Comptes Rendus
On the Lagrange problem about the optimal form for circular hollow columns
Comptes Rendus. Mécanique, Volume 331 (2003) no. 10, pp. 699-704.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2003.07.001
Keywords: Computational solid mechanics, Lagrange problem, Optimal column
Mot clés : Mécanique des solides numérique, Problème de Lagrange, Colonne optimale

Youri V. Egorov 1

1 Paul Sabatier University, UFR MIG, Labo MIP, UMR 5640, 118, route de Narbonne, 31062 Toulouse cedex 4, France
@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},
}
TY  - JOUR
AU  - Youri V. Egorov
TI  - On the Lagrange problem about the optimal form for circular hollow columns
JO  - Comptes Rendus. Mécanique
PY  - 2003
SP  - 699
EP  - 704
VL  - 331
IS  - 10
PB  - Elsevier
DO  - 10.1016/j.crme.2003.07.001
LA  - en
ID  - CRMECA_2003__331_10_699_0
ER  - 
%0 Journal Article
%A Youri V. Egorov
%T On the Lagrange problem about the optimal form for circular hollow columns
%J Comptes Rendus. Mécanique
%D 2003
%P 699-704
%V 331
%N 10
%I Elsevier
%R 10.1016/j.crme.2003.07.001
%G en
%F CRMECA_2003__331_10_699_0
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/

[1] A.P. Seyranian On a Lagrange problem, Izv. AN USSR Ser. Mech. Solids, Volume 2 (1984), pp. 101-111

[2] N. Olhoff; F.I. Niordson Some problems concerning singularities of optimal beams and columns, Z. Angew. Math. Mech., Volume 59 (1979) no. 3, p. T16-T26

[3] A.P. Seyranian, The Lagrange problem on the optimal column design, Preprint of The Institute of Mechanics of MSU, Moscow, 60-2000, pp. 1–63

[4] Yu.V. Egorov On the Lagrange problem about the strongest column, C. R. Acad. Sci. Paris, Ser. I, Volume 335 (2002), pp. 997-1002

[5] Yu.V. Egorov On the Lagrange problem about the optimal design of a column, Dokl. Ros. Akad. Nauk, Volume 392 (2003) no. 5, pp. 1-5

Cited by Sources:

Comments - Policy