The objective of this investigation is to develop a nonlinear finite element formulation for the elastic-plastic analysis of flexible multibody systems. The Lagrangian plasticity theory based on flow theory is used to account for the effect of plasticity in flexible multibody dynamics. It is demonstrated that the principle of objectivity that is an issue when existing finite element formulations using rate-type constitutive equations are used is automatically satisfied when the stress and strain rate are directly calculated in the Lagrangian descriptions using the absolute nodal coordinate formulation employed in this investigation. 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. As a consequence, the numerical algorithm used to determine the plastic deformations such as the radial return algorithm becomes much simpler when the absolute nodal coordinate formulation is used as compared to existing finite element formulations that employ incrementally objective algorithms. Several numerical examples are presented in order to demonstrate the use of the formulations presented in the paper.
Application of Plasticity Theory and Absolute Nodal Coordinate Formulation to Flexible Multibody System Dynamics
Contributed by the Mechanisms and Robotics Committee for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received January 2003; revised November 2003. Associate Editor: J. Michael McCarthy.
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Sugiyama , H., and Shabana, A. A. (November 1, 2003). "Application of Plasticity Theory and Absolute Nodal Coordinate Formulation to Flexible Multibody System Dynamics ." ASME. J. Mech. Des. May 2004; 126(3): 478–487. https://doi.org/10.1115/1.1737491
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