Dynamic Shakedown of Structures under Repeated Seismic Loads

Abstract

Elastic, perfectly plastic structures are considered under the action of repeated short-duration exitations of seismic type acting in an unknown time sequence, but belonging to a given polyhedral excitation domain. The basic excitations (vertices of the polyhedron) are chosen as discrete-spectrum waves each with frequencies coincident with the first natural frequencies of the structure, and amplitudes related to the ground features and earthquake intensity (according to the Kanai and Tajimi filter model) in such a way that every admissible excitation—obtained as a linear convex combination of the basic ones—has a maximum power not exceeding a given value. In the framework of unrestricted dynamic shakedown, the classic shakedown theorems are suitably cast and used for establishing alternative methods for the computation of the shakedown limit load multiplier. Considerable computational savings are obtained substituting the preceding basic excitations with single-frequency waves. Particular attention is devoted to bending frame structures. A numerical example is presented.