A new model for thin plates with rapidly varying thickness. II. A convergence proof
Authors:
Robert V. Kohn and Michael Vogelius
Journal:
Quart. Appl. Math. 43 (1985), 1-22
MSC:
Primary 73K10
DOI:
https://doi.org/10.1090/qam/782253
MathSciNet review:
782253
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Abstract: Our recent paper [6] presented a model for thin plates with rapidly varying thickness, distinguishing between thickness variation on a length scale longer than, on the order of, or shorter than the mean thickness. We review the model here, and identify the case of long scale thickness variation as an asymptotic limit of the intermediate case, where the scales are comparable. We then present a convergence theorem for the intermediate case, showing that the model correctly represents the solution of the equations of linear elasticity on the three-dimensional plate domain, asymptotically as the mean thickness tends to zero.
R. Brizzi and J. P. Chalot, Homogénéisation de Frontière, Thèse, Université de Nice, 1978
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R. V. Kohn and M. Vogelius, A new model for thin plates with rapidly varying thickness, Int. J. Solids & Structures 20, 333–350 (1984)
- A. E. H. Love, A treatise on the Mathematical Theory of Elasticity, Dover Publications, New York, 1944. Fourth Ed. MR 0010851
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R. Brizzi and J. P. Chalot, Homogénéisation de Frontière, Thèse, Université de Nice, 1978
D. Caillerie, Homogénéisation des équations de la diffusion stationnaire dans les domaines cylindriques aplatis, R.A.I.R.O. Analyse numérique, 15, 295–319 (1981)
D. Caillerie, Thin elastic and periodic plates, preprint; see also Plaques élastiques minces à structure périodique de période et d’épaisseur comparables. C. R. Acad. Sci. 294-II, 159–162 (1982)
D. Cioranescu, and J. Saint Jean Paulin, Homogenization in open sets with holes, J. Mathematical Anal. Appl. 71, 590–607 (1979)
J. Gobert, Une inéquation fondamentale de la théorie de l’élasticité, Bull. Soc. Roy. Sci. Liège, 31, 182–191 (1962)
R. V. Kohn and M. Vogelius, A new model for thin plates with rapidly varying thickness, Int. J. Solids & Structures 20, 333–350 (1984)
A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity, 4th edition, Dover, 1944
D. Morgenstern and I. Szabo, Vorlesungen über Theoretische Mechanik, Springer-Verlag, 1961
R. P. Nordgren, A bound on the error in plate theory, Quart. Appl. Math. 28 587–595 (1971)
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© Copyright 1985
American Mathematical Society
