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For structural health monitoring systems or non-destructive testing, it is crucial to study the interactions of ultrasonic-guided waves with inhomogeneities or damage in structural components. Simulation of these interactions poses a challenge.
After the wave-damage interaction, the numerical model must reproduce features like mode conversion or wave scattering. Mathematically, damages are discontinuities in a computational domain, and each interacts diversely depending on its geometrical features. We propose a quadtree-based meshing in the current contribution to capture these geometrical
characteristics.
This kind of discretisation approach requires special techniques to couple cells of different sizes since, after a quadtree decomposition, the problem of so-called hanging nodes may arise. Transition elements based on high-order transfinite shape functions are used to solve this issue. The advantage is that these elements allow the correct coupling of the cells while retaining a high-order interpolation. Moreover, the reuse of the dynamic stiffness matrices can be exploited based on the similarity of the cells. This procedure renders the approach very efficient.
Examples show the scattering characteristics of different guided wave modes after interacting with inhomogeneities and discontinuities in a plate.