A Logarithmic Complexity Divide-and-Conquer Algorithm for Multi-flexible Articulated Body Dynamics

This paper presents an efficient algorithm for the dynamics simulation and analysis of multi-flexible-body systems. This algorithm formulates and solves the nonlinear equations of motion for mechanical systems with interconnected flexible bodies subject to the limitations of modal superposition, and body substructuring, with arbitrarily large rotations and translations. The large rotations or translations are modelled as rigid body degrees of freedom associated with the interconnecting kinematic joint degrees of freedom. The elastic deformation of the component bodies is modelled through the use of modal coordinates and associated admissible shape functions. Apart from the approximation associated with the elastic deformations, this algorithm is exact, non-iterative, and applicable to generalized multi-flexible chain and tree topologies. In its basic form, the algorithm is both time and processor optimal in its treatment of the $nb$ joint variables, providing $O(log(nb))$ turnaround time per temporal integration step, achieved with $O(nb)$ processors. The actual cost associated with the parallel treatment of the $nf$ flexible degrees of freedom depends on the specific parallel method chosen for dealing with the individual coefficient matrices which are associated locally with each flexible body.