Voir la notice de l'article provenant de la source Math-Net.Ru
@article{TM_2010_271_a13, author = {Yu. L. Sachkov and S. V. Levyakov}, title = {Stability of inflectional elasticae centered at vertices or inflection points}, journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova}, pages = {187--203}, publisher = {mathdoc}, volume = {271}, year = {2010}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/TM_2010_271_a13/} }
TY - JOUR AU - Yu. L. Sachkov AU - S. V. Levyakov TI - Stability of inflectional elasticae centered at vertices or inflection points JO - Trudy Matematicheskogo Instituta imeni V.A. Steklova PY - 2010 SP - 187 EP - 203 VL - 271 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TM_2010_271_a13/ LA - ru ID - TM_2010_271_a13 ER -
%0 Journal Article %A Yu. L. Sachkov %A S. V. Levyakov %T Stability of inflectional elasticae centered at vertices or inflection points %J Trudy Matematicheskogo Instituta imeni V.A. Steklova %D 2010 %P 187-203 %V 271 %I mathdoc %U http://geodesic.mathdoc.fr/item/TM_2010_271_a13/ %G ru %F TM_2010_271_a13
Yu. L. Sachkov; S. V. Levyakov. Stability of inflectional elasticae centered at vertices or inflection points. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and topology. II, Tome 271 (2010), pp. 187-203. http://geodesic.mathdoc.fr/item/TM_2010_271_a13/
[1] Agrachev A.A., Sachkov Yu.L., Geometricheskaya teoriya upravleniya, Fizmatlit, M., 2004 | Zbl
[2] Korobeinikov S.N., “Vtorichnaya poterya ustoichivosti szhatogo sharnirno opertogo sterzhnya”, Lavrentevskie chteniya po matematike, mekhanike i fizike, Tez. dokl. IV Mezhdunar. konf., In-t gidrodinamiki SO RAN, Novosibirsk, 1995, 104
[3] Krylov A.N., “O formakh ravnovesiya szhatykh stoek pri prodolnom izgibe”, Izbr. trudy, Izd-vo AN SSSR, L., 1958, 486–538
[4] Kuznetsov V.V., Levyakov S.V., “O vtorichnoi potere ustoichivosti eilerova sterzhnya”, Prikl. mekh. i tekhn. fiz., 40:6 (1999), 184–185
[5] Kuznetsov V.V., Levyakov S.V., “Elastika eilerova sterzhnya s zaschemlennymi kontsami”, Prikl. mekh. i tekhn. fiz., 41:3 (2000), 184–186 | MR | Zbl
[6] Lyav A., Matematicheskaya teoriya uprugosti, ONTI, M.; L., 1935
[7] Pontryagin L.S., Boltyanskii V.G., Gamkrelidze R.V., Mischenko E.F., Matematicheskaya teoriya optimalnykh protsessov, Fizmatgiz, M., 1961
[8] Popov E.P., Teoriya i raschet gibkikh uprugikh sterzhnei, Nauka, M., 1986
[9] Sausvell R.V., Vvedenie v teoriyu uprugosti dlya inzhenerov i fizikov, Izd-vo inostr. lit., M, 1948
[10] Sachkov Yu.L., “Polnoe opisanie stratov Maksvella v obobschennoi zadache Didony”, Mat. sb., 197:6 (2006), 111–160 | DOI | MR
[11] Uitteker E.T., Vatson Dzh.N., Kurs sovremennogo analiza, URSS, M., 2002
[12] Eiler L., “Prilozhenie I: Ob uprugikh krivykh”, Metod nakhozhdeniya krivykh linii, obladayuschikh svoistvami maksimuma libo minimuma, ili reshenie izoperimetricheskoi zadachi, vzyatoi v samom shirokom smysle, Gostekhteorizdat, M.; L., 1934, 447–572
[13] Agrachev A.A., “Geometry of optimal control problems and Hamiltonian systems”, Nonlinear and optimal control theory, Lect. Notes Math., 1932, Springer, Berlin, 2008, 1–59 | DOI | MR | Zbl
[14] Bisshopp K.E., Drucker D.C., “Large deflection of cantilever beams”, Quart. Appl. Math., 3 (1945), 272–275 | MR | Zbl
[15] Born M., Untersuchungen über die Stabilität der elastischen Linie in Ebene und Raum, unter verschiedenen Grenzbedingungen, Diss., Dieterich, Göttingen, 1906; “Ausgewählte Abhandlungen”, Verzeichnis der wissenschaftlichen Schriften, Bd. 1, Vandenhoeck und Ruprecht, Göttingen, 1963, 5–101
[16] Chen J.-S., Lin Y.-Z., “Snapping of a planar elastica with fixed end slopes”, J. Appl. Mech., 75:4 (2008), Pap. 041024 | DOI
[17] Domokos G., “Global description of elastic bars”, Ztschr. angew. Math. und Mech., 74:4 (1994), T289–T291 | MR | Zbl
[18] Domokos G., Fraser W.B., Szeberényi I., “Symmetry-breaking bifurcations of the uplifted elastic strip”, Physica D, 185:2 (2003), 67–77 | DOI | MR | Zbl
[19] Fried I., “Stability and equilibrium of the straight and curved elastica—finite element computation”, Comput. Methods Appl. Mech. and Eng., 28 (1981), 49–61 | DOI | Zbl
[20] Frisch-Fay R., Flexible bars, Butterworths, London, 1962 | Zbl
[21] Glassmaker N.J., Hui C.Y., “Elastica solution for a nanotube formed by self-adhesion of a folded thin film”, J. Appl. Phys., 96:6 (2004), 3429–3434 | DOI
[22] Greenhill A.G., The applications of elliptic functions, Macmillan, New York, 1892 | Zbl
[23] van der Heijden G.H.M., Neukirch S., Goss V.G.A., Thompson J.M.T., “Instability and self-contact phenomena in the writhing of clamped rods”, Intern. J. Mech. Sci., 45 (2003), 161–196 | DOI | Zbl
[24] Jairazbhoy V.A., Petukhov P., Qu J., “Large deflection of thin plates in cylindrical bending—non-unique solutions”, Intern. J. Solids and Struct., 45 (2008), 3203–3218 | DOI | Zbl
[25] Jin M., Bao Z.B., “Sufficient conditions for stability of Euler elasticas”, Mech. Res. Commun., 35 (2008), 193–200 | DOI | MR | Zbl
[26] Jurdjevic V., Geometric control theory, Cambridge Univ. Press, Cambridge, 1997 | MR | Zbl
[27] Kuznetsov V.V., Levyakov S.V., “Complete solution of the stability problem for elastica of Euler's column”, Intern. J. Non-Lin. Mech., 37 (2002), 1003–1009 | DOI | Zbl
[28] Lardner T.J., “A note on the elastica with large loads”, Intern. J. Solids and Struct., 21 (1985), 21–26 | DOI | MR
[29] Lawden D.F., Elliptic functions and applications, Springer, New York, 1989 | MR | Zbl
[30] Levyakov S.V., “Stability analysis of curvilinear configurations of an inextensible elastic rod with clamped ends”, Mech. Res. Commun., 36 (2009), 612–617 | DOI | Zbl
[31] Levyakov S.V., Kuznetsov V.V., “Stability analysis of planar equilibrium configurations of elastic rods subjected to end loads”, Acta mech., 211 (2010), 73–87 | DOI | Zbl
[32] Maddocks J.H., “Stability of nonlinearly elastic rods”, Arch. Ration. Mech. Anal., 85 (1984), 311–354 | DOI | MR | Zbl
[33] Mikata Y., “Complete solution of elastica for a clamped–hinged beam, and its applications to a carbon nanotube”, Acta mech., 190 (2007), 133–150 | DOI | Zbl
[34] El Naschie M.S., “Thermal initial post buckling of the extensional elastica”, Intern. J. Mech. Sci., 18 (1976), 321–324 | DOI
[35] Panayotounakos D.E., Theocaris P.S., “Analytic solutions for nonlinear differential equations describing the elastica of straight bars: Theory”, J. Franklin Inst., 325:5 (1988), 621–633 | DOI | MR | Zbl
[36] Raboud D.W., Lipsett A.W., Faulkner M.G., Diep J., “Stability evaluation of very flexible cantilever beams”, Intern. J. Non-Lin. Mech., 36 (2001), 1109–1122 | DOI | Zbl
[37] Sachkov Yu.L., “Maxwell strata in the Euler elastic problem”, J. Dyn. and Control Syst., 14:2 (2008), 169–234 | DOI | MR | Zbl
[38] Sachkov Yu.L., “Conjugate points in the Euler elastic problem”, J. Dyn. and Control Syst., 14:3 (2008), 409–439 | DOI | MR | Zbl
[39] Seide P., “Large deflections of a simply supported beam subjected to moment at one end”, J. Appl. Mech., 51 (1984), 519–525 | DOI
[40] Stampouloglou I.H., Theotokoglou E.E., Andriotaki P.N., “Asymptotic solutions to the non-linear cantilever elastica”, Intern. J. Non-Lin. Mech., 40 (2005), 1252–1262 | DOI | MR | Zbl
[41] Tang T., Glassmaker N.J., “On the inextensible elastica model for the collapse of nanotubes”, Math. and Mech. Solids., 15:5 (2010), 591–606 | DOI | Zbl
[42] Wang C.Y., “Post-buckling of a clamped-simply supported elastica”, Intern. J. Non-Lin. Mech., 32 (1997), 1115–1122 | DOI | Zbl
[43] Wolfram S., Mathematica: A system for doing mathematics by computer, Addison-Wesley, Reading (MA), 1991