Mass matrix modeling approaches with flexible multibody dynamics: Consequences of consistent and lumped approaches for simulation, sensitivity analysis and design optimization

This paper demonstrates how the lumped mass approach enables the decoupling of dynamic simulation and sensitivity analysis of flexible multibody dynamics from the finite-element model. This decoupling facilitates efficient design optimization of flexible multibody systems using a general finite-element solver and a general element type, eliminating the need for access to the formulation of the element shape functions. The decoupling of the dynamic simulation with the floating frame of reference formulation is achieved as the lumped mass approach calculates the multibody invariants needed to evaluate nonlinear system parameters by summation operations, while the consistent mass approach evaluates inertia shape integrals by the use of element shape functions. The same decoupling is achieved for the sensitivity analysis through the analytical derivatives of the nonlinear system parameters and the use of the multibody invariant sensitivities evaluated prior to the time integration. The implications of employing a lumped mass approach, particularly in terms of the number of elements, body properties, dynamic and sensitivity responses and numerical design optimization, are evaluated in comparison to the consistent mass approach.