A complete analytical solution for the dynamic plastic response of fully clamped and simply supported beams subjected to localized impulsive loading

This study addresses the research gap in systematic theoretical solutions for plastic hinge motion, velocity history, and complete deformation profiles of beams under localized impulsive loading. We present a complete analytical solution developed within small-deflection theory for fully clamped and simply supported beams that explicitly encompasses: (i) plastic hinge migration mechanisms, (ii) velocity-time histories, (iii) dynamic deformation evolution, and (iv) final plastic deformation profiles. Systematic comparisons with finite element simulations demonstrate strong agreement, establishing clear domains of applicability for the analytical formulations. The theoretical framework provides a fundamental basis for rapid performance assessment and resilient design of bending-dominated beam structures subjected to localized impulsive loading, while offering critical insights into underlying response mechanisms.