Computing smooth solutions of DAEs for elastic multibody systems

Multibody systems are considered which involve combinations of rigid and elastic bodies. Discretizations of the PDEs, describing the elastic members, lead to a semidiscrete system of ODEs or DAEs. Asymptotic methods are introduced which provide a theoretical basis of various known engineering results for the ODE case. These results are then extended to the DAE case by means of suitable local ODE representations. The recently developed MANPAK algorithms for computations on implicitly defined manifolds form the basic tools for a computational method which provides consistent approximate solutions of the semidiscrete DAE that satisfy all constraints and are close to the smooth motion and an average solution. Several numerical examples indicate the effectiveness of this asymptotic method for elastic multibody systems.