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

Kinds of tubular string are widely used in oil exploration and development. These tubular strings are usually approximately seen as homogeneous thin elastic rods without connectors constrained in a straight cylinder or torus. Recent research has shown that connectors play an important role on rod deflection problem. On the basis of the preceding studies, this paper provides an analytical model to describe the sinusoidal buckling behaviors of a rod with connectors constrained in a torus. The new model is solved by using the classical beam-column model. The relationship rod and torus is divided into three cases: no contact, point contact and wrap contact, and the rod buckling state is divided into initial plane configuration, sinusoidal buckling and helical buckling. The deflections of the rod in the initial plane and sinusoidal buckling configurations and critical conditions from initial plane configuration to sinusoidal buckling configuration and from no contact to point contact are studied. These results show that the deflections and critical conditions are closely related to the torus curvature radius, rod buckling state and rod weight. The effect of torus curvature radius, rod buckling, rod weight and connectors on bending moment is also analyzed at last.