Efficient calculation of the inertia terms in floating frame of reference formulations for flexible multibody dynamics

Abstract

One of the characteristics of floating frame of reference (FFR) formulations for flexible multibody dynamics is the fact that the inertia terms are highly non-linear. At every time-step, both the mass matrix and the velocity-dependent forces vector must be updated, and this can become the most CPU intensive task. This work studies the efficiency of two different methods for performing this operation, when applied to both a formulation in absolute coordinates and another in relative coordinates. The first method calculates the inertia terms by projecting the finite element (FE) mass matrix into the generalized coordinates, by means of a variable projection matrix. The second one calculates the inertia shape integrals at a preprocessing stage and uses them for obtaining the inertia terms in a more efficient way, at the cost of a more involved implementation. Both methods have been tested when used in combination with either the FFR absolute or relative formulation, by simulating a vehicle with 12 flexible elements. The results show that the performance can be considerably increased by means of the preprocessing method, especially in the case of large FE models, whereas, for small models, the projection method can be more convenient due to its simplicity.