Abstract :
[en] This talk addresses the simulation of mechanical systems including rigid and flexible bodies, kinematic joints and frictionless contact conditions. The condition of impenetrability of the bodies in contact is expressed as a unilateral constraint, with the consequence that impacts and/or instantaneous changes in the velocities may arise in the dynamic response. Also, the flexibility of the structural components may lead to vibrations phenomena which should also be captured by the simulation algorithm. As an example, the dynamic response of wind turbines is characterized by a coupling between smooth motions and vibrations of large structural components, such as the blades and the tower, and nonsmooth dynamic phenomena in the gearbox and in the transmission line.
The objective of this work is to develop numerical time integration schemes able to deal properly and in an integrated way with impacts and vibration phenomena. More precisely, the proposed method is inspired from the Moreau--Jean time stepping method in nonsmooth contact dynamics. The Moreau--Jean method, which does not adapt its time step on events, is known for its robustness even when the number of contacts is large. However, it is only first-order accurate, which is quite penalizing when structural vibrations need to be described, and it does not guarantee the satisfaction of the unilateral and bilateral constraints at position level.
These observations motivate the development of a new nonsmooth solver, the so-called nonsmooth generalized-alpha method, which relies on a hybrid time discretization of the dynamics. The motion is decomposed into smooth contributions which are discretized using the second-order generalized-alpha method known in structural dynamics and nonsmooth contributions which are discretized using a first-order scheme as in the Moreau--Jean method. I will show that this strategy leads to a better qualitative description of the dynamics and of the energy behaviour of the system. Also, the constraints can be exactly satisfied by the numerical solution both at velocity and position levels. This property results from the development and implementation of a Gear-Gupta-Leimkuhler formulation and a dedicated constraint activation strategy within the solver.
The last part of the talk briefly addresses the modelling of contacts between flexible bodies with complex shapes, as encountered in mechanical transmissions. In order to avoid a blow-up of the CPU time by the use of detailed finite element models, the development of a contact model between superelements is discussed. This means that the elastic deformations are described using a few number of well-selected mode shapes and that the geometry of the skin is implicitly reconstructed from the modal coordinates in order to formulate the contact conditions. Some applications in gear dynamics are shown to illustrate the proposed method.
