A collaboration led by Dr Rehan Shah in conjunction with UCL academic Prof Gert van der Heijden has resulted in a publication in the reputed Journal of the Mechanics and Physics of Solids (JMPS) and is available as an open access paper on https://doi.org/10.1016/j.jmps.2023.105464

In this paper, a comprehensive, geometrically-exact theory for an end-loaded heavy rod constrained to deform on a cylindrical surface is developed. The cylinder can have arbitrary orientation relative to the direction of gravity. By viewing the rod-cylinder system as a special case of an elastic braid, all forces and moments imparted by the deforming rod to the cylinder as well as all contact reactions are able to be obtained. This framework allows for the monitoring of stresses to ascertain whether the cylinder, along with its end supports, is able to sustain the rod deformations.

As an application of the theory, buckling of the constrained rod under compressive and torsional loads, as well as the tendency of the rod to lift off the cylinder under further loading is studied. The cases of a horizontal and vertical cylinder, with gravity having only a lateral or axial component, are amenable to exact analysis, while numerical results map out the transition in buckling mechanism between the two extremes. Weight has a stabilising effect for near-horizontal cylinders, while for near-vertical cylinders it introduces the possibility of buckling purely due to self-weight. The results are relevant for many engineering and medical applications in which a slender structure is inserted into a cylindrical cavity.

Updated by: Rehan Shah