DETECTION OF A THROUGH-THICKNESS CRACK BASED ON ELASTIC WAVE SCATTERING IN PLATES PART I: FORWARD SOLUTION

In the first part of the present paper, a numerical method called spectral finite element method (SFEM) is presented, which is able to simulate wave scattering phenomena in plates. Combining excellent characteristics of classical finite element method (FEM) and spectral elements, SFEM not only exhibits flexibility and ease of formulation, which is a FEM character, but also exploiting high order spectral elements leads to a significant superiority over FEM from the viewpoints of solution precision and computation costs. The excellent characteristic of SFEM is its diagonal mass matrix because of the choice of the Lagrange interpolation function supported on Legendre-Gauss-Lobatto (LGL) points in conjunction with LGL integration rule. Therefore numerical calculations can be significantly efficient in comparison with the classical FEM. In this paper, a SFEM-based code is represented and verified, and then some wave propagation problems in elastic solid domains are solved using this code to show the capabilities of SFEM in solving elastodynamic problems. The problems are solved using different spectral elements, and then solution accuracy and computational costs in different solutions are compared to analytical and/or numerical solutions available in the literature. In the second part of this paper, the result of this part as forward solution is used for detection of through-thickness crack in plates.