Nonunit quaternion parametrization of a Petrov–Galerkin Cosserat rod finite element

Abstract

AbstractThe 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 minimize the number of required theoretical concepts. The chosen discretization preserves objectivity and allows for large displacements/rotations and for large strains. The orientation parametrization with nonunit quaternions results in a singularity‐free formulation.