Ingenieurwissenschaften und zugeordnete Tätigkeiten
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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.
Ultrasonic guided waves interacting with complex geometrical features are of high interest in the SHM field. For example, investigations into the extent to which a small change in defect geometry affects wave propagation have applications in Probability of Detection and defect reconstruction. These fields have to be supported by numerical tools aiming to retrieve accurate and reliable results and, thus, more realistic modeling.
Due to the short wavelengths of ultrasonic waves and the relatively large domains in which the waves propagate, fine grid resolution for the entire domain is usually not possible due to limited computational resources. One solution is to partition the domain into different subdomains and use a specific, efficient approach for each subdomain.
This contribution shows a combination of methods that aims to study these wave defect interactions in an elastic media. Firstly we introduce high-order 3D meshes that can resolve very fine geometrical details and are based on an Octree discretisation technique that employs special transition shape functions to resolve the hanging nodes that may appear due to the nature of the method. Afterward, the Octree mesh is embedded in a prismatic wave-guide based on the semi-analytical formulation of the SBFEM in 3D. To couple the different domains, we employ the mortar method, which enforces the continuity of the wave field across the internal boundaries of the domains. Examples show the power of the approach especially when it comes to parametric analysis.