caa a22 4500 475805348 CHVBK 20180406123745.0 cr unu---uuuuu 170329e20000801xx s 000 0 eng 10.1007/s003320010002 doi (NATIONALLICENCE)springer-10.1007/s003320010002 Euler Buckling in a Potential Field [Elektronische Daten] [P. Holmes, G. Domokos, G. Hek] Summary. : We consider elastic buckling of an inextensible rod with free ends, confined to the plane, and in the presence of distributed body forces derived from a potential. We formulate the geometrically nonlinear (Euler) problem with nonzero preferred curvature, and show that it may be written as a three-degree-of-freedom Hamiltonian system. We focus on the special case of an initially straight rod subject to body forces derived from a quadratic potential uniform in one direction; in this case the system reduces to two degrees of freedom. We find two classes of trivial (straight) solutions and study the primary non-trivial branches bifurcating from one of these classes, as a load parameter, or the rod's length, increases. We show that the primary branches may be followed to large loads (lengths) and that segments derived from primary solutions may be concatenated to create secondary solutions, including closed loops, implying the existence of disconnected branches. At large loads all finite energy solutions approach homoclinic and heteroclinic orbits to the other class of straight states, and we prove the existence of an infinite set of such 'sspatially chaotic' solutions, corresponding to arbitrary concatenations of 'ssimple' homoclinic and heteroclinic orbits. We illustrate our results with numerically computed equilibria and global bifurcation diagrams. Springer-Verlag New York Inc., 2000 Holmes P. Program in Applied and Computational Mathematics and Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA, US aut Domokos G. Department of Strength of Materials, Technical University of Budapest, H-1521 Budapest, Hungary, HU aut Hek G. Mathematisch Instituut, Universiteit Utrecht, P.O. Box 80.010, 3508 TA Utrecht, The Netherlands, NL aut Journal of Nonlinear Science Springer-Verlag 10/4(2000-08-01), 477-505 0938-8974 10:4<477 2000 10 332 https://doi.org/10.1007/s003320010002 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s003320010002 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Holmes P. Program in Applied and Computational Mathematics and Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA, US aut NATIONALLICENCE 700 1- Domokos G. Department of Strength of Materials, Technical University of Budapest, H-1521 Budapest, Hungary, HU aut NATIONALLICENCE 700 1- Hek G. Mathematisch Instituut, Universiteit Utrecht, P.O. Box 80.010, 3508 TA Utrecht, The Netherlands, NL aut NATIONALLICENCE 773 0- Journal of Nonlinear Science Springer-Verlag 10/4(2000-08-01), 477-505 0938-8974 10:4<477 2000 10 332 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer