Flexible multibody dynamics: From finite element formulations to control and optimization

Today, state-of-the-art simulation packages in flexible multibody dynamics allow the high-fidelity analysis of industrial mechanisms and machines with many application fields including robotics, automotive systems, aeronautics, deployable structures or wind turbines. However, some classes of problems still remain difficult to solve, such as control and optimization problems or problems with unilateral contact conditions. These problems motivate the development of innovative finite element (FE) formulations which are under study in our research group.

This talk will present an overview of these activities. I will introduce a local frame FE formulation for flexible multibody systems, which is based on the theory of differential-geometry and Lie groups. I will show that this framework significantly simplifies the development of the finite element library and of the related transient solvers. Then, more advanced solvers will be addressed for various problems such as semi-analytical methods for sensitivity analysis, inverse dynamics solvers for the control of flexible robots and optimization methods for the design of structural components. The application of this formalism in the context of nonsmooth contact dynamics problems would be an interesting perspective of this work.