A comparative study of bounding techniques in dynamic shakedown of elasto‐plastic structures

Two conceptually different procedures to obtain upper bounds to displacements and deformations developed in the dynamic evolution of elasto‐plastic structures are considered. Computationally, both methods require the dynamic analysis of a linear system and a sequence of constrained optimization problems, each roughly analogous to a limit analysis procedure in the quasi‐static range, with a substantial saving in effort when compared to an incremental analysis of the plasto‐dynamic response. A discrete model for frames is proposed and the two approaches are reformulated in a convenient matrix form. The approaches are then compared on the basis of the information needed (total or plastic displacements, deformations, dissipated energy), of the usefulness of results obtained and of the computational effort involved. The results seem to indicate the practical usefulness of these techniques and encourage the extension of the study to broader classes of structures.