Reference : Simultaneous enforcement of constraints at position and velocity levels in the nonsmo...
Scientific journals : Article
Engineering, computing & technology : Mechanical engineering
http://hdl.handle.net/2268/171024
Simultaneous enforcement of constraints at position and velocity levels in the nonsmooth generalized-alpha scheme
English
Bruls, Olivier mailto [Université de Liège - ULiège > Département d'aérospatiale et mécanique > Laboratoire des Systèmes Multicorps et Mécatroniques >]
Acary, Vincent []
Cardona, Alberto []
2014
Computer Methods in Applied Mechanics & Engineering
Elsevier Science
281
131-161
Yes (verified by ORBi)
International
0045-7825
Lausanne
Switzerland
[en] nonsmooth contact dynamics ; flexible multibody system ; time integration ; generalized-alpha method ; time-stepping scheme ; index reduction
[en] This paper presents a formalism for the transient simulation of nonsmooth dynamic mechanical systems composed of rigid and flexible bodies, kinematic joints and frictionless contact conditions. The proposed algorithm guarantees the exact satisfaction of the bilateral and unilateral constraints both at position and velocity levels. Thus, it significantly differs from penalty techniques since no penetration is allowed. The numerical scheme is obtained in two main steps. Firstly, a splitting method is used to isolate the contributions of impacts, which shall be integrated with only first-order accuracy, from smooth contributions which can be integrated using a higher order scheme. Secondly, following the idea of Gear, Gupta and Leimkuhler, the equations of motion are reformulated so that the bilateral and unilateral constraints appear both at position and velocity levels. After time discretization, the equations of motion involve two complementarity conditions and it can be solved at each time step using a monolithic semi-smooth Newton method. The numerical behaviour of the proposed method is studied and compared to other approaches for a number of numerical examples. It is shown that the formulation offers a unified and valid approach for the description of contact conditions between rigid bodies as well as between flexible bodies.
Researchers ; Professionals ; Students
http://hdl.handle.net/2268/171024
10.1016/j.cma.2014.07.025

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