A new approach to the problem of finding the form of the strongest clamped circular column with thin walls of fixed volume and height is proposed. The same model describes also the form of the horizontal beam with rectangular vertical sections of a fixed height and variable widths. The existence and the uniqueness of the optimal column are proved here for the first time and the optimal form is found.
On propose une nouvelle approche au problème de la forme de la colonne encastrée la plus solide aux parois minces aux volume et hauteur fixés. Le même modèle décrit aussi le problème de la forme optimale d'une poutre horisontale aux sections verticales rectangulaires dont l'hauteur est fixée et la largeur est variable. On montre l'existence et l'unicité d'une telle colonne par la première fois ici et on trouve la forme optimale.
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Mots-clés : Mécanique des solides numérique, Problème de Lagrange, Colonne optimale
Youri V. Egorov 1
@article{CRMECA_2003__331_10_699_0, author = {Youri V. Egorov}, title = {On the {Lagrange} problem about the optimal form for circular hollow columns}, journal = {Comptes Rendus. M\'ecanique}, pages = {699--704}, publisher = {Elsevier}, volume = {331}, number = {10}, year = {2003}, doi = {10.1016/j.crme.2003.07.001}, language = {en}, }
Youri V. Egorov. On the Lagrange problem about the optimal form for circular hollow columns. Comptes Rendus. Mécanique, Volume 331 (2003) no. 10, pp. 699-704. doi : 10.1016/j.crme.2003.07.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2003.07.001/
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