Concurrent simulation and constraint stabilization for flexible multibody systems

Abstract

This dissertation presents a family of computationally efficient methods for the simulation of large, flexible multibody systems. Non-recursive order N formulations for the transient dynamic analysis of multibody systems can be achieved using range space methods. Unlike the recursive methods, this formulation does not rely on system topology to induce parallelism. These methods induce concurrency via the method of subdomain decomposition, and it is shown that they are amenable to implementation on the forthcoming class of highly parallel architectures. This class of formulations can be distinguished from other variants of sub-domain decomposition in that redundant degrees of freedom are retained, and the coupling of substructures is achieved by explicitly calculating the coupling forces in an order N computational cost. A preconditioned conjugate gradient method is used for the range space solution, with a preconditioner motivated by the directed graph of multibody systems with no closed chains. The method is shown to be rapidly convergent for linear and nonlinear structural systems with a large number of degrees of freedom. One potential drawback of the range space formulation is the well known constraint violation drift associated with redundant formulations of transient multibody dynamics. This dissertation introduces a family of concurrent constraint violation stabilization algorithms that retain the order N computational cost of the range space formulation, while ensuring simulation fidelity. The hybrid methods introduced are based upon penalty multibody formulations and augmented Lagrangian formulations. Explicit bounds on measures of the constraint violation are presented. It is shown that, in the augmented Lagrangian method, the number of fixed iterations per time step dictate the diameters of the attractors of constraint violations in phase space. Several numerical examples of simulation and control are presented including simulations of the Space Station Freedom, the NASA Langley Control Structure Interaction Evolutionary model and nonlinear, multi-rigid bodies articulating in space.