IJPAM: Volume 43, No. 1 (2008)
THE CONTROLLED PLATE MODEL
Department of Mathematics
Technical University of Denmark
Kgs. Lyngby, DK 2800, DENMARK
Abstract.In this paper we study the Mindlin-Timoshenko plate model. The model comes from the so-called Kirchoff plate model after a weakening of the Kirchoff hypothesis by removing the assumption that the filaments of the plate remain perpendicular to the deformed middle surface, but keeping the assumption that they remain straight and undergo no strain deformation.
The derivations of the model in the literature are typically not completely rigorous, but Ciarlet has in [#!ciarlet1!#] shown how this model (and many others) are ``correct" in the sense that it is the natural first ``term" in an expansion of a full, nonlinear model.
The derivation that follows is rather standard, but with the additional purpose of being able to formulate the boundary control problem in a variational
setting there are some modifications in comparison to the derivations from mechanical engineering and the works of Lagnese and Lions, [#!lagneselions!#], [#!lagnese!#].
The question of well-posedness and choice of
``state-space" is approached by application of variational theory.
Received: August 27, 2007
AMS Subject Classification: 74A05, 35A15
Key Words and Phrases: controlled plate model, Mindlin-Timoshenko plate model, Kirchoff plate model, derivations of the model
Source: International Journal of Pure and Applied Mathematics