Non-unit quaternion parametrization of a Petrov-Galerkin Cosserat rod finite element
Numerical Analysis
2023-07-11 v1 Numerical Analysis
Mathematical Physics
math.MP
Abstract
The application of the Petrov-Galerkin projection method in Cosserat rod finite element formulations offers significant advantages in simplifying the expressions within the discrete virtual work functionals. Moreover, it enables a straight-forward and systematic exchange of the ansatz functions, specifically for centerline positions and cross-section orientations. In this concise communication, we present a total Lagrangian finite element formulation for Cosserat rods that attempts to come up with the least required concepts. The chosen discretization preserves objectivity and allows for large displacements/rotations and for large strains. The orientation parametrization with non-unit quaternions results in a singularity-free formulation.
Keywords
Cite
@article{arxiv.2307.04554,
title = {Non-unit quaternion parametrization of a Petrov-Galerkin Cosserat rod finite element},
author = {Jonas Harsch and Simon R. Eugster},
journal= {arXiv preprint arXiv:2307.04554},
year = {2023}
}