Elastic effects on the dynamic plastic deflection of pulse-loaded beams

Beams under intense dynamic pulse loading may experience large elastic-plastic deformation. Despite numerous studies have been conducted based on the rigid-perfectly plastic idealization of material, it is of great interest in both theoretical modeling and practical application to characterize and evaluate the effect of elastic deformation on the dynamic behavior of structures. This paper is aimed to examine the range of applicability of rigid-plastic theoretical solutions on large deflection of beams in response to dynamic pulse loading. The energy ratio R and the characteristic time ratio are first precisely defined by referring to the characteristics of a "plastic string", which represents the ultimate status of beams under very large deformation. Based on the recently published complete solutions on the dynamic response of fully-clamped and simply-supported rigid-plastic beams subjected to uniformly distributed rectangular pressure pulse, the discrepancies in final deflection and in saturated impulse of the rigid-plastic theoretical predictions from the elastic-plastic simulation results are evaluated and analyzed. It is revealed that if the energy ratio R>5 (with no limitation to the pulse duration), the rigid-plastic solutions can provide reliable predictions on final deflection and saturated impulse for the usage in engineering design. Then, the effects of the key dimensionless parameters related to the energy ratio R (e.g., the structural and material parameters as well as the loading one) on the discrepancies in final deflection and in saturated impulse are thoroughly examined. Finally, a unified dimensionless stiffness is identified to characterize the combined effect of structural and material parameters. For the cases of zeta <= 1.581, which represent most of the practically used beams, 1/(2R) and 1/(3R) could provide upper bounds to the absolute value of the discrepancy in final deflection for fully-clamped and simply-supported beams, respectively.