Dynamic behaviour of elastic-plastic free-free beams subjected to impulsive loading

doi:10.1016/0020-7683(95)00169-7

International Journal of Solids and Structures

Volume 33, Issue 18, July 1996, Pages 2659-2680

https://doi.org/10.1016/0020-7683(95)00169-7 Get rights and content

Abstract

A dynamic analysis of an elastic-plastic free-free beam subjected to impact by a projectile at the mid-span or to triangularly distributed impulsive loading along the span is presented. Attention is focused on the dynamic behaviour of the beam in the early, transient stage of the response. Details of the interactions between the plastic flexural wave and the elastic flexural wave reflected from the free ends are described, which assist in understanding how the elastic effect modifies the deformation history of a beam and finally leads to a somewhat different configuration from that based on a rigid-perfectly plastic model. The partitioning of the energy in the deformed beam is also examined and a rigid-plastic model with a rotational elastic-plastic spring at the mid-span of the beam is proposed in order to estimate the proportions of elastic energy and plastic dissipation. To verify the theoretical predictions, a group of high-speed photographs obtained experimentally for central impact of a free-free beam is presented and compared with the numerical results on the instantaneous profiles of the beam.

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In fact, the deflected profile is no longer triangular and a distinct hinge separating the deflected and the un-deflected regions of the beam cannot be identified. Rather dynamic deflection occurs in a more classical sense by the propagation of an elastic/plastic flexural wave that emanates from the impact site (Yu et al., 1996). Therefore a simple analytical model for the overall deflection mode can no longer be developed and readers are referred to Stronge (2000) for a detailed exposition of the elastic-plastic dynamic deflection of Euler-Bernoulli beams.
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They found that, for a free–free beam subjected to a triangular impulsive loading, 25% of the input energy is converted into plastic work and remaining 75% results in rigid-body motion. Later, it was observed by Yu et al [17] through finite difference simulations that, for elastic-perfectly-plastic material, the above estimate of energy partitioning is reasonably good if 25% of the input energy is much larger than the elastic strain energy capacity of the beam. It was also observed that while the kinetic energy of rigid body motion remains the same (i.e. 75%) the plastic work significantly depends on the energy ratio which is defined as the ratio (R) of initial kinetic energy and maximum elastic strain energy.
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^∗: Current address: Department of Mechanical Engineering, Hong Kong University of Science and Technology, Hong Kong.

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Dynamic behaviour of elastic-plastic free-free beams subjected to impulsive loading

Abstract

Int. J. Mech. Sci.

Int. J. Impact Engng

Int. J. Impact Engng

J. Mech. Phys. Solids