Shm via topological derivative

Resumen

This thesis focuses on the investigation of the usage of a relatively novel mathematical tool, the so-called topological derivative, for Structural Health Monitoring. In essence, the topological derivative approach minimizes a scalar objective function that measures the least squares difference between response to excitation of healthy and damaged structures. In contrast to conventional SHM methods, which usually draw on the processing of the time-lags between the transmitted and received pulse signals, the topological derivative requires to solve the full elasto-dynamic equations; this permits locating flaws in fairly demanding scenarios due to the necessity of considering the whole physics of the problem. In the chapters of the present work, the new method will by applied to aluminum plates with different kinds of shape complexities such as material inclusions, air slits, and thickness variations, in order to demonstrate its effectiveness in somewhat intricate situations. Furthermore, these plates will be excited by means of transmitters and receivers configurations positioned very close to the boundaries, which introduces even more complicatedness to an already challenging problem.