Parallel computational methods for constrained mechanical systems

Abstract

Two methods suitable for parallel computation in the study of mechanical systems with holonomic and nonholonomic constraints are presented: one is an explicit solution based on generalized inverse algebra; the second solves problems of this class through the direct application of Gauss' principle of least constraint and genetic algorithms. Algorithms for both methods are presented for sequential and parallel implementations. The method using generalized inverses is able to solve problems that involve redundant, degenerate and intermittent constraints, and can identify inconsistent constraint sets. It also allows a single program to perform pure kinematic and dynamic analyses. Its computational cost is among the lowest in comparison with other methods. In addition, constraint violation control methods are investigated to improve integration accuracy and further reduce computational cost. Constrained dynamics problems are also solved using optimization methods by applying Gauss' principle directly. An objective function that incorporates constraints is derived using a symmetric scheme, which is implemented using genetic algorithms in a parallel computing environment. It is shown that this method is capable of solving the same cases of constraints as the former method. Examples and numerical experiments demonstrating the applications of the two methods to constrained multiparticle and multibody systems are presented.