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A numerical strategy for vibrations of elasto-plastic beams with rigid-body degrees-of-freedom is presented. Beams vibrating in the small-strain regime are considered. Special emphasis is laid upon the development of plastic zones. An elasto-plastic beam performing plane rotatory motions about a fixed hinged end is used as example problem. Emphasis is laid upon the coupling between the vibrations and the rigid body rotation of the pendulum. Plastic strains are treated as eigenstrains acting in the elastic background structure. The formulation leads to a non-linear system of differential algebraic equations which is solved by means of the Runge-Kutta midpoint rule. A low dimension of this system is obtained by splitting the flexural vibrations into a quasi-static and a dynamic part. Plastic strains are computed by means of an iterative procedure tailored for the Runge-Kutta midpoint rule. The numerical results demonstrate the decay of the vibration amplitude due to plasticity and the development of plastic zones. The pendulum approaches a state of plastic shake-down after sufficient time.
Institute of Mechanics and Machine Design, Division of Technical Mechanics, Johannes Kepler University of Linz, Altenbergerstr. 69, A-4040 Linz, Austria
Institute of Mechanics and Machine Design, Division of Technical Mechanics, Johannes Kepler University of Linz, Altenbergerstr. 69, A-4040 Linz, Austria