Structural Reliability Analysis Based on the Dynamic Integrity of an Attractor: Part I

This chapter addresses the reliability analysis of a dynamical system attractor, provided its dynamic-integrity measure has been previously assessed in terms of a meaningful parameter for which the probability density function is known. The probability that the dynamic-integrity measure should be equal or larger than a prescribed safe reference value, for the attractor to be considered “reliable,” is sought. Although the ideas addressed here are applicable to any dynamical system, the structural stability case is focused herewith for the sake of an illustration, aiming at characterizing the safe loading threshold in an archetypal model liable to elastic buckling. By assuming that the buckling strength is an input Gaussian random variable, the basic statistical properties of the output variable, namely, the dynamic-integrity measure, are estimated, from which a simple procedure to obtain a reliability appraisal is proposed. Another procedure is also addressed, considering a more formal way to obtain the output statistical properties. It is expected that both the simplified and the more formal procedures may help the assimilation of reliability analysis within current structural engineering design practices.