Abstract
In this dissertation, the analytical sensitivities of flexible multibody dynamics are novelly developed for use in efficient gradient-based design optimization. The governing equations with the floating frame of reference formulation are directly differentiated in terms of the invariants and their sensitivities to be independent of the finite-element solver as well as general with respect to finite-element type and for a wide range of design variables. Design optimization is a powerful tool to optimally design mechanical systems and launch the virtuous circle of lightweight design, in which reduced loads allow for use of smaller drives and propulsion, leading to savings in energy consumption and costs that can be reinvested into new materials and technologies to further reduce the mass and resuming the circle. This is especially the case for dynamically loaded systems in which self-mass directly affects the mechanical response. Mechanical systems consisting of rigid and deformable bodies being connected by kinematic joints are accurately analyzed with flexible multibody dynamics. In commercial multibody software, the dynamic simulations are typically performed decoupled from the finite-element solver after importing the finite-element model. The floating frame of reference formulation allows the dynamic simulation to be decoupled from the finite-element model by inertia shape integrals, referred as invariants. This standard framework is extended with analytical design sensitivities by the developed methodology where the dynamic simulation including sensitivity analysis is decoupled from the finite-element solver and requires only the finite-element model, invariants and their sensitivities. The time integration is novelly differentiated with respect to the design variables for the generalized-α family of integrators including Baumgarte stabilization to suppress drift associated with the utilized formulation of index-1 differential-algebraic equations. The developed methodology is shown with three examples: a slider crank mechanism, a morphing wing leading edge and a Tyrolean weir cleaning mechanism. Numerical investigations include a comparison of time integration methods in terms of numerical aspects. Design variables for multibody problems are categorized and then examined in regards to their impact on numerical and semi-analytical approaches. Finally, design optimization of flexible multibody systems is carried out with the lightweight design formulation.