The Spatial Complexity of Localized Buckling in Rods with Noncircular Cross Section

Abstract

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 reversible three-degrees-of-freedom Hamiltonian system. For rods with noncircular cross section, this dynamical system is in general nonintegrable and in dimensionless form depends on two parameters: a unified load parameter and a geometric parameter measuring the anisotropy of the cross section.Previous work has given strong evidence of the existence of a countable infinity of localized buckling modes which in the dynamic analogy correspond to N-pulse homoclinic orbits to the trivial solution representing the straight rod. This paper presents a systematic numerical study of a large sample of these buckling modes. The solutions are found by applying a recently developed shooting method which exploits the reversibility of the system. Subsequent continuation of the homoclinic orbits as parameters are vari...