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

Ciarlet, P. G. ; Kesavan, S. (1981) Two-dimensional approximations of three-dimensional eigenvalue problems in plate theory Computer Methods in Applied Mechanics and Engineering, 26 (2). pp. 145-172. ISSN 0045-7825

Full text not available from this repository.

Official URL: http://linkinghub.elsevier.com/retrieve/pii/004578...

Related URL: http://dx.doi.org/10.1016/0045-7825(81)90091-8

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:Article
Source:Copyright of this article belongs to Elsevier Science.
ID Code:16327
Deposited On:15 Nov 2010 13:51
Last Modified:03 Jun 2011 11:52

Repository Staff Only: item control page