Geometrically exact 3D beam element for arbitrary large rigid-elastic deformation analysis of aerospace structures

Abstract

This paper presents a geometrically exact beam theory and a corresponding displacement-based finite-element formulation for modeling and analysis of highly flexible beam components of multibody systems undergoing huge static/dynamic rigid-elastic deformations. This beam theory fully accounts for geometric nonlinearities and initial curvatures of beams by using Jaumann strains, concepts of local displacements and orthogonal virtual rotations, and three Euler angles to exactly describe the coordinate transformation between the undeformed and deformed configurations. To demonstrate the accuracy and capability of this nonlinear beam element, nonlinear static/dynamic analyses of three highly flexible beams are performed, including the free falling of a flexible beam after releasing from a statically twisted and bended configuration, the slewing of a flexible horizontal beam with/without a tip mass, and the spinup of a flexible helicopter rotor blade. These numerical results reveal that the proposed nonlinear beam element is accurate and versatile for modeling and analysis of multibody systems with highly flexible beam components.