Archive | 2019
Implementation of Linear Springs and Dampers in a Newmark Second Order Direct Integration Method for 2D Multibody Dynamics
Abstract
This paper presents the mathematical developments required to introduce both linear springs and dampers into the second order Newmark method for the integration of Multibody System Dynamics (MBSD) for bidimensional problems. The advantage of the Newmark approach is that it integrates directly the second order differential equations found in MBSD, thus not duplicating variables and reducing computational cost [1]. The use of Newmark approach for MBSD is not new, but it is solved usually in a quasi-Newton procedure [2], which is easier to implement, but has worse convergence than a full Newton approach. For the full Newton approach to be achieved, however, all derivatives have to be computed analytically. In a previous work [3], the analytical derivatives needed for simple mechanisms including Bodies, Revolute and Prismatic joints were presented. The novelty presented in this document is the development of the derivatives needed for the introduction of linear springs and dampers. The resultant Karush-Kuhn-Tucker system is solved by means of the null space method ([4, 5]). The method has been developed and tested using Newton-Euler formalism and Cartesian coordinates to solve several 2D problems. Some examples are included, which have been contrasted with ADAMS. This is a preliminary work in order to afterwards develop the method for three dimensional problems.