From direct to inverse analysis in flexible multibody dynamics

Today, state-of-the-art simulation packages in flexible multibody dynamics allow the high-fidelity analysis of industrial mechanisms and machines in many application fields including robotics, automotive systems, aeronautics, deployable structures or wind turbines. The dynamic response of a given system can thus be evaluated in the time-domain for given load cases and given initial values. However, in many practical cases, the engineer does not have a precise knowledge of the mechanical design, the loading conditions and the initial state. This situation occurs for example in structural optimization, optimal control, experimental identification and health monitoring problems. The complexity of simulation codes and the computational cost of high-fidelity models are still important obstacles for the development of efficient resolution methods for these inverse problems. A current challenge is thus to elaborate simplified and more efficient modelling strategies in flexible multibody dynamics in order to enable the development of inverse analysis methods.
The talk is divided into three parts. The first part provides an overview of available simulation techniques for flexible mechanisms with a particular emphasis on finite element-based approaches and time integration methods. Some illustrations are presented in the fields of deployable structures, vehicle dynamics and wind turbines. In the second part, optimization problems in flexible multibody dynamics are addressed and solved using gradient-based methods. Efficient methods for sensitivity analysis are discussed and special problems are treated such as the structural optimization of mechanical components or the numerical solution of inverse dynamics problems. The third part discusses a recently-developed Lie group approach which allows the formulation of the equations of motion of a multibody system in a parameterization-free setting. Based on this general formalism, which is characterized by an increased modularity and a reduced complexity, a large variety of Lie group solvers are foreseen not only for time integration but also for model reduction, sensitivity analysis and optimization.