesungen über theoretische Mechanik. Springer.CrossRefGoogle Scholar
[P2]Percivale, D. 1992 Folded shells: a variational approach. Ann. Scuola Norm. Sup. Pisa, Cl. Sci. 19(2), 207–221.Google Scholar
[PG1]Podio-Guidugli, P. 1989 An exact derivation of the thin plate equation. J. Elasticity 22, 121–133.CrossRefGoogle Scholar
[PG2]Podio-Guidugli, P. 1990 Constraint and scaling methods to derive shell theory from three dimensional elasticity. Riv. Mat. Univ. Parma 16, 78–83.Google Scholar