Consistent Treatment of Link and Writhe for Open Rods, and their Relation to End Rotation. Modelling, and Analysis and Simulation (MAS)

摘要

We combine and extend the work of Alexander & Antman (3) and Fuller (11, 12) to give a framework within which precise definitions can be given of topological and geometrical quantities characterizing the contortion of open rods undergoing large deformations under end loading. We use these definitions to examine the extension of known results for closed rods to open rods. In particular, we formulate the analogue of the celebrated formula Lk=tw+wr (link equals twist plus writhe) for open rods and proposed an end rotation, throught which the applied end moment does work, in the form of an integral over the lenght of the rod. The results serve to promote the variational analysis of boundary-value problems for rods undergoing large deformations.