A new approach is proposed to the study of the classical problem about the highest column. The existence and the uniqueness of the solution is proved for the first time. The method is based on the study of critical points of a suitable nonlinear functional.
On propose une nouvelle approche au problème classique de la forme d'une colonne la plus haute. On prouve pour la première fois qu'une telle colonne existe et est unique. La méthode est basée sur l'étude des points critiques d'une fonctionnelle nonlinéaire.
Accepted:
Published online:
Mots-clés : Solides et structures, La plus haute colonne, Problème de min–max, Fonctionelle nonlinéaire
Youri V. Egorov 1
@article{CRMECA_2010__338_5_266_0, author = {Youri V. Egorov}, title = {On the tallest column}, journal = {Comptes Rendus. M\'ecanique}, pages = {266--270}, publisher = {Elsevier}, volume = {338}, number = {5}, year = {2010}, doi = {10.1016/j.crme.2010.05.001}, language = {en}, }
Youri V. Egorov. On the tallest column. Comptes Rendus. Mécanique, Volume 338 (2010) no. 5, pp. 266-270. doi : 10.1016/j.crme.2010.05.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2010.05.001/
[1] Determinatio onerum, quae columnae gestare valent, Leonhardi Euleri Opera Omnia 2, vol. 17, 1982, pp. 232-251 (Switzerland)
[2] The tallest column, J. Math. Mech., Volume 16 (1966), pp. 433-446
[3] The shape of the tallest column, SIAM J. Math. Anal., Volume 29 (1998) no. 3, pp. 547-554
[4] On the Lagrange problem about the strongest column, C. R. Acad. Sci. Paris, Ser. I, Volume 335 (2002), pp. 997-1002
Cited by Sources:
Comments - Policy