Two-dimensional approximations of 3-dimensional eigenvalue problems in plate-theory

Ciarlet, PG and Kesavan, S (1981) Two-dimensional approximations of 3-dimensional eigenvalue problems in plate-theory. In: Computer Methods in Applied Mechanics and Engineering, 26 (2). pp. 145-172.

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Abstract

The eigenvalues and eigenfunctions corresponding to the three-dimensional equations for the linear elastic equilibrium of a clamped plate of thickness 2ϵ, are shown to converge (in a specific sense) to the eigenvalues and eigenfunctions of the well-known two-dimensional biharmonic operator of plate theory, as ϵ approaches zero. In the process, it is found in particular that the displacements and stresses are indeed of the specific forms usually assumed a priori in the literature. It is also shown that the limit eigenvalues and eigenfunctions can be equivalently characterized as the leading terms in an asymptotic expansion of the three-dimensional solutions, in terms of powers of ϵ. The method presented here applies equally well to the stationary problem of linear plate theory, as shown elsewhere by P. Destuynder.

Item Type:	Journal Article
Publication:	Computer Methods in Applied Mechanics and Engineering
Publisher:	Elsevier Science
Additional Information:	Copyright of this article belongs to Elsevier Science.
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	08 Feb 2012 09:44
Last Modified:	12 Oct 2018 15:27
URI:	http://eprints.iisc.ac.in/id/eprint/43347

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