A Multibody Formulation for Three Dimensional Brick Finite Element Based Parallel and Scalable Rotor Dynamic Analysis

This paper presents a unified formulation for a 3-dimensional finite element based non-linear multibody analysis for helicopter rotors. Special multibody brick elements are developed which can be used to embed arbitrary joint rotations within a 3-dimensional structure. A multi-level iterative substructuring algorithm, that is parallel and scalable, is redesigned to accommodate multibody components in a manner that maintains its underlying numerical scalability. The brick multibody formulation is then used to study the impact of non-linear 3-dimensional hub end effects in rotors that are not modeled by current generation beam based models. The constraints that arise from a physical 3-D connection of a rotor blade to a joint are shown to alter the internal stresses at its hub end and impact torsion dynamics significantly - a physics that is uniquely rotary wing in nature. Large scale structural models are then constructed for a hingeless, an articulated, and a bearingless rotor, consisting of multiple flexible components and multibody connections near the hub end, and containing up to 0.48 million degrees of freedom. The models are analyzed for scalability and timing for hover and forward flight solutions on up to 128 processors. The key conclusion is that multibody components can indeed be incorporated within a fully parallel multi-level iterative substructuring algorithm without impacting its numerical scalability. And, integrated carefully within 3-dimensional brick elements, they open new opportunities for capturing fundamental physics of 3-dimensional stress fields on rotary wing structures.