Post-Buckling Analysis of a Rod Confined in a Cylindrical Tube

Abstract

Understanding the buckling and post-buckling behavior of rods confined in a finite space is of both scientific and engineering significance. Under uniaxial compression, an initially straight and slender rod confined in a tube may buckle into a sinusoidal shape and subsequently evolve into a complicated, three-dimensional (3D) helical shape. In this paper, we combine theoretical and numerical methods to investigate the post-buckling behavior of confined rods. Two theoretical models, which are based on the inextensible and extensible rod theories, respectively, are proposed to derive the analytical expressions for the axial compressive stiffness in the sinusoidal post-buckling stage. The former is concise in formulation and can be easily applied in engineering, while the latter works well in a broader scope of post-buckling analysis. Both methods can give a good approximation to the sinusoidal post-buckling stiffness and the former model is proved to be a zeroth-order approximation of the latter. The flexible multibody dynamics method based on the Timoshenko's geometrically exact beam theory is used to examine the accuracy of the two models. The methods presented in this work can be used in, for example, drilling engineering in oil and gas industries.