Sinusoidal buckling of a thin rod with connectors constrained in a cylinder

• This paper provides an analytical model for describing the sinusoidal buckling behaviors of a rod with connectors.
• The critical conditions from no contact to point contact, from point contact to wrap contact are obtained.
• The critical conditions from initial vertical plane configuration to sinusoidal configuration are obtained.
• The effects of connectors on deflection curve, bending stress and contact force are analyzed.

Kinds of tubular strings with connectors are widely used in petroleum exploration and development field. In previous research, tubular strings are usually treated as homogeneous thin elastic rods constrained in a cylinder and few studies have been made on the effect of connectors.This paper builds a model to describe the sinusoidal buckling behaviors of a rod with connectors. The three-dimensional buckling problem is divided into two lateral buckling problems in two mutual-perpendicular planes and the buckling solutions are obtained by solving the two lateral buckling equations.There are two buckling states for the rod, including initial plane configuration and sinusoidal configuration. And there are three contact cases between the rod and the cylinder, including no contact, point contact and wrap contact. The critical condition from initial plane configuration to sinusoidal configuration is approximately obtained from the results of no connector rod, and the critical conditions between different contact states are obtained by solving the model numerically. The effects of geometric parameters of the connectors and weight of the rod on critical conditions are analyzed. For the no contact and point contact cases, the deflection curves of a rod in the initial plane configuration and sinusoidal configuration are calculated in this paper. The effects of connectors on bending stress and contact force of the rod are analyzed.The results indicate that buckling states and contact states depend on the combination of the dimensionless axial compression Ku, the ratio of rod/cylinder radial clearance to connector/cylinder radial clearance Kr and the dimensionless weight per unit length of the rod μ. Compared with the no connector case, connectors have a great influence on the deflection curve, bending moment and contact force of the rod. All the results from the model indicate that the effects of connectors cannot be ignored in sinusoidal buckling analyses.