Preconditioning strategies for linear dependent generalized component modes in 3D flexible multibody dynamics

Abstract

The trend away from physical towards virtual prototyping as well as increasing industrial demands require advanced simulation tools for dynamical systems. Virtually all engineering systems are assemblies and are associated with stresses, noise and vibrations; therefore, flexible multibody simulations are inevitable for accurate predictions. However, real-world finite element models contain millions of degrees of freedom that cannot be reasonably handled without model reduction techniques. Generalized component mode synthesis is a promising tool for flexible 3D multibody systems, since the generalized component modes not only represent the deformation modes in any possible orientation, but also rigid body motion, which preserves a linear configuration space, yielding a constant mass matrix, a co-rotated but constant stiffness matrix, no quadratic velocity vector and a simple structure of the equations of motion. In this novel framework, the displacement is approximated by a linear combination of generalized component modes generated from vibration eigenmodes, undeformed nodal coordinates and the Cartesian base vectors. The emerging system matrices may be ill-conditioned and may introduce significant numerical errors, because of linearly dependent generalized component modes and due to different orders of magnitude of their Euclidean norm. However, this issue has not received much attention in the open literature despite its importance. Hence, the current contribution sheds light on this problem and derives preprocessing procedures to convert ill-conditioned into well-conditioned problems, which shall improve the formulation’s applicability. The new findings are illustrated by numerical experiments of simple bodies and a crankshaft.