On extracting the positions of multiple unknown cracks that occur on the junction line of two elastic plates

2022/04/15 by Masaru Ikehata, Ikehata, Masaru, Hiromichi Itou +1
Engineering · Mathematics · #35R30 #74B05 #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Structural Health Monitoring Techniques #Ultrasonics and Acoustic Wave Propagation

paper · pdf · doi:10.48550/arxiv.2204.07295

openalex publication_date 2022/04/15 · openalex created_date 2022/04/19 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with the reconstruction issue of an inverse crack problem in a two-dimensional bounded domain which may have a possible application to the nondestructive evaluation of materials. It is assumed that the domain consists of two elastic plates welded together and has some unknown cracks on the junction line and the governing equation of in-plane displacement is Navier's equation. The problem is to extract information about the location of cracks from the observation data which is a single set of a loading surface traction and the resulted in-plane displacement field on the boundary of the domain. It is shown that the enclosure method combined with the Kelvin transform yields explicit extraction formulae of such information from the observation data.

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