Comptes Rendus
no. 12
On the Lagrange problem about the strongest column
[Sur le problème de Lagrange de la forme optimale d'une colonne]
Youri V. Egorov1
1 Laboratoire des mathématiques pour l'industrie et la physique, UMR 5640, Université Paul Sabatier, UFR MIG, 118, route de Narbonne, 31062 Toulouse, France
Comptes Rendus. Mathématique, Volume 335 (2002) no. 12, pp. 997-1002.

On propose une nouvelle approche au problème classique de Lagrange de la forme d'une colonne encastrée la plus solide à volume et hauteur fixés. On montre l'existence d'une telle colonne et on donne un algorithme pour la calculer.

A new approach to the classical Lagrange problem about the form of the strongest clamped column of fixed volume and height is proposed. The existence of the optimal column is proved and a method to find its design is given.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)02607-9
Youri V. Egorov 1

1 Laboratoire des mathématiques pour l'industrie et la physique, UMR 5640, Université Paul Sabatier, UFR MIG, 118, route de Narbonne, 31062 Toulouse, France 
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Youri V. Egorov. On the Lagrange problem about the strongest column. Comptes Rendus. Mathématique, Volume 335 (2002) no. 12, pp. 997-1002. doi : 10.1016/S1631-073X(02)02607-9. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02607-9/

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[7] N. Olhoff Maximizing higher order eigen – frequencies of beams with constraints on the design geometry, J. Struct. Mech, Volume 5 (1977) no. 2, pp. 107-134

[8] N. Olhoff; S.H. Rasmussen On single and bimodal optimum buckling loads of clamped columns, Internat. J. Solids Structures, Volume 13 (1977) no. 7, pp. 605-614

[9] A.P. Seyranian On a solution of the Lagrange problem, Dokl. Akad. Nauk USSR, Volume 271 (1983) no. 2, pp. 337-340

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