Post-buckling analysis of two-layer contact concentric tubular strings in pipe

Abstract Buckling of concentric tubular strings in pipe is an essential problem in the fields of medical, biological, and nanomaterials, especially in petroleum engineering. Completely different from the buckling of the classic Euler compression columns, the buckling of concentric tubular strings involves geometric nonlinearity and contact nonlinearity, and has more complicated geometric deformations and buckling configurations. In this paper, a finite element method combining the spatial beam element and the two-layer contact gap element is proposed, and a virtual transient dynamic method is introduced to solve the static buckling of concentric tubular strings. The internal concentric tubular strings are discretized into spatial beam elements, and the contact relationships between tubular strings are described by two-layer contact gap element. Meanwhile, the larger damping is used to attenuate the dynamic response of the system, so as to find the static part of the transient dynamic solution. Appropriate damping and element length are determined by numerical simulation. The structural characteristics and contact states of eight post-buckling configurations are studied. The helix pitch values of specific configurations are in good agreement with the theoretical solutions. In addition, the distribution of bending moment, shear force and contact force in various post-buckling configurations is studied. For the full helical buckling, it is found that there is only one non-contact section in the transition section of inner tube and two non-contact sections in the transition section of middle tube. The research results of this paper provide a theoretical basis and reference for further study on the buckling of multi-layer concentric tubular strings.