Progress in Engineering Computational Technology
Chapter 11 H. Sugiyama and A.A. Shabana
Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, Illinois, United States of America Keywords: flexible multibody system dynamics, nonlinear finite element methods, large deformation, elasto-plasticity, joint constraints, computer simulations.
In the general theory of continuum mechanics, the state of rotation and deformation of material points can be uniquely defined from the displacement field by using the nine independent components of the displacement gradients. For this reason, the use of the absolute rotation parameters as nodal coordinates, without relating them to the displacement gradients, leads to coordinate redundancy that leads to numerical and fundamental problems in many existing large rotation vector formulations. No special measures need to be taken in order to satisfy the principle of work and energy when the finite element absolute nodal coordinate formulation is used. This formulation does not suffer from the problem of coordinate redundancy and ensures the continuity of the stresses and strains at the nodal points. The computer implementation of this formulation for multibody system applications is discussed. A Lagrangian plasticity formulation that can be used with the absolute nodal coordinate formulation in the analysis of flexible multibody dynamics is also proposed. It is demonstrated that the principle of objectivity can be automatically satisfied when the stress and strain rate are directly calculated using the Lagrangian descriptions. This is attributed to the fact that, in the finite element absolute nodal coordinate formulation, the position vector gradients can completely define the state of rotation and deformation within the element.
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