On the use of the rotation parameters in the large displacement analysis of beams

This paper discusses the use of the finite rotation coordinates in the large displacement analysis of flexible bodies. These rotation coordinates are at the core of the large rotation vector formulation (LRVF), which has been used to simulate the dynamics of bodies experiencing large rotation and deformation. The LRVF uses two independently interpolated meshes for describing the flexible body dynamics: the position mesh and the rotation mesh. The use of these to geometrically independent meshes can lead to coordinate and invariant redundancy. The two independent definitions for the geometry can pose serious problems in the analysis of large deformation since most multibody system (MBS) formulations are based on the assumption that the nodes share the same material location (total Lagrangian approach). This paper aims to demonstrate that the two geometry meshes can define different space curves, which can differ by arbitrary rigid body displacements. Simple examples are also shown in order to shed light on this fundamental issue.