Integration of the Equations of Motion of Multibody Systems Using Absolute Nodal Coordinate Formulation

Recently, a finite element formulation, called the absolute nodal coordinate formulation (ANCF), was proposed for the large rotation and deformation analysis of flexible bodies. In this formulation, absolute position and slope coordinates are used to define the finite element configuration. Infinitesimal or finite rotations are not used as nodal coordinates. The ANCF finite elements have many unique features that distinguish them from other existing finite element methods used in the dynamic analysis of the flexible multibody systems. In such systems, there appears the necessity of solving systems of differential-algebraic equations (DAEs) of index 3. Accurate solving of the DAEs is a non-trivial problem. However, in the literature about the ANCF one can hardly find any detailed information about the procedures that are used to solve the DAEs. Therefore, the current paper is devoted to the analysis of selected DAE solvers, which are applied to simulations of simple mechanisms.