Damage Detection in Plane Linear Elastic Bodies UsingLinear Sampling Method

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Dehghan Manshadi S.H.

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Journal: Modares Civil Engineering journal Year:2021 | Volume:21 | Issue:6 Page(s): 215-226

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Title

Damage Detection in Plane Linear Elastic Bodies UsingLinear Sampling Method

Author(s)

Dehghan Manshadi S.H. | Issue Writer Certificate

Keywords

Qualitative inverse problems

linear sampling method

damage detection

elastodynamic

spectral finite element method

Abstract

In this paper, solution of inverse problems in a plane linear elastic bodies are investigated. In recent years, many studies have been conducted to develop effective approaches for damage detection in structural components. The efforts made over the last decades to overcome the mathematical challenges encountered in non-linear inverse problems may be categorized in two procedures: traditional methods, and qualitative methods. Although satisfactory results can be obtained using traditional approaches, they impose long reconstruction times associated with necessity of an accurate initial guess. These schemes require a priori information that may not be necessarily available. Consequently, the mentioned limitations have led to the conceptually distinct class of inverse scattering solutions, known as “, qualitative methods. ”,These methods are based on non-iterative obstacle reconstruction from far-and/or near-field measurements of the scattered field which avoids incorrect model assumption. Qualitative methods may be considered as probe/sampling methods such as linear sampling method, topological sensitivity, factorization method, and point source method, which seek to determine the geometric properties of scatterers. In this regard, the LSM and the FM introduced in the inverse scattering literature of far-field acoustics for the first time, are particularly attractive. This is due to the abilities of these methods to provide accurate reconstruction of the location and shape of the unknown scatterer from measurements of near-or far-field patterns, by monitoring the behavior of the norm of regularized solution. This norm is bounded inside the targets and unbounded elsewhere. Moreover, the most interesting feature of qualitative methods is that they do not require a priori information/assumption on the scatterer and/or the investigation domain. In addition, these methods may handle multiple scatterers as easily as single ones. Furthermore, these methods involve relatively low computational cost and can be applied to various types of defects such as non-convex and not-connected ones. For this purpose, sampling method in frequency domain is introduced for cavity/crack detection in a structural element such as plate. This goal is followed by partitioning the investigated region into an arbitrary grid of sampling points, in which a linear equation is solved. The main idea of the linear sampling method is to search for a superposition of differential displacement fields which matches with a prescribed radiating solution of the homogeneous governing equation in Ω, (D), for each sampling point. Although this method has been used in the context of inverse problems such as acoustics, and electromagnetism, there is no specific attempt to apply this method to identification of crack/cavities in a structural component. This study emphasizes the implementation of the sampling method in the frequency domain using spectral finite element method. A set of numerical simulations on two-dimensional problems is presented to highlight many effective features of the proposed qualitative identification method.

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APA: Copy

Dehghan Manshadi, S.H.. (2021). Damage Detection in Plane Linear Elastic Bodies UsingLinear Sampling Method. MODARES CIVIL ENGINEERING JOURNAL, 21(6 ), 215-226. SID. https://sid.ir/paper/1036337/en

Vancouver: Copy

Dehghan Manshadi S.H.. Damage Detection in Plane Linear Elastic Bodies UsingLinear Sampling Method. MODARES CIVIL ENGINEERING JOURNAL[Internet]. 2021;21(6 ):215-226. Available from: https://sid.ir/paper/1036337/en

IEEE: Copy

S.H. Dehghan Manshadi, “Damage Detection in Plane Linear Elastic Bodies UsingLinear Sampling Method,” MODARES CIVIL ENGINEERING JOURNAL, vol. 21, no. 6 , pp. 215–226, 2021, [Online]. Available: https://sid.ir/paper/1036337/en

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