Qualitative and Quantitative Investigation of Planar Multibody Dynamics Encompassing GSSSS Family of Algorithms - A Novel In-depth Look

Abstract

Growing interest in the simulation of constrained rigid/flexible multibody systems has prompted the development of a wide variety of time integration methods for the differential-algebraic equations (DAEs) inherent to these systems. The vast majority of these methods require refor- mulation of the natural index 3 equations of motion leading to additional computational cost and the need to control drift phenomena, citing instability of direct index 3 methods. In the past 50 years, most researchers developed varieties of ways to decreasing the influence of instability of index 3 DAE system, and also sought for distinct formulation to equation of motion for the pur- poses of better physics. This research, within the generalized single step single solve (GSSSS) family of algorithms, investigates algorithm designs and framework capable of overcoming the instability and various problems encountered by previous researchers. A precise understanding of the equation of motion time level concept as well as novel methods for extending linear par- ent algorithms to nonlinear dynamic applications has enabled an indepth search of unique ways to the area. Also, various formulations of equations of motion and stabilization techniques are investigated which enable various approaches for simulating rigid/flexible body physics. In the end, design spaces for simulation in multibody dynamics algorithmic frameworks are identified which overcome previous limitations and are capable of providing stable, robust, and accurate simulating DAEs for both rigid and rigid/flexible multibody dynamics applications.