Summary: A new time-finite-element implicit integration scheme for
multibody system dynamics simulation
Mojtaba Oghbaei, Kurt S. Anderson *
Department of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180, United States
Received 22 June 2004; received in revised form 22 April 2005; accepted 22 April 2005
When performing the dynamic simulation of stiff mechanical systems, implicit type integration schemes are usually required to pre-
serve stability. This article presents a new implicit time integrator, which is a particular application of a novel state-time formulation
recently developed by the authors in a more general scope. The proposed scheme is constructed with the intent of benefitting from
the accuracy and apparent robustness thus far achieved with this algorithm in an integration context. This is realized by first setting
up the weighted residual equations for the system in a form associated with the application of a time marching integration scheme.
The resulting algebraic equations are then solved, minimizing the error of integration time step in a generalized energy sense, allowing
one to capture the stiff behavior of solution in an efficient manner. Examples are provided to show the proposed method performance
when dealing with a stiff system.
Ó 2005 Elsevier B.V. All rights reserved.
Keywords: Multibody dynamics; State-time formulation; Implicit integration scheme; Stiff mechanical systems
Multibody systems (MBS) can be described as a collection of rigid and/or flexible bodies that are connected through
different types of joints. Such systems can be found in various applications ranging widely from terrestrial vehicles, air
and space applications to MEMS devices and biomechanical applications. Multibody dynamics, as a discipline describing