Detecting an Inclusion in an Elastic Body by Boundary Measurements
نویسندگان
چکیده
We consider the problem of determining an inclusion D made of di erent elastic material in an elastic isotropic body from boundary measurements of traction and displacement. We prove that the volume of D can be estimated, from above and below, by an easily expressed quantity related to work, only depending on the boundary traction and displacement.
منابع مشابه
Stable determination of an inclusion in an inhomogeneous elastic body by boundary measurements
In this paper we consider the stability issue for the inverse problem of determining an unknown inclusion contained in an elastic body by all the pairs of measurements of displacement and traction taken at the boundary of the body. Both the body and the inclusion are made by inhomogeneous linearly elastic isotropic material. Under mild a priori assumptions about the smoothness of the inclusion ...
متن کاملAlgorithm for the determination of a linear crack in an elastic body
In this paper we consider the inverse problem of identifying a linear inclusion inside an elastic body from exterior boundary measurements. Based on the asymptotic formula by Beretta and Francini (2006 SIAM J. Math. Anal. 38 1249–61), we design an effective reconstruction algorithm to find the endpoints and the thickness of a linear inclusion. Numerical experiments show that the algorithm is ef...
متن کاملIdentification of elastic inclusions and elastic moment tensors by boundary measurements
We consider the problem of identifying unknown inclusions inside an elastic body by means of traction–displacement relations measured on the boundary. Based on the asymptotic formula of Ammari et al (2003 J. Elast. at press), we propose an algorithm to reconstruct unknown inclusions. The algorithm of this paper detects the location and the elastic moment tensors (elastic Pólya–Szegö tensors) of...
متن کاملDetecting Rigid Inclusions, or Cavities, in an Elastic Body
In this paper we address the following problem of nondestructing testing: to determine, within an elastic body , the possible presence of defects in the form of either cavities or rigid inclusions, from measurements of traction and displacement taken at the exterior boundary of . Let us denote by D the unknown, possibly disconnected, defect and let us assume that D is an open set compactly cont...
متن کاملA Contact Problem of an Elastic Layer Compressed by Two Punches of Different Radii
The elasticity mixed boundary values problems dealing with half-space contact are generally well resolved. A large number of these solutions are obtained by using the integral transformation method and methods based the integral equations. However, the problems of finite layer thicknesses are less investigated, despite their practical interests. This study resolves a quasi-stationary problem of...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- SIAM J. Math. Analysis
دوره 33 شماره
صفحات -
تاریخ انتشار 2002