On the generalized von Kármán equations and their approximation

Ciarlet, Philippe G. ; Gratie, Liliana ; Kesavan, Srinivasan (2007) On the generalized von Kármán equations and their approximation Mathematical Models and Methods in Applied Sciences, 17 (4). pp. 617-633. ISSN 0218-2025

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Official URL: http://ejournals.worldscientific.com.sg/m3as/17/17...

Related URL: http://dx.doi.org/10.1142/S0218202507002042


We consider here the "generalized von Kármán equations", which constitute a mathematical model for a nonlinearly elastic plate subjected to boundary conditions "of von Kármán type" only on a portion of its lateral face, the remaining portion being free. As already shown elsewhere, solving these equations amounts to solving a "cubic" operator equation, which generalizes an equation introduced by Berger and Fife. Two noticeable features of this equation, which are not encountered in the "classical" von Kármán equations are the lack of strict positivity of its cubic part and the lack of an associated functional. We establish here the convergence of a conforming finite element approximation to these equations. The proof relies in particular on a compactness method due to J. L. Lions and on Brouwer's fixed point theorem. This convergence proof provides in addition an existence proof for the original problem.

Item Type:Article
Source:Copyright of this article belongs to World Scientific Publishing Company.
Keywords:Nonlinear Plate Theory; Brouwer's Theorem; Finite Element Method
ID Code:75407
Deposited On:23 Jun 2012 14:08
Last Modified:23 Jun 2012 14:08

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