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Approximation of the elastic deformation of a thin cylinder

Published online by Cambridge University Press:  26 September 2008

Sisto Baldo
Affiliation:
Dipartimento di Matematica, Università di Trento, 38050 Povo (Trento), Italy

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
Copyright
Copyright © Cambridge University Press 1995

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References

[AcBuPl]Acerbi, E., Buttazzo, G. & Percivale, D. 1988 Thin inclusion in linear elasticity: a variational approach. J. Reine Angew. Math. 386, 99115.Google Scholar
[AcBuP2]Acerbi, E., Buttazzo, G. & Percivale, D. 1991 Non linear elastic strings. J. Elasticity 25 (2), 137148.CrossRefGoogle Scholar
[AB]Anzellotti, G. & Baldo, S. 1994 Asymptotic development by Γ-convergence. Appl. Math. Opt. 27, 105123.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, 61100.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, 10171024.Google Scholar
[C]Ciarlet, P. G. 1980 A Justification of the von Karman equation. Arch. Rat. Mech. Anal. 73, 349389.CrossRefGoogle Scholar
[Cl]Ciarlet, P. G. 1990 Plates and Junctions in Elastic Multi-Structures. Masson.Google Scholar
[CD]Ciarlet, P. G. & Destuynder, P. 1979 A justification of the two-dimensional linear plate model. J. de Mécanique 18 (2), 315344.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, 147172.CrossRefGoogle Scholar
[D]Destuynder, P. 1981 Comparaison entre les modèles tridimensionnels et bidimensionnels de plaques en élasticité. RAIRO Analyse Numérique 15, 331369.CrossRefGoogle Scholar
[DGF]De Giorgi, E. & Franzoni, T. 1979 Su un tipo di convergenza variazionale. Rend. Sem. Mat. Brescia 3, 63101.Google Scholar
[ET]Ericksen, J. L. & Truesdell, C. 1979 Exact theory of stress and strain in rods and shells. Arch. Rat. Mech. Anal. 1, 295323.CrossRefGoogle Scholar
[GT]Goodier, J. N. & Timoshenko, S. P. 1970 Theory of Elasticity. McGraw-Hill.Google Scholar
[H]Hay, G. E. 1942 The finite displacement of thin rods. Trans. Am. Math. Soc. 51, 65102.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, 122.CrossRefGoogle Scholar
[MS]Morgenstern, D. & Szabo, I. 1961 Vorlesungen über theoretische Mechanik. Springer.CrossRefGoogle Scholar
[PI]Percivale, D. 1990 Perfectly elastic plates. J. reine angew. Math. III, 3950.Google Scholar
[P2]Percivale, D. 1992 Folded shells: a variational approach. Ann. Scuola Norm. Sup. Pisa, Cl. Sci. 19(2), 207221.Google Scholar
[PG1]Podio-Guidugli, P. 1989 An exact derivation of the thin plate equation. J. Elasticity 22, 121133.CrossRefGoogle Scholar
[PG2]Podio-Guidugli, P. 1990 Constraint and scaling methods to derive shell theory from three dimensional elasticity. Riv. Mat. Univ. Parma 16, 7883.Google Scholar