Dynamic Analysis of Constrained Nonlinear Multibody Systems with Intermittent Contact

This work deals with the dynamic analysis of constrained nonlinear multibody systems undergoing contact between rigid bodies. Contact can occur between two bodies of the system or with an external body. Intermittent contact can be, for example, accidental such as the impact of a member of the system on an unexpected object (obstacle).

The different approaches to model intermittent contact can be classified according to the assumed duration of the contact: (a) the duration of contact is assumed to tend to zero (contact is treated as a discontinuity) and (b) the duration of the impact is finite and the history of the forces acting between the contacting bodies is explicitly computed during the simulation. In this work, the contact event is assumed to be of finite duration.

The unilateral contact condition is expressed in terms of the relative distance q between the bodies with 0 q ≥. The contact condition is enforced through a purely kinematic condition

q

–

r

2

=0, where r is a slack variable used to assure the positiveness of q. This approach is shown to yield a discrete version of the principle of impulse and momentum [

1

].

The use of unconditional stable schemes is relevant in intermittent contact problems whose dynamic response is very complex due to the large and rapidly varying contact forces applied to the system. A scheme based on Time Continuous Galerkin approximations applied to the equations of motion proposed by Lens et al. [

2

] is used in the frame of a variational formulation. The energy preservation argument is used to prove its unconditional stability [

3

]. Kinematic constraints are enforced via the Lagrange multipliers technique.