Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-06T00:23:03.119Z Has data issue: false hasContentIssue false
  • English
  • Français

Approximation of the elastic deformation of a thin cylinder

Published online by Cambridge University Press:  26 September 2008

Sisto Baldo
Sisto Baldo
Affiliation:
Dipartimento di Matematica, Università di Trento, 38050 Povo (Trento), Italy
Get access Rights & Permissions [Opens in a new window]

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
European Journal of Applied Mathematics , Volume 6 , Issue 4 , August 1995 , pp. 373 - 381
Copyright
Copyright © Cambridge University Press 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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
[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), 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
[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, 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
[PI]Percivale, D. 1990 Perfectly elastic plates. J. reine angew. Math. III, 39–50.Google 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