A self-stabilized algorithm for enforcing constraints in multibody systems

A new algorithm is developed for the enforcement of constraints within the framework of nonlinear, flexible multibody system modeled with the finite element approach. The proposed algorithm exactly satisfies the constraints at the displacement and velocity levels, and furthermore, it achieves nonlinear unconditional stability by imposing the vanishing of the work done by the constraint forces when combined with specific discretizations of the inertial and elastic forces. Identical convergence rates are observed for the displacements, velocities, and Lagrange multipliers. The proposed algorithm is closely related to the stabilized index-2 or GGL method, although no additional multipliers are introduced in the present approach. These desirable characteristics are obtained without resorting to numerically dissipative algorithms. If high frequencies are present in the system, i.e. the system is physically stiff, dissipative schemes become necessary; the proposed algorithm is extended to deal with this situation.