Abstract
This paper introduces analytical sensitivity analysis of flexible multibody dynamics with Baumgarte stabilization. Flexible multibody dynamics is formulated with the floating frame of reference formulation as an index-1 differential algebraic equation. Baumgarte stabilization is utilized to counteract numerical drift of the kinematic constraints associated with the index-1 formulation. As such, it alleviates the related errors in both the system responses and their design sensitivities of the formulated optimization problem. Without stabilization, these errors lead to problems further exacerbated when using gradient-based optimization algorithms. Direct differentiation is utilized for the sensitivity analysis of flexible multibody dynamics through governing equation, time integration and nonlinear solver. After a review of kinematic constraint stabilization methods and specifically Baumgarte stabilization with attention to sensitivity, the developed method is numerically validated with a demonstration example. The slider–crank mechanism is modeled with flexible multibody dynamics and three-dimensional beam elements. Further parameter studies examine the influence of the values of the Baumgarte stabilization constants on primal analysis and sensitivity analysis. Attention is paid to the effects of drift and constraint stabilization on different types of system responses. The consequences on design optimization of flexible multibody systems and related problem formulations are discussed.