NEW MODEL FOR THIN PLATES WITH RAPIDLY VARYING THICKNESS. II: A CONVERGENCE PROOF.

Robert Kohn, Michael Vogelius

Research output: Contribution to journalArticle

Abstract

In a recent paper the authors 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. They 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. They 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.

Original languageEnglish (US)
Pages (from-to)1-22
Number of pages22
JournalQuarterly of Applied Mathematics
Volume43
Issue number1
StatePublished - Apr 1985

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Thin Plate
Elasticity
Model
Asymptotic Limit
Linear Elasticity
Convergence Theorem
Length Scale
Tend
Three-dimensional
Zero

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

NEW MODEL FOR THIN PLATES WITH RAPIDLY VARYING THICKNESS. II : A CONVERGENCE PROOF. / Kohn, Robert; Vogelius, Michael.

In: Quarterly of Applied Mathematics, Vol. 43, No. 1, 04.1985, p. 1-22.

Research output: Contribution to journalArticle

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