Abstract
Summary A complete analysis of the large deformation response of a plastic string resting on a plastic foundation and undergoing localized mass impact, is presented. The formulation is based on the conservation of linear momentum and the kinematic and dynamic continuity conditions on a moving wave front. A closed-form solution is obtained for the instantaneous velocity and deflection profiles as well as for the final permanent deformed shape of the string and the magnitude of the maximum central deflection. An approximate expression for the central deflection amplitude is also derived using the solution of the corresponding static problem. Finally, the string-on-foundation problem is related to the large deflection dynamic plastic response of a cylindrical shell subjected to mass impact. A parametric study is performed to assess the effect of the impacting mass, the impact velocity, and the shell parameters on the magnitude of the permanent displacements and deformed shape of the shell.
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