Abstract
Homogenization techniques were used by Duvaut (1976,1978) in asymptotic analyse of 3-dimensional periodic continuum problems and periodic von Kármán plates.
In this paper we homogenize Budiansky-Sanders linear, elastic shells with material parameters rapidly oscillating on the shell surface. We obtain a homogenized shell model which is elliptic and depends on explicitly calculated effective material parameters. We show that the solution of the periodic shell model converges weakly to the solution of the homogenized model when the period tends to zero.
Similar content being viewed by others
References
R.A. Adams, Sobolev Spaces, Academic Press, New York (1975).
M. Artola and G. Duvaut, Homogénésation d'une plaque renforcée. C.R. Acad. Sc. Paris, Série A 284 (1977) 707–710.
I. Babuška, Solution of interface problems by homogenization I, II and III. SIAM J. Math. Anal. 7 (1976) 603–634, 635–645; 8 (1977) 923–937.
A. Bensoussan, J.L. Lions and G. Papanicolau, Asymptotic Analysis for Periodic Structures. North-Holland, Amsterdam (1978).
M. Bernadou and P.G. Ciarlet, Sur l'ellipticité du modèle linéaire de coques ed. W.T. Koiter. Computing Methods in Applied Sciences and Engineering, Lecture Notes in Economics and Mathematical Systems 134, Springer-Verlag, Berlin (1976) pp. 89–138.
B. Budiansky and J.L. Sanders, On the “best” first-order linear shell theory, Progress in Applied mechanics, W. Prager Anniversary Volume, Macmillan, New York (1967) pp. 129–140.
D. Cioranescu, J. Saint-Jean-Paulin and H. Lanchon, Elastoplastic torsion of heterogeneous cylindrical bars. J. Inst. Maths. Applics. 24 (1979) 353–378.
P. Destuynder, Sur une justification des modèles de plaques et de coques par les methodes asymptotiques. Thèse, Université Paris VI (1980).
G. Duvaut, Analyse Fonctionnelle et mécanique des milieux continus. Application à l'étude des Matériaux composites élastiques à structure périodique-homogénéisation. In: W.T. Koiter (Ed.) Theoretical and Applied Mechanics, North-Holland (1976) pp. 110–132.
G. Duvaut, Homogénéisation des plaques à structure périodique en Théorie non-linéaire de von Kármán. Journées d'Analyse Non-Linéaire, Lecture Notes in Mathematics 665, Springer-Verlag, Berlin (1978) pp. 56–69.
G. Duvaut and J.L. Lions, Les inéquations en mécanique et en physique. Dunod, Paris (1972).
E.de Giorgi, Convergence problems for functionals and operators. In: E.de Giorgi, E. Magenes and U. Mosco (eds.) Proc. of the Int. Meeting on Recent Methods in Non-Linear Analysis, Pitagora Editrice, Bologna (1978) pp. 131–188.
A. Lutoborski, and J.J. Telega, Homogenization of a plane elastic arch. J. Elasticity 14 (1984) 65–77.
L. Tartar. Cours Peccot, Collège de France (1977).
R. Valid, La mécanique des milieux continus et le calcul des structures. Eyrolles, Paris (1977).
V.V. Zhikov, S.M. Kozlov, O.A. Oleinik and Kha Thien Ngoan, Homogenization and G-convergence of differential operators. Uspekhi Mat. Nauk 34 (1979) 65–133.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lutoborski, A. Homogenization of linear elastic shells. J Elasticity 15, 69–87 (1985). https://doi.org/10.1007/BF00041306
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00041306