Detection of multiple flaws in piezoelectric structures using XFEM and level sets

An iterative procedure to solve the inverse problem of detecting multiple voids in piezoelectric structure is proposed. In each iteration the forward problem is solved for various void configurations, and at each iteration, the mechanical and electrical responses of a piezoelectric structure is minimized at known specific points along the boundary to match the measured data. The Extended Finite Element method (XFEM) is employed for determining the responses as it allows the use of a fixed mesh for varying void geometries. The numerical method based on combination of classical shape derivative and of the level-set method for front propagation used in structural optimization is utilized to minimize the cost function. The results obtained show that this method is effectively able to determine the number of voids in a piezoelectric structure and its corresponding locations and shapes.