Download PDFOpen PDF in browserHigher-Order Interpolation of Cosserat Beam DeformationsEasyChair Preprint 137042 pages•Date: June 19, 2024AbstractA 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: Lie groups, geometrically exact beam theory, interpolation, singularities
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