The Lagrange problem of the optimal shape of a column. (English. Russian original) Zbl 1126.49035
Dokl. Math. 68, No. 2, 253-257 (2003); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 392, No. 5, 598-602 (2003).
Summary: In this paper, for the first time, the existence and uniqueness theorem for solutions to the Lagrange problem for columns of various configurations is proved. We suggest a new approach based on studying the properties of a certain nonlinear functional. In [Yu. V. Egorov, C. R., Math., Acad. Sci. Paris 335, 997–1002 (2002; Zbl 1014.74055)], we prove the existence of a solution to the Lagrange problem for columns that are bodies of revolution, but we could not prove it uniqueness.
MSC:
| 49Q10 | Optimization of shapes other than minimal surfaces |
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
| 74P05 | Compliance or weight optimization in solid mechanics |
