Higher-Order Interpolation of Cosserat Beam Deformations

EasyChair Preprint no. 13704

Abstract

A Cosserat beam is a one-dimensional continuum whose deformation field is described by a curve in SE(3). In this paper a cubic and quartic interpolation scheme is presented. The interpolation is respects initial and terminal values of the body-fixed strain measure. These 3rd- and 4th-order interpolation scheme allows exactly reconstructing the displacement of a beam (with constant cross section or cross linearly changing cross sections) subjected to a general wrench applied at the beam. The displacement is represented by means of the exponential on SE(3) in terms of canonical coordinates. The A novel expression for the 3rd- and 4th-order approximation of these canonical coordinates is presented. It is shown that this parameterization is singularity free, and applicable for singularity avoiding handling of slender semi-deformable objects (SDLO), i.e. deformable element including rigid parts as connectors.

Keyphrases: geometrically exact beam theory, interpolation, Lie groups, singularities

@Booklet{EasyChair:13704,
  author = {Andreas Muller and Tobias Marauli and Hubert Gattringer},
  title = {Higher-Order Interpolation of Cosserat Beam Deformations},
  howpublished = {EasyChair Preprint no. 13704},

  year = {EasyChair, 2024}}