The floating frame of reference formulation is currently the most widely used approach in flexible multibody simulations. The use of this approach, however, has been limited to small deformation problems. In this investigation, the computer implementation of the new absolute nodal co-ordinate formul
ON THE USE OF THE DEGENERATE PLATE AND THE ABSOLUTE NODAL CO-ORDINATE FORMULATIONS IN MULTIBODY SYSTEM APPLICATIONS
β Scribed by A.A. SHABANA; A.M. MIKKOLA
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 121 KB
- Volume
- 259
- Category
- Article
- ISSN
- 0022-460X
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β¦ Synopsis
The purpose of this paper is to discuss the fundamental differences between the degenerate plate element formulations [1-3] and the plate and shell formulations obtained using the absolute nodal co-ordinate formulation introduced for the large rotation and deformation analysis of flexible bodies [4][5][6][7][8]. It is demonstrated in this investigation that existing large rotation degenerate plate formulations, that employ a displacement field that is linear in the nodal co-ordinates, can only be used in the framework of incremental solution procedures due to the limitations that arise from the kinematic motion description. Such limitations do not apply to the absolute nodal co-ordinate formulation, and as a consequence, this formulation can be used with a non-incremental solution procedure. The assumptions used in the degenerate plate formulations are explained using Rodriguez formula for the finite rotation [4]. It is shown in this investigation that, due to these assumptions, the displacement field in the degenerate plate formulations cannot be defined in the global inertial frame of reference, unless this displacement field is expressed as a non-linear function of the nodal co-ordinates. As a consequence, the use of degenerate plate and shell formulations that provide information about the nodal rotations leads to a non-linear inertia matrix and non-zero centrifugal and Coriolis inertia forces. Furthermore, the existing degenerate plate formulations do not ensure the continuity of all the displacement gradients at the nodal points and they may lead to linearized kinematic equations for large rotation problems. As demonstrated in this paper, the use of linearized equations for the finite rotations can lead to a violation of the principle of work and energy. This is not the case with the finite element absolute nodal co-ordinate formulation that is based on a displacement field defined in the global co-ordinate system. This could be achieved by using global displacements and slopes as nodal co-ordinates, thereby avoiding interpolation of rotations or unit vectors. The absolute nodal co-ordinate formulation leads to a constant mass matrix, and as a consequence, the centrifugal and Coriolis inertia forces are identically equal to zero. Unlike the degenerate plate
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