Generalized Finite Element Approach to Dynamics Modeling of Rigid and Flexible Systems#

Abstract

This paper proposes a general algorithm for computer code generation of dynamic equations of rigid and flexible multibody systems. It is shown that the approach used in classical finite element theory to derive node inertia forces of flexible elements is not precise. Generalized Newton–Euler equations are applied for computation of the inertia terms in the dynamic equations. The equations discussed here are invariant to the coordinates and, as for the classical Newton–Euler equations, are derived with respect to the linear and angular velocities and accelerations of the rigid bodies and flexible nodes. This method enables both absolute and relative nodal coordinates to be used. The advantages of the algorithm are demonstrated modeling vibration and large deflections, as well as deployment bifurcation of an extremely flexible tethered system with two branches. The simulation process is stable during the long operating time and could be applied for predicting and design of stable periodic motion.