A direct differentiation method based on forward recursive formulation for flexible multibody system sensitivity analysis

Sensitivity analysis plays a significant role in the dynamic optimization of flexible multibody systems. The forward recursive formulation (FRF) is widely used for the dynamic modeling of multibody systems. However, it has not yet been extended to sensitivity analysis. In this paper, a new direct differentiation method is developed based on FRF for flexible multibody systems sensitivity analysis. The recursive nature of FRF allows for the Jacobian derivatives to be derived recursively, with detailed matrix expressions provided to facilitate implementation in computer code. The validity and correctness of the presented direct sensitivity analysis method based on FRF are verified by numerical examples. Besides, a modified staggered direct scheme is presented to improve the efficiency of the sensitivity analysis. In this scheme, different update strategies are adopted by different components of the tangent stiffness matrix for the implicit integrator, which balances the iteration performance and the additional computational cost. The presented scheme is compared with two conventional schemes through three examples. It demonstrates that the presented scheme can significantly improve the computational efficiency of the sensitivity analysis, particularly for complex problems, when the appropriate update strategies are employed.