Inverse reconstruction problem of structural faults - Silva, Andressa Alves Machado da (2024)
This thesis deals with inverse reconstruction problem of structural faults. The faults identification process in its initial stage is essential in many physical and engineering problems and has significant contributions reported in the literature. In particular, we consider damage identification in plate structures and reconstruction of micro-cracks in plates as well as three-dimensional elastic bodies. The related forward problems are governed by the elastodynamic models in the frequency domain. We start by considering damage identification problem in Kirchhoff and Reissner-Mindlin plate structures. The damage is given by a variation in the thickness in a small region of the plate, which is assumed to be given by a piecewise constant function. More precisely, we want to find a set of distributed damages from pointwise domain measurements of the plate displacement field. A shape functional measuring the misfit between the available data (measurements) and the displacements computed from the model is minimized with respect to the geometrical support of the unknown damage distribution by using the topological derivative method. Next, we consider the spatial reconstruction and characterization of micro-seismic events via joint source location and moment tensor inversion into three-spatial dimensions. Seismic events representing micro-cracks are described by a combination of dipoles specified in terms of seismic moment tensor. The basic idea consists in minimizing a functional measuring the misfit between observed and predicted data with respect to the set of admissible solutions, leading to a non-iterative second-order reconstruction algorithm. At last, a new micro-seismic opening model for the fault reconstruction in plates is proposed. The model problem into three spatial dimensions is particularized by taking into account the kinematic assumptions associated with the Reissner-Mindlin plate bending model. Therefore, we are interested in the delamination process represented by a micro-fault lying in the middle plane of a plate structure, orthogonal to its cross-section. In this way, the micro-cracks are completely characterized by their locations and strengths, leading to a simplified model in comparison with its three-dimensional counterpart. Finally, for each problem we are dealing with, a set of numerical experiments is presented, showing different features of the proposed approaches.