Asymptotic formulae for the risk of failure related to an elasto-plastic problem withnoise

Cyril Feau; Mathieu Laurière; Laurent Mertz

doi:10.3233/ASY-171445

Asymptotic formulae for the risk of failure related to an elasto-plastic problem withnoise

Cyril Feau
, Mathieu Laurière^*
, Laurent Mertz

^*Corresponding author for this work

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

4 Citations (Scopus)

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.

Original language	English
Pages (from-to)	47-60
Journal	Asymptotic Analysis
Volume	106
Issue number	1
DOIs	https://doi.org/10.3233/ASY-171445
Publication status	Published - 2017
Externally published	Yes

Bibliographical note

Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

Funding

The authors would like to thank George Papanicolaou for his suggestions helping to improve the manuscript. LM would like to thank François Delarue for his question (during the seminar of January 16 2014 at University of Nice Sophia Antipolis) regarding a functional central limit theorem for the plastic deformation of a white noise driven EPPO. We hope that this work answer his question. The authors would like to thank Alain Bensoussan, Stéphane Menozzi and Eric Vanden-Eijnden for stimulating discussions. LM expresses his sincere gratitude to the Courant Institute for being supported as Courant Instructor in 2014 and 2015, when this work was done. LM is also supported by a faculty discretionary fund from NYU Shanghai and the National Natural Science Foundation of China, Research Fund for International Young Scientists under the project #1161101053 entitled “Computational methods for non-smooth dynamical systems excited by random forces” and the Young Scientist Program under the project #11601335 entitled “Stochastic Control Method in Probabilistic Engineering Mechanics”.

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 11 Sustainable Cities and Communities

Research Keywords

Donsker Invariance Principle
elasto-plastic oscillator
Risk analysis
stochastic variational inequalities
white noise

Access Output

10.3233/ASY-171445

Other Access Options

Check CityUHK Library

Permanent Link

Right click to copy link

Cite this

@article{74d408df80e140a5aafd8bb6a566fa8b,

title = "Asymptotic formulae for the risk of failure related to an elasto-plastic problem withnoise",

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.",

keywords = "Donsker Invariance Principle, elasto-plastic oscillator, Risk analysis, stochastic variational inequalities, white noise",

author = "Cyril Feau and Mathieu Lauri{\`e}re and Laurent Mertz",

note = "Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected]. ",

year = "2017",

doi = "10.3233/ASY-171445",

language = "English",

volume = "106",

pages = "47--60",

journal = "Asymptotic Analysis",

issn = "0921-7134",

publisher = "Sage Publications",

number = "1",

}

TY - JOUR

T1 - Asymptotic formulae for the risk of failure related to an elasto-plastic problem withnoise

AU - Feau, Cyril

AU - Laurière, Mathieu

AU - Mertz, Laurent

N1 - Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

KW - Donsker Invariance Principle

KW - elasto-plastic oscillator

KW - Risk analysis

KW - stochastic variational inequalities

KW - white noise

UR - https://www.scopus.com/pages/publications/85036465809

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85036465809&origin=recordpage

U2 - 10.3233/ASY-171445

DO - 10.3233/ASY-171445

M3 - RGC 21 - Publication in refereed journal

SN - 0921-7134

VL - 106

SP - 47

EP - 60

JO - Asymptotic Analysis

JF - Asymptotic Analysis

IS - 1

ER -

Asymptotic formulae for the risk of failure related to an elasto-plastic problem withnoise

Abstract

Bibliographical note

Funding

UN SDGs

Research Keywords

Access Output

Other Access Options

Permanent Link

Other Files and Links

Fingerprint

Cite this