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Volumetric locking suppression method for nearly incompressible nonlinear elastic multi-layer beams using ANCF elements

Orzechowski G., Frączek J.

Journal of Theoretical and Applied Mechanics

2017

Vol. 55 nr 3

977--990

The analysis and solution of many modern flexible multibody dynamic problems require formulations that are able to effectively model bodies with nonlinear materials undergoing large displacements and deformations. The absolute nodal coordinate formulation (ANCF) in connection with a continuum-based approach is one way to deal with these systems. The main objective of this work is to extend an existent approach for the modelling of slender structures within the ANCF framework with nonlinear, nearly incompressible materials using the volumetric energy penalty technique. The main part of the study is devoted to the evaluation of multi-layer beam models and simplifications in the locking suppression method based on F-bar projection. The results present significantly better agreement with the reference solution for multi-layer structures built with the standard ANCF beam element as compared with the earlier implementation.

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

Orzechowski G., Frączek J.

Acta Mechanica et Automatica

2012

Vol. 6, no. 2

75-83

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.