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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.
Structural health monitoring techniques associate strongly with damage detection and characterization. Ultrasonic guided waves (UGW), for such scope, arise as one of the most promising methods for many reasons i.e. UGW are able to travel long distances and they have high sensitivity to damage. In this context, the necessity to model realistic wave-defect interaction occurs to be critical.
Realistic damage scenarios can be modeled through the usage of image-based quadtree meshes. Images, such as the outcome from X-ray scans, C-scans, etc., can be converted into meshes for further integration in a computational domain. Quadtree meshes are created by converting the intensity of the pixels to quadrilateral cells. Homogeneous regions inside one image result in one quad, whereas fine features such as discontinuities can be described with smaller quads.
This contribution proposes an efficient methodology to model wave defect interaction, using as a framework the scaled boundary finite element method (SBFEM) and quadtree meshes. Problems as non-conforming regions in the mesh due to the space tree decomposition can be easily avoided using SBFEM’s polygonal elements. Moreover, the semi-analytical nature of the SBFEM allows the modeling of arbitrarily long prismatic/undamaged regions of the waveguides without an increase in the computational burden.