An Efficient Newton-Type Iteration for the Numerical Solution of Highly Oscillatory Constrained Multibody Dynamic Systems

Abstract

In this paper we present a coordinate-split (CS) technique for the numerical solution of the equations of motion of constrained multibody dynamic systems. We show how the CS technique can be implemented within the context of commonly used solution methods, for increased efficiency and reliability. A particularly challenging problem for multibody dynamics is the numerical solution of highly oscillatory nonlinear mechanical systems. Highly stable implicit integration methods with large stepsizes can be used to damp the oscillation, if it is of small amplitude. However, the standard Newton iteration is known to experience severe convergence difficulties which force a restriction of the stepsize. We introduce a modified coordinate-split (CM) iteration which overcomes these problems. Convergence analysis explains the improved convergence for nonlinear oscillatory systems, and numerical experiments illustrate the effectiveness of the new method.