An Augmented Lagrangian Formulation of the Planar Elastica in Constrained Environments

EasyChair Preprint 13551

Abstract

Flexible endoscopes are medical devices that can be modelled as beams due to their slender geometry and non-linear behaviour. When simulating endoscopic procedures, the contact between the beam model and the surrounding has to be considered in the mathematical model. We present a variational formulation of Euler's elastica described by an augmented Lagrangian with unilateral contact potentials. We show preliminary results for the elastica in contact with walls, whose geometry is of particular interest for our industrial application, and give an outlook on possible future implementations.

Keyphrases: Endoscopes, Euler elastica, Lagrangian mechanics, contact

@booklet{EasyChair:13551,
  author    = {Martina Stavole and Rodrigo T. Sato Martin de Almagro and Giuseppe Capobianco and Olivier Bruls and Sigrid Leyendecker},
  title     = {An Augmented Lagrangian Formulation of the Planar Elastica in Constrained Environments},
  howpublished = {EasyChair Preprint 13551},
  year      = {EasyChair, 2024}}