Investigation On The Buckling Problem Of Thin And Long Bars With Connectors In A Circular Cylinder

The stability of drill-strings is important in the advances of drilling technologies in the oilindustry. Almost every drill-string was modeled as a uniform beam with the same diameter in pastresearches. But drill-string in a real well is composed by many drill pipes connected by connectors.Therefore, the research on the buckling behavior of a slender rod with connectors constrained by acircular cylinder is more applicable in drill engineering. Available researches on the bucklingbehavior of constrained thin rods with connectors subjected to axial compression and gravitationalloads are rare and all based on the assumption of that the connectors are fully contact with theouter cylinder and drill-string is hanged in the air. Governing differential equations are derived onEuler-Bernoulli beam model which causes that no external force supports the self-weightcomponent of the hanging drill-string. Through actual computation, it is found that the shortconnectors are not fully contact with the outer cylinder. The connector contacts only with the outercylinder at its two endpoints and all rest part has an upward displacement. Though thedisplacement is very small and negligible, however, it proves that the reaction force exerted by theout cylinder is concentrated at two endpoints of the connector. Based on this observation, thisarticle assumes that the connector is only contact with the outer cylinder at its two endpoints. Inother words, except the two endpoints of each connector connecting with the drill-string, the restpart of the entire strings is all hanging in the air. The governing differential equations are derivedby using the method of sections in Mechanics of Materials. Four simple models are given.Differential quadrature element method (DQEM) is utilized to solve the established differentialequations. Detailed formulations and solution procedures are given and several examples areanalyzed. Finally conclusion is made based on the results reported herein and some future researchtopics are given.