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 elementmethod (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 FEMcharacter, but also exploiting high order spectral elements leads to a significant superiorityover FEM from the viewpoints of solution precision and computation costs. The excellentcharacteristic of SFEM is its diagonal mass matrix because of the choice of the Lagrangeinterpolation function supported on Legendre-Gauss-Lobatto (LGL) points in conjunctionwith LGL integration rule. Therefore numerical calculations can be significantly efficient incomparison with the classical FEM. In this paper, a SFEM-based code is represented andverified, 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. Theproblems are solved using different spectral elements, and then solution accuracy andcomputational costs in different solutions are compared to analytical and/or numericalsolutions 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.