【直播】【力学交叉融合全球前沿学科系列讲座】Alexander N. Galybin 院士学术报告

KouShare 蔻享学术 2023-08-02

讲座名称：

Inverse and semi-inverse problems for fracture detection in layered media

讲座时间：

2023年4月27日（周四）17:00

报告嘉宾：

Alexander N. Galybin 院士

主办单位：

重庆大学国际合作与交流处、重庆大学航空航天学院

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报告人介绍

Alexander N. Galybin 院士

Alexander N. Galybin教授，俄罗斯科学院地球物理学Schmidt研究所（IPE RAS）首席研究科学家，拥有超过40年的固体力学、地球物理学和应用数学研究经验，主要聚焦断裂和岩石力学、不适定弹性边值问题、应力场重建理论和计算方法等。[Biography: Alexander N. Galybin, principal research scientist at Schmidt Institute of Physics of the Earth of the Russian Academy of Sciences (IPE RAS), has more than 40 years of research experience in the field of solid mechanics, geophysics and applied mathematics. In 1979 he graduated from the Faculty of Mechanics and Mathematics of Moscow State University with a degree in mechanics. He obtained his PhD in 1988 from the same university in mechanics of solids. In 2017 he received DSc in geophysics from IPE RAS. Until March 1995, he has been working in Moscow in various scientific and teaching positions, in 1995-2005 at the University of Western Australia, in 2006-11, appointed as a Professor and Head of the of Damage Mechanics Division at the Wessex Institute of Technology, UK, since 2011 works in IPE RAS. His main results are obtained in the areas of fracture and rock mechanics, ill-posed elastic boundary value problems, theory and computational methods for stress field reconstruction. In recent years he received a number of different national and international grants in 3 different countries. Since 2006 Prof Galybin is a permanent member of the scientific committee of the International Conference on Boundary Elements. Member of the editorial boards of “Engineering Analysis With Boundary Elements” (2006) and “Physics of the Solid Earth” (2020).]

报告简介

This study is aimed at the development of mathematical methods for non-destructive identification of interfacial defects in layered media based on the consideration of incorrectly posed elastic boundary value problems, BVP. A package of dissimilar elastic layers bonded to elastic half-plane (substrate)is considered. Continuity conditions for the stress and displacement vectors are accepted on the interfaces between the layers. The interface between the layers and substrate may be damaged, which is modeled by an interface crack or by a pure sliding crack (slip). It is supposed that the upper boundary is loaded by concentrated forces only and its displacements are measured on the stress-free part. Thus the number of boundary conditions is over-specified. Two types of BVP are analysed for the plane case: (i) the Cauchy initial problem in which 4 conditions are given on the boundary and no conditiond on the interface (inverse problem) and (ii) 3 conditions on top boundary and 1 on the interface (semi-inverse problem). In all these cases the Fourier transforms are used in order to derive analytic solution in the Fourier space. Inversion of the Fourier transform leads to the problem of the inversion of the Stieltjes integral that is unstable. It is shown that the SVD regularisation is capable to obtain stable solution, which is illustrated by examples.

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