Use of Lumped Mass Formulation in the Design Sensitivity Analysis of Flexible Multibody Dynamics

The lumped mass approach is shown in this paper to enable a decoupling of the dynamic simulation and sensitivity analysis of flexible multibody systems from the finite-element model. The lumped and consistent mass approaches are compared within a modeling framework utilizing the floating frame of reference formulation. The invariants required for nonlinear system parameters are obtained by summation operations with the lumped mass approach, allowing for a decoupling from the finite-element formulation. This is in contrast to the consistent mass approach, where inertia shape integrals are evaluated based on the element shape functions. The derivatives of the system parameters and the sensitivities of the invariants enable the same decoupling for the sensitivity analysis. Further consequences of using a lumped mass approach regarding number of elements, dynamic and sensitivity responses and computation time is compared with a consistent mass approach.