Dr Rehan Shah has been awarded funding from the Quarterly Journal of Mechanics and Applied Mathematics Fund (QJMAM) administered by the Institute of Mathematics and its Applications (IMA) to attend and present his latest research at the International Council for Industrial and Applied Mathematics (ICIAM) being held in July 2027 at The Hague, Netherlands.

Dr Shah will present research findings through a mini-symposia talk from his latest work focusing on the problem of a rod deforming on a torus, which is soon to be published as a third paper in a series (first two papers: Shah and van der Heijden, 2023 and Shah and van der Heijden, 2024, both in the Journal of Mechanics and Physics of Solids), stemming from his collaboration with Prof Gert van der Heijden from University College London.

The work outlines the development of a comprehensive geometrically-exact theory for an end-loaded elastic rod constrained to deform on rigid tubular surfaces. As applications of the theory, the problem of a rod constrained to lie on a toroidal surface is investigated under the influence of axially applied end loads subject to frictionless and frictional contact, finding critical loads to depend on the friction parameters. This scenario is typically encountered during the tubular buckling of drill strings in curved borewells, in the inspection of curved pipelines by inspection robots navigating elbow joints and in the structural organisation of closed, toroidal DNA condensates in bacteriophages, viruses and sperm chromatin.

The theory is utilised to derive the governing equilibrium equations for the problem, in order to procure solutions to various nonlinear boundary-value problems, using a combination of analytical and numerical approaches. The results obtained include the determination of critical compressive and torsional buckling loads and post- buckled solutions for the the buckling of a rod pushed into a 90-degree bend (quarter torus) of a pipe system and the geometrical twist-bend instabilities observed in liquid crystal toroids under shrinking toroidal radius.