This talk addresses some recent extensions of the finite element approach for the analysis, design and control of flexible mechanisms. A particular attention is devoted to modular simulation concepts, advanced time integration methods, efficient sensitivity analysis and topology optimization problems. Practical applications of those techniques can be found in various fields of engineering, e.g. in automotive engineering (vehicle suspensions, powertrains), aerospace engineering (landing gears, flaps, deployable space structures), robotics, machine tools, biomechanics or biomedical instruments. Firstly, an integrated simulation approach will be presented for articulated systems composed of rigid bodies, flexible bodies, kinematic joints, actuators, sensors and control units. I will focus on some numerical aspects concerning the time integration of the equations of motion which have the structure of strongly coupled differential-algebraic equations on a Lie group. The treatment of large rotation variables and the coupling between control state variables and mechanical generalized coordinates will be discussed in more detail. Secondly, based on this simulation tool, a particular class of optimization problems in multibody dynamics will be considered, i.e. the topology optimization of structural components. Generally, topology optimization techniques use simplified quasi-static load cases to mimic the complex dynamic loadings in service. In contrast, I will present an optimization procedure which properly accounts for the actual dynamic interactions which occur during the motion of the flexible multibody system. The method relies on an efficient sensitivity analysis based on a semi-analytical direct differentiation approach. In order to illustrate the benefits of the proposed design approach, the optimization of a two degrees-of-freedom robot arm with flexible truss linkages will be analyzed. Finally, I will discuss some perspectives for the integrated control-structure optimization of multibody systems.
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