A Hybrid Parallelizable Algorithm for Computer Simulation of the Motion Behaviors of a Branched Multibody System

Abstract

This paper presents a hybrid parallelizable algorithm for the computer-aided modeling of the dynamic behavior of multibody open tree systems. The method is based on cutting certain system interbody joints at branched bodies so that a system of largely independent multibody subchains is formed. These subchains interact with one another through associated unknown constraint forces fc at the cut joints. The increased parallelism is obtainable through cutting joints and the explicit determination of associated constraint forces combined with a sequential O(n) procedure. Consequently, the sequential O(n) procedure is carried out within each subchain to form and solve the equations of motion, while parallel strategies are performed between the subchains to form and solve constraint equations concurrently. Two extreme cutting procedures are further discussed to conduct a comparison of computational efficiency. One case is to cut the joints at branched bodies so that the longest lengths of subchains are obtained and the other is to cut the joints at branched bodies so that the shortest lengths of subchains are formed. The algorithm can easily accommodate the available number of processors while maintaining high efficiency. The algorithm will also be implemented on both parallel homogeneous computing (PHC) systems and network-distributed heterogeneous computing (DHC) environment. The implementation of the algorithm in a DHC environment will permit engineers and researchers to conduct distributed simulation of dynamic behaviors of large and complex multibody systems on ubiquitous network-distributed PC workstations in their workplace. In short, the exploration of the parallelizable algorithm for a multibody tree system will provide a deep understanding of the relationship between computational load balancing and optimal joint locations to be cut. The computational efficiency of the algorithm can be increased further.