Mathematical Problems in Engineering
Volume 4 (1998), Issue 1, Pages 1-19

Antioptimization of earthquake exitation and response

G. Zuccaro,1 I. Elishakoff,2 and A. Baratta3

1Centro di Ricerca Interdipartimentale, LUPT, University of Naples, Italy
2Department of Mechanical Engineering, Florida Atlantic University, Boca Raton 33431-0991, FL, USA
3Dipartimento di Scienza delle, University of Naples, Italy

Received 3 March 1995; Revised 14 July 1997

Copyright © 1998 G. Zuccaro et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The paper presents a novel approach to predict the response of earthquake-excited structures. The earthquake excitation is expanded in terms of series of deterministic functions. The coefficients of the series are represented as a point in N-dimensional space. Each available ccelerogram at a certain site is then represented as a point in the above space, modeling the available fragmentary historical data. The minimum volume ellipsoid, containing all points, is constructed. The ellipsoidal models of uncertainty, pertinent to earthquake excitation, are developed. The maximum response of a structure, subjected to the earthquake excitation, within ellipsoidal modeling of the latter, is determined. This procedure of determining least favorable response was termed in the literature (Elishakoff, 1991) as an antioptimization. It appears that under inherent uncertainty of earthquake excitation, antioptimization analysis is a viable alternative to stochastic approach.