Abstract
This paper shows a semi-analytical approach for the efficient sensitivity analysis of flexible multibody systems for gradient-based design optimization. The developed method is based on the floating frame of reference formulation, where the system matrices and vectors are parameterized by means of inertia shape integrals or invariants that are evaluated prior to the dynamic simulation and enable the decoupling from the finite-element model. The direct differentiation method is applied to the three block solution scheme including governing equations, generalized-α time integration and nonlinear solver. Analogously to the dynamic simulation, the sensitivity analysis is decoupled from the finite-element model by means of the design sensitivities of the invariants. These are evaluated once per design prior to the dynamic simulation and are computed numerically, allowing for a semi-analytical approach with high computational efficiency and generality with respect to the design variables. The method is applied to the design optimization of a Tyrolean weir cleaning mechanism with the lightweight design approach, where the cross-sectional dimensions of the beam elements are designed to minimize the structural mass and limiting the maximum stress in the flexible bodies during the motion of the mechanism.