Analytical sensitivity analysis of dynamic problems with direct differentiation of generalized-α time integration

Abstract

Generalized-α time integration is a generalization of several time integration schemes that can be use in the analysis of dynamic systems. Sensitivity analysis is used in numerical methods of design optimization, uncertainty analysis, parameter fitting and for simply calculating the sensitivities of a design to certain parameters. Analytical sensitivity analysis reduces the computational effort compared with numerical analysis and is therefore essential in efficient gradient-based design optimization. In this study, the sensitivity equations of the generalized-α time integration via direct differentiation are introduced. These are then compared with numerical sensitivities via forward differencing and Newmark-β in terms of accuracy and performance. An example is shown for both linear structural dynamics and flexible multibody dynamics.