On the Lagrange problem about the strongest column
[Sur le problème de Lagrange de la forme optimale d'une colonne]
Comptes Rendus. Mathématique, Tome 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
Egorov, Youri V. 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
@article{CRMATH_2002__335_12_997_0,
     author = {Egorov, Youri V.},
     title = {On the {Lagrange} problem about the strongest column},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {997--1002},
     publisher = {Elsevier},
     volume = {335},
     number = {12},
     year = {2002},
     doi = {10.1016/S1631-073X(02)02607-9},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/S1631-073X(02)02607-9/}
}
TY  - JOUR
AU  - Egorov, Youri V.
TI  - On the Lagrange problem about the strongest column
JO  - Comptes Rendus. Mathématique
PY  - 2002
SP  - 997
EP  - 1002
VL  - 335
IS  - 12
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/S1631-073X(02)02607-9/
DO  - 10.1016/S1631-073X(02)02607-9
LA  - en
ID  - CRMATH_2002__335_12_997_0
ER  - 
%0 Journal Article
%A Egorov, Youri V.
%T On the Lagrange problem about the strongest column
%J Comptes Rendus. Mathématique
%D 2002
%P 997-1002
%V 335
%N 12
%I Elsevier
%U http://www.numdam.org/articles/10.1016/S1631-073X(02)02607-9/
%R 10.1016/S1631-073X(02)02607-9
%G en
%F CRMATH_2002__335_12_997_0
Egorov, Youri V. On the Lagrange problem about the strongest column. Comptes Rendus. Mathématique, Tome 335 (2002) no. 12, pp. 997-1002. doi : 10.1016/S1631-073X(02)02607-9. http://www.numdam.org/articles/10.1016/S1631-073X(02)02607-9/

[1] Cox, S.J. The shape of the ideal column, Math. Intelligencer, Volume 14 (1992) no. 1, pp. 16-24

[2] Cox, S.J.; Overton, M.L. On the optimal design of columns against buckling, SIAM J. Math. Anal, Volume 23 (1992) no. 2, pp. 287-325

[3] Egorov, Yu.V.; Kondratiev, V.A. On the Spectral Theory of Elliptic Operators, Operator Theory, 89, Basel, Birkhäuser, 1996

[4] Keller, J.B. The shape of the strongest column, Arch. Rational Mech. Anal, Volume 4 (1960), pp. 275-285

[5] Keller, J.B.; Tadjbakhsh, I. Strongest columns and isoperemetric inequalities for eigenvalues, Trans. ASME J. Appl. Mech, Volume 29 (1962) no. 1, pp. 159-164

[6] J.-L. Lagrange, Sur la figure des colonnes, in: Oeuvres de Lagrange (Publ. de M.J.-A. Serret), Vol. 2, Gauthier-Villars, Paris, 1868, pp. 125–170

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

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

[10] 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

Cité par Sources :