Sensitivity analysis for dynamic systems with finite rotations

Optimisation methods usually require efficient algorithms to compute the sensitivities of the simulation results with respect to design parameters. Compared to finite difference schemes, the direct differentiation technique that is considered in this talk leads to a significant reduction in the computational cost of the sensitivities.

Our personal contribution is related with the treatment of large rotations, which arise for instance in multibody systems. Several time integrators are developed in order to compute the sensitivities together with the original solution in a single but extended simulation. In particular, three formulations of the generalized-alpha method are discussed and compared for a simple benchmark : a residual form, a linear form, and a geometric form.