On the post-buckling analysis of a circular column with cylindrical constraint under concentrated torque loading

With the hypotheses of small deformation and Bernoulli-Euler beam, a gap element is introduced to describe the contact between the circular column and the external cylinder. The dynamic relaxation method is used to calculate the static equilibrium of the twisted column constrained by the cylinder. The post-budding modes of a torsional column in a cylinder are investigated for the deformation configurations of one-point, two-point, three-point, and point-line-point contact. It is found that the end constraint has an effect on the length of the two suspended sections of helical buckling mode, but has no effect on the length of the continuous contact section in the middle. The relations have been derived among critical torque, post-buckling modes, lengths of each section, and loads (including shear, bending moment, and contact force). Finally, the torsional buckling has been investigated for sucker rods and drill pipes with lengths of 1 km. It is found that the helical buckling of multiple pitches occurs. The results of the current study provide theoretical guidance for the design of centralizer spacing in oil and gas engineering applications.