Comptes Rendus
On the optimization of higher eigenvalues
Comptes Rendus. Mécanique, Volume 332 (2004) no. 8, pp. 673-678.

A new approach is proposed for the study of the classical Lagrange problem on the optimal form of a column with clamped ends and a fixed volume. It is proved that there exists a column with the maximal possible value of the kth eigenvalue and that such a column is unique. A method for the numerical solution is proposed. The method is based on the analysis of the critical points of a non-linear functional related to the Lagrange problem.

On propose une nouvelle approche au problème classique de Lagrange de la forme optimale de la colonne encastrée aux volume et hauteur fixés. On prouve qu'il existe une colonne avec la valeur de la k-ième valeur propre maximale et que telle colonne est unique. La méthode est basée sur l'étude des points critiques d'une fonctionnelle nonlinéaire. Une méthode pour la solution numerique du problème est proposée.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2004.03.008
Keywords: Computational solid mechanics, Lagrange problem, Optimization of eigenvalues, Optimal column
Mot clés : Mécanique des solides numérique, Problème de Lagrange, Optimisation de valeurs propres, Colonne optimale

Youri V. Egorov 1

1 Université Paul Sabatier, UFR MIG, labo MIP, UMR 5640, 118, route de Narbonne, 31062 Toulouse cedex 4, France
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Youri V. Egorov. On the optimization of higher eigenvalues. Comptes Rendus. Mécanique, Volume 332 (2004) no. 8, pp. 673-678. doi : 10.1016/j.crme.2004.03.008. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2004.03.008/

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