@article{VMJ_2010_12_1_a4,
author = {Yu. A. Ustinov},
title = {Justification of the principle of {Saint} {Venant} for a~naturally twisted rod},
journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
pages = {53--67},
year = {2010},
volume = {12},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VMJ_2010_12_1_a4/}
}
Yu. A. Ustinov. Justification of the principle of Saint Venant for a naturally twisted rod. Vladikavkazskij matematičeskij žurnal, Tome 12 (2010) no. 1, pp. 53-67. http://geodesic.mathdoc.fr/item/VMJ_2010_12_1_a4/
[1] Saint-Venant B., “Memoire sur la torsin des prisms, avec des conciderations sur leur flexion, ainsi que sur l'equilibre interieur des solides elastiques en general, et des formules pratiques pour le calcul de leur resistance a divers efforts s'exercant simultanement”, Mem. Savants Etrang, 14 (1856), 233–560
[2] Saint-Venant B., “Memoire sur la flaxion des prismes, etc.”, J. Math.—Liouville, 1 (1856), 89–189
[3] Sen-Venan B., Memuar o kruchenii prizm. Memuar ob izgibe prizm, Klassiki estestvoznaniya, Fizmatgiz, M., 1961, 518 pp.
[4] Mathieu E. L., Théorie de l'elasticite des corps solides, Paris, 1883
[5] Clebsch R., “Saint-Venant's principle”, Arch. Ration. Mech. and Analysis, 18:2 (1965), 83–96 | MR
[6] Oleinik O. A., Iosifyan G. A., “Ob usloviyakh zatukhaniya i predelnom povedenii na beskonechnosti reshenii sistemy uravnenii teorii uprugosti”, Dokl. AN SSSR, 258:3 (1981), 550–553 | MR | Zbl
[7] Ustinov Yu. A., “K obosnovaniyu printsipa Sen-Venana”, Izv. vuzov Sev.-Kavk. reg., 1994, 91–92
[8] Ustinov Yu. A., Zadachi Sen-Venana dlya psevdotsilindrov, Fizmatlit, M., 2003, 125 pp.
[9] Vorovich I. I., Babeshko V. A., Dinamicheskie smeshannye zadachi teorii uprugosti dlya neklassicheskikh oblastei, M., 1973, 320 pp. | MR
[10] Kostyuchenko A. G., Orazov M. B., “Zadacha o kolebaniyakh uprugogo polutsilindra i svyazannye s nei samosopryazhennye kvadratichnye puchki”, Tr. seminara im. I. G. Petrovskogo, 6, 1981, 97–146 | MR | Zbl
[11] Getman I. P., Ustinov Yu. A., Matematicheskaya teoriya neregulyarnykh tverdykh volnovodov, Izd-vo RGU, Rostov-na-Donu, 1993, 144 pp.
[12] Druz A. N., Polyakov N. A., Ustinov Yu. A., “Odnorodnye resheniya i zadachi Sen-Venana dlya estestvenno zakruchennogo sterzhnya”, PMM, 60:4 (1996), 660–668 | MR | Zbl