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

Abstract

In this paper, the direct differentiation of generalized-α time integration is derived, equations are introduced and results are shown. Although generalized-α time integration has found usage, the derivation and the resulting equations for the analytical sensitivity analysis via direct differentiation are missing. Thus here, the sensitivity equations of generalized-α time integration via direct differentiation are provided. Results with generalized-α are compared with Newmark-β and their sensitivities with numerical sensitivities via forward finite differencing in terms of accuracy and performance. An example is shown for each linear structural dynamics and flexible multibody dynamics.