Damage Detection in Plane Linear Elastic Bodies Using Linear Sampling Method

In this paper, solution of inverse problems in a plane linear elastic bodies are investigated. For this purpose, sampling method in frequency domain is introduced for cavity/crack detection in a structural element such as plate. This method is categorized as a qualitative approach to image the geometrical features of unknown targets. 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.