A uniform discretization approach to flexible multibody systems

AbstractThe present contribution deals with a unified approach to the discretization of flexible multibody systems. We present a rotationless description of rigid body motions, augmented by the incorporation of additional rotational coordinates, as presented in [1,2]. Accordingly, the motion of rigid bodies is governed by differential–algebraic equations (DAEs) which are amenable to the design of energy–momentum conserving integration schemes. The comparatively large number of unknowns due to the presence of redundant coordinates and Lagrange multipliers can be reduced by applying specific reduction techniques, such as the discrete null space method [3].In nonlinear elastodynamics, conserving schemes have been under investigation for several years. Recent works [4,5] turn out to be especially well suited for accurate and robust long term simulations. The underlying finite element discretization in space makes possible the use of arbitrary constitutive laws.In essence, the present approach leads to a uniform algorithmic treatment of translations and rotations which turns out to be especially beneficial to the simulation of multibody systems. Moreover, the underlying DAE structure of the discrete equations of motion facilitates the straightforward connection of flexible and rigid components belonging to a specific multibody system. In addition to that, the design of conserving schemes can be accomplished easily. Representative numerical examples will demonstrate the advantageous behavior of the proposed uniform discretization approach to flexible multibody systems. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)