Fully coupled simulation of mechatronic and flexible multibody systems: An extended finite element approach

In this talk, I will discuss some extensions and refinements of classical finite element tools for the numerical simulation of complex mechatronic systems. The presentation will be divided into three main parts.

In the first part, I will show how this approach allows the modeling of dynamic systems with large amplitude motions composed of rigid bodies, flexible bodies, kinematic joints, actuators, sensors and control units. A fully coupled model of a semi-active suspension will be used to illustrate the methodology.

The second part 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 of the coupling between control state variables and mechanical generalized coordinates will be discussed in more detail.

In the third part, the simulation tool will be exploited for the topology optimization of structural components embedded in multibody systems. 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. In order to illustrate the benefits of this integrated design approach, the optimization of a two degrees-of-freedom robot arm with flexible truss linkages will be analyzed.