Buckling of a slender rod confined in a circular tube: Theory, simulation, and experiment

Abstract

Understanding the buckling behaviors of rods confined in a finite space is of paramount importance in a diversity of engineering fields. In this paper, theoretical analyses, numerical simulations and experimental measurements are combined to investigate the buckling and postbuckling of a long rod confined in a circular tube. Under uniaxial compression, the initially straight rod first buckles into a sinusoidal shape, followed by the occurrence of snap-through instability or helical buckling, which leads to a complicated, three-dimensional configuration consisting of serially connected sinusoids and helices. A new theoretical model is presented to analyze the sinusoidal and helical buckling processes of the confined rod. The complete load–displacement curve of the buckled system during loading and unloading can be well predicted by the present theory. The critical conditions are obtained for the occurrence of the sinusoidal buckling and the sinusoid–helix transitions of buckling modes. It is found, both theoretically and experimentally, that the morphological evolution during unloading exhibits distinctly different features from that during loading due to the peculiar energetic features of snap-through instability. A flexible multibody dynamics method on the basis of the geometrically exact beam theory is employed to numerically explore the buckling behavior of slender rods and to reveal the underlying energetic mechanisms. The theoretical, numerical, and experimental results agree with each other very well. The theoretical model and the numerical method presented in this work are expected to analyze some other problems of confined rods, beams, and their combined systems.