Use of independent rotation field in the large displacement analysis of beams

This paper examines the effect of using independent finite rotation field in the large displacement analysis of flexible bodies. This finite rotation description is at the core of the large rotation vector formulation (LRVF), which has been used in the dynamic analysis of bodies experiencing large rotation and deformation. The LRVF employs two independently interpolated meshes for describing the flexible body dynamics: the position mesh and the rotation mesh. The use of these two geometrically independent meshes can lead to coordinate and geometric invariant redundancy that can be the source of fundamental problems in the analysis of large deformations. It is demonstrated in this paper that the two geometry meshes can define different space curves, which can differ by arbitrary rigid-body displacements. The material points of the two meshes occupy different positions in the deformed configuration, and as a consequence, the geometries of the two meshes can differ significantly. The paper also discusses other issues including the inextensibility of the rotation mesh. Simple examples are presented in order to shed light on these fundamental issues.