Abstract
This paper introduces Baumgarte stabilization and generalized-α time integration to the sensitivity analysis of flexible multibody dynamics. This is done to counteract numerical drift and numerical noise in the system responses and the design sensitivities, which can lead to problems when used in concert with gradient-based optimization algorithms. Therefore, analytical direct differentiation is applied to the steps of the primal analysis: governing equation, time integration and nonlinear solver. The method is numerically validated with a slider–crank mechanism modeled with flexible multibody dynamics and three-dimensional beam elements. A parameter study is carried out by varying the values of the generalized-α integration constants and the Baumgarte stabilization constants. The results are compared and the effects on numerical drift and numerical noise are shown for both the primal analysis and the sensitivity analysis. With an appropriate choice of the examined parameters, the system responses and design sensitivities take an appropriate form for processing with gradient-based optimization algorithms.