On the approximation and the optimization of plates

Abstract

this paper, we use such an approach to develop numerical approximation methods both for Eq. (1.1) and for various optimization problems (optimal control or optimal shape design) that may be associated to it. In Sect. 2, we study the numerical treatment of the clamped plate via second order elliptic systems. Section 3 is devoted to optimization questions. Relevant numerical examples illustrate the application of the proposed methods. In particular, we perform a numerical study of the Hadamard [4] conjecture on the maximum principle for (1.1), (1.3) and its counter-examples. All the experiments have been made in plane domains given by ellipses with the