Integration of Large Deformation Finite Element and Multibody System Algorithms

Abstract

This paper presents an overview of research and development efforts that are currently being devoted to integrate large deformation finite element formulations with flexible multibody system algorithms. The goal is to develop computer simulation capabilities for the analysis of physics and engineering models with significant details. The successful development of such new and integrated algorithms will also allow modeling and simulation of systems that cannot be solved using existing computer algorithms and codes. One of the main difficulties encountered in this integration process is attributed to the fact that the solution procedures used in finite element codes differ significantly from those used in general-purpose flexible multibody system codes. Finite element methods employ the corotational formulations that are often used with incremental solution procedures. Flexible multibody computer codes, on the other hand, do not, in general, use incremental solution procedures. Three approaches are currently being explored by academic institutions and the software industry. In the first approach, gluing algorithms that aim at performing successful simulations by establishing an interface between existing codes are used. Using different coordinates and synchronizing the time stepping are among several challenging problems that are encountered when gluing algorithms are used. In the second approach, multibody system capabilities are implemented in existing finite element algorithms that are based on large rotation vector formulations. For the most part, corotational formulations and incremental solution procedures are used in this case. In the third approach, a new large deformation finite element formulation that can be successfully implemented in flexible multibody system computer algorithms that employ nonincremental solution procedures is introduced. The approach that is now being developed in several institutions is based on the finite element absolute nodal coordinate formulation. Such a formulation can be systematically implemented in general-purpose flexible multibody system computer algorithms. Nonlinear constraint equations that describe mechanical joints between different bodies can be formulated in terms of the absolute coordinates in a straightforward manner. The coupling between the motion of rigid, flexible, and very flexible bodies can also be accurately described. The successful integration of large deformation finite element and multibody system algorithms will lead to a new generation of computer codes that can be systematical and efficiently used in the analysis of many engineering applications.