A logarithmic complexity divide-and-conquer algorithm for multi-flexible-body dynamics including large deformations

A new algorithm is presented for the modeling and simulation of multi-flexible-body systems. This algorithm is built upon a divide-and-conquer-based multibody dynamics framework, and it is capable of handling arbitrary large rotations and deformations in articulated flexible bodies. As such, this work extends the current capabilities of the flexible divide-and-conquer algorithm (Mukherjee and Anderson in Comput. Nonlinear Dyn. 2(1):10-21, 2007), which is limited to the use of assumed modes in a floating frame of reference configuration. The present algorithm utilizes the existing finite element modeling techniques to construct the equations of motion at the element level, as well as at the body level. It is demonstrated that these equations can be assembled and solved using a divide-and-conquer type methodology. In this respect, the new algorithm is applied using the absolute nodal coordinate formulation (ANCF) (Shabana, 1996). The ANCF is selected because of its straightforward implementation and effectiveness in modeling large deformations. It is demonstrated that the present algorithm provides an efficient and robust method for modeling multi-flexible-body systems that employ highly deformable bodies. The new algorithm is tested using three example systems employing deformable bodies in two and three spatial dimensions. The current examples are limited to the ANCF line or cable elements, but the approach may be extended to higher order elements. In its basic form, the divide-and-conquer algorithm is time and processor optimal, yielding logarithmic complexity O(log(N (b) )) when implemented using O(N (b) ) processors, where N (b) is the number of bodies in the system.