Analytical modelling of Kirschner wires in Ilizarov circular external fixator as pretensioned slender beams

摘要

Transfixing thin Kirschner wires(K-wires)are the key components of the Ilizarov fixator regarding its axial stiffness,which affects the mechanobiological environment in which bone is healed.Mechanically speaking,K-wires are slender beams that are axially tensioned,then fixed and transversely loaded.The existing solutions to such a problem either do not accommodate any axial loading prior to transverse loading,or do not account for the change in the axial load(reaction)due to transverse loading.Their applicability is also limited vis-a-vis applied loads and beam dimensions.This work seeks to address those problems by providing a mathematical formulation for a pretensioned slender beam that accounts for the change in the beam tension due to lateral loading.Central loading of a pretensioned beam was studied and new polynomial equations have been derived,the roots of which yield the final tension for a(i)long,slender and heavily loaded beam and(ii)relatively thicker beam subjected to a lower load.Results were produced and discussed for the specific application of pretensioned K-wires in circular(ring)external fixators,in orthopaedics(such as Ilizarov's),which were checked(validated)via two-and three-dimensional finite-element analyses.