A volume of fluid method for structural damage identification

In the field of engineering, Structural Health Monitoring (SHM) is crucial for identifying damage in continuum structures. Traditional damage identification methods often reformulate the problem as an inverse problem, leveraging frequency-based approaches. While the effectiveness of these methods is well-established, they have certain limitations. Specifically, they require prior knowledge of the topology of damaged regions, which can complicate and extend the detection process. Furthermore, incorrect initial conditions can lead to inaccuracies in identifying these damaged regions. To address these issues, we propose an innovative damage identification method utilizing the Volume of Fluid (VOF) approach. This method transforms the conventional inverse problem of natural frequencies into a shape optimization problem by representing damaged regions as a VOF function. The VOF method simplifies the identification process into the convection motion of material density, governed by a Hamilton-Jacobi equation. We present a comprehensive mathematical model, detail the numerical implementation, and validate the method through various examples. Moreover, numerical comparisons with similar methods are included in the case studies to demonstrate the feasibility of the approach proposed in this paper. Our results demonstrate the effectiveness and accuracy of this approach in identifying damage without dependency on initial topology, providing a valuable alternative to traditional methods.