An efficient, floating-frame-of-reference-based recursive formulation to model planar flexible multibody applications

This paper describes a floating-frame-of-reference-based (FFRF-based) recursive formulation for flexible bodies. A new definition of the joint coordinate system is introduced that makes it simpler to formulate more concise velocity transformation matrices. A path matrix, which defines the connectivity of the mechanism for the open loop system, simplifies introducing the topology of the rigid and/or flexible spanning tree. The flexible multibody system is often subjected to large reference motion but small deformations. Both Euler-Bernoulli-based beam (EBB) and continuum-mechanics-based beam (CMB) elements are implemented to validate the proposed approach. The reference conditions mentioned here are used to eliminate the rigid body motion from the deformation field, i.e., removal of the coordinate redundancy, in the FFRF. Thus, different reference conditions, such as simply supported, single-cantilever, and double-cantilever are used. Finally, it is demonstrated that the proposed approach is not limited by the choice of reference conditions, which helps the modeler to apply the approach to different multibody applications.In the numerical analysis, the results of the total energy variation and constraint violations of the close loop systems are fulfilled with good accuracy by using both penalty formulation with augmented Lagrangian method and coordinate partitioning approach for constraint stabi-lization. Furthermore, the proposed semi-recursive method produces dynamic analysis results comparable to the ANCF with better computational efficiency. In the end, compared to fully recursive approach, the proposed semi-recursive approach shows better efficiency and easier implementation.