Variable Thickness in Plates—A Solution for SHM Based on the Topological Derivative

The topological derivative tool is applied here in structural health monitoring (SHM) problems to locate small defects in a material plate with complex geometry that is subject to permanent multifrequency guided waves excitation. Compared to more standard SHM methods, based in measuring the time-lag between emitted and received propagative pulses plus some postprocessing, the topological derivative somehow compares the measured and computed (solving the full elasto-dynamic equations) response of the damaged plate, instead of relying on only the time of flight of the wave. Thus, the method profits the knowledge behind the physics of the problem and can cope with scenarios in which classical methods give poor results. The authors of this paper have already used the topological derivative in rectangular plates with constant thickness, but with defects consisting simply in both through slits and inclusions of a different material, and actuators/sensors located near the boundary, which makes very difficult to use standard SHM methods. This is an extension of the method, also considering the much more difficult to analyze case of plates with variable thickness and complex (non-rectangular) planform.