Abstract :
[en] The dynamic performance of complex mechanisms, such as machine tools, manipulators, vehicles, engines or foldable structures, can be strongly affected by flexible phenomena. Therefore, the deformation effects should be considered as soon as possible in the design procedure, which motivates the development of automatic optimization techniques for flexible multibody systems. Advanced software tools are able to simulate the dynamic behaviour of such systems, but they typically involve extensive numerical treatments. Hence, gradient-based optimization methods are of special interest since they require a quite low number of simulations, but an important problem is to obtain the sensitivities of the objective function with respect to the design parameters. Since finite difference approaches lack robustness and computational efficiency, we propose to investigate analytical or semi-analytical sensitivity analysis.
Several difficulties are inherent to the simulation of flexible mechanisms. A consistent geometric formulation is necessary to describe large amplitude motion as well as possible large deformations. Here, according to the nonlinear finite element formulation, the motion is parameterized using absolute nodal coordinates, and an updated Lagrangian point of view is adopted for the rotation parameters. The joints and the rigid-body conditions are represented by algebraic constraints between the nodal coordinates, leading to differential algebraic equations of motion (DAEs). Finally, the computation of the trajectories requires a reliable simulation algorithm for nonlinear DAEs.
A strong advantage of the finite element method comes from its very systematic implementation, which facilitates the development of a semi-analytical sensitivity analysis. In this work, sensitivity analysis is performed for beam elements, rigid bodies and ideal joints. The global sensitivity is then obtained by numerical assembly of the elementary contributions and by integration in the time domain. Thus, a single but extended simulation is sufficient to compute the sensitivities with respect to all parameters.
In order to illustrate the method and to demonstrate its efficiency, we consider the optimal design of a car engine, where the flexibility of the connecting rods between the crankshaft and the pistons is taken into account. The objective is to find a feasible mechanical design which minimizes the level of vibrations.
