Affiliations: [a] EMSI laboratory, CEA, DEN, DM2S, SEMT, F-91191 Gif-sur-Yvette, France | [b] ECNU-NYU Institute of Mathematical Sciences, NYU Shanghai, Shanghai, China. E-mail: laurent.mertz@nyu.edu
Abstract: The risk of failure of mechanical structures under random forcing is an important concern in earthquake engineering. For a class of simple structures that can be modeled by an elasto-plastic oscillator, the risk of failure can be expressed in terms of the probability that, on a certain interval of time, the plastic deformation goes beyond a threshold related to a failure zone. In this note, asymptotic formulae for the risk of failure of an elasto-perfectly-plastic oscillator excited by a white noise are proposed. Our approach exploits the long cycle (repeating pattern) property of the aforementioned oscillator as introduced in A. Bensoussan, L. Mertz, S.C.P. Yam, Long cycle behaviour of the plastic deformation of an elasto-perfectly-plastic oscillator with noise, C. R. Acad. Sci. Paris Ser. I, 2012. We show that asymptotically the plastic deformation behaves like a Wiener process for which analytical formulae are available. Our result is a consequence of the Anscombe–Donsker Invariance Principle. Numerical experiments and comments are carried out.
