Finite Element Formulations for Fast Computation of Large and Moderately Large Deformations

The paper presents finite element formulations aimed at fast computation of large and moderately large flexible body deformations in the fields of virtual reality technology and multibody dynamics. In many areas of application, virtual reality requires real-time or nearly real-time simulation of deformable objects’ behaviour, quite often with deformations involving large local rotations. The well-known simplified approach based on mass-spring systems is shortly discussed with advantages and disadvantages pointed out. This is followed by a co-rotational 3DFEM approach based on rigid-body rotations performed on element level. The approach accounts for large local rigid-body rotations and yields satisfying accuracy combined with high numerical efficiency. Since force feedback is very important in certain virtual reality applications, special attention is given to the issue. Furthermore, novel formulations for consideration of geometrical nonlinearities in the modal space are presented. For bodies which do not undergo large configuration changes throughout the deformation, an approach based on inclusion of the geometric stiffness matrix is proposed. The second approach is aimed at nonlinearities, which are a consequence of moderately large rotations of some parts of the flexible body. Examples for all proposed approaches are provided, demonstrating their characteristics.