THE SPATIAL COMPLEXITY OF LOCALIZED BUCKLING IN RODS WITH NONCIRCULARCROSS-SECTION

We study the postbuckling behavior of long, thin elastic rods subject to end moment and tension. This problem in statics has the well-known Kirchhoff dynamic analogy in rigid body mechanics consisting of a reve rsible three-degrees-of-freedom Hamiltonian system. For rods with nonc ircular cross section, this dynamical system is in general nonintegrab le and in dimensionless form depends on two parameters: a unified load parameter and a geometric parameter measuring the anisotropy of the c ross section. Previous work has given strong evidence of the existence of a countable infinity of localized buckling modes which in the dyna mic analogy correspond to N-pulse homoclinic orbits to the trivial sol ution representing the straight rod. This paper presents a systematic numerical study of a large sample of these buckling modes. The solutio ns are found by applying a recently developed shooting method which ex ploits the reversibility of the system. Subsequent continuation of the homoclinic orbits as parameters are varied then yields load-deflectio n diagrams for rods with varying load and anisotropy. From these resul ts some structure in the multitude of buckling modes can be found, all owing us to present a coherent picture of localized buckling in twiste d rods.