Application of an augmented Lagrangian approach to multibody systems with equality motion constraints

• Published in: Nonlinear dynamics Vol. 99; no. 1; pp. 753 - 776
• Main Authors: Potosakis, N., Paraskevopoulos, E., Natsiavas, S.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.01.2020; Springer Nature B.V
• Subjects: Automotive Engineering; Classical Mechanics; Control; Differential equations; Dynamical Systems; Engineering; Equations of motion; Mathematical analysis; Mechanical Engineering; Mechanical systems; Multibody systems; Nonlinear equations; Optimization; Ordinary differential equations; Original Paper; Time integration; Vibration; Analytical dynamics; Multibody dynamics; Generalized Gauss principle; Augmented Lagrangian formulation; Bilateral constraints; Weak form of equations of motion
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-019-05059-6

The focus of this work is on dynamics of multibody systems subject to bilateral motion constraints. First, a new set of equations of motion is employed, expressed as a coupled system of strongly nonlinear second-order ordinary differential equations. After putting these equations in a weak form, the position, velocity and momentum type quantities are assumed to be independent. This leads to a three-field set of equations of motion. Next, an alternative formulation is developed, based on optimization principles. It is shown that the equations of motion can eventually be cast in a form obtained by application of an augmented Lagrangian formulation, after introducing an appropriate set of penalty terms. This final set of equations is then used as a basis for developing a new time integration scheme. The validity and numerical efficiency of this scheme is verified by applying it to several example systems. In those examples, special emphasis is put on illustrating the advantages of the new method when applied to selected mechanical systems, involving redundant constraints or singular configurations.