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

Area of Science:

• Mechanical Engineering
• Materials Science
• Applied Physics

Background:

• Classical structural health monitoring (SHM) methods often rely on time-of-flight measurements, which can be insufficient for complex geometries.
• Existing SHM techniques struggle with defects in plates of variable thickness and non-rectangular shapes.
• Multifrequency guided waves offer rich data but require advanced analysis for defect localization.

Purpose of the Study:

• To extend the application of the topological derivative for defect detection in structural health monitoring.
• To address the challenges of analyzing plates with complex geometries and variable thickness.
• To improve defect localization accuracy compared to traditional SHM methods.

Main Methods:

• Utilized the topological derivative as an inverse analysis tool for defect identification.
• Employed multifrequency guided waves for excitation and response measurement.
• Solved full elasto-dynamic equations to compute the plate's response and compared it with measured data.

Main Results:

• The topological derivative successfully located small defects in plates with complex geometries and variable thickness.
• The method demonstrated superior performance over classical time-of-flight based SHM techniques.
• Accurate defect detection was achieved even in challenging scenarios where standard methods yield poor results.

Conclusions:

• The topological derivative is a robust and effective tool for structural health monitoring, particularly for complex plate structures.
• This advanced method leverages the physics of wave propagation for more reliable defect detection.
• The study validates the topological derivative's capability for analyzing variable thickness plates and complex planforms.