Asymptotic Analysis - Volume 106, issue 1

Authors: Lin, Yi-Hsuan

Article Type: Research Article

Abstract: The nearly cloaking via transformation optics approach for the isotropic elastic wave fields is considered. This work extends the study of the nearly cloaking scheme to the elasticity system with residual stress in R N for N = 2 , 3 , which is an anisotropic elasticity system. It is worth mentioning that there are no minor symmetric properties for the elastic tensor with residual stress and this system is invariant under a coordinate transformation. Therefore, we think the elasticity system residual stress model is more natural than the isotropic elasticity system …in designing the elastic cloaking medium in the physical sense. In addition, the main difficulty of treating this problem lies in the fact that there are no layer potential theory for the residual stress system. Instead, we will derive suitable elliptic estimates for the elasticity system residual stress by comparing with the Lamé system to achieve desired results. Show more

Keywords: Elastic cloaking, nearly cloaking, anisotropic elasticity system, residual stress

DOI: 10.3233/ASY-171439

Citation: Asymptotic Analysis, vol. 106, no. 1, pp. 1-23, 2018

Authors: Krupchyk, Katya | Uhlmann, Gunther

Article Type: Research Article

Abstract: We obtain sharp uniform bounds on the low lying eigenfunctions for a class of semiclassical pseudodifferential operators with double characteristics and complex valued symbols, under the assumption that the quadratic approximations along the double characteristics are elliptic.

Keywords: Semiclassical operators, double characteristics, low lying eigenfunctions

DOI: 10.3233/ASY-171442

Citation: Asymptotic Analysis, vol. 106, no. 1, pp. 25-46, 2018

Authors: Feau, Cyril | Laurière, Mathieu | Mertz, Laurent

Article Type: Research Article

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. Show more

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

DOI: 10.3233/ASY-171445

Citation: Asymptotic Analysis, vol. 106, no. 1, pp. 47-60, 2018