Dr Rehan Shah invited to deliver research seminar at the Mathematical Institute, University of Oxford

9 April 2024

Mathematical Institute, University of Oxford
Mathematical Institute, University of Oxford

Dr Rehan Shah has been specially invited to deliver a research seminar to academic colleagues from the Oxford Centre for Industrial and Applied Mathematics (OCIAM) at his alma mater, the Mathematical Institute at the University of Oxford.

The title of Dr Shah's seminar 'Static friction models, buckling and lift-off for a rod deforming on a cylinder' is based on his recently published papers (Shah and van der Heijden, 2023) and (Shah and van der Heijden, 2024) from the Journal of Mechanics and Physics of Solids (JMPS) from his ongoing work in this area conducted in collaboration with Prof Gert van der Heijden from UCL.

The talk will outline the development of a comprehensive geometrically-exact theory for an end-loaded elastic rod constrained to deform on a cylindrical surface. By viewing the rod-cylinder system as a special case of an elastic braid, the theory allows determination of all forces and moments imparted by the deforming rod to the cylinder as well as all contact reactions. The framework also provides a complete treatment of static friction consistent with force and moment balance and also accounts for a cylinder with an arbitrary orientation to account for the effects of gravity.

Applications of the theory include buckling of the constrained rod under compressive and torsional loads, finding critical loads that depend on Coulomb-like friction parameters and investigating the the tendency of a rod to lift off the cylinder under further loading due to friction and/or gravity. The results are relevant for many engineering and medical applications in which a slender structure winds inside or outside a cylindrical boundary.

The event will certainly be a trip down memory lane for Dr Shah, who was once a student in the same department at Oxford, and will now be delivering a research seminar to academic colleagues whom he was once himself taught by.

Contact:Rehan Shah
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