Buckling and lift-off of a heavy rod compressed into a
cylinder
R. Shah & G.H.M. van der Heijden
We develop a comprehensive, geometrically-exact theory for an end-loaded
heavy rod constrained to deform on a cylindrical surface. 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, we are able
to obtain all forces and moments imparted by the deforming rod to the
cylinder as well as all contact reactions. 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 we study 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. 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. Our results are
relevant for many engineering and medical applications in which a slender
structure is inserted into a cylindrical cavity.
keywords: elastic rod, surface constraint, contact pressure, gravity,
buckling, mode-switching, lift-off
J. Mech. Phys. Solids 182, 105464 (2024)