TY - CONF A1 - Bulling, Jannis T1 - A Combination of the Scaled Boundary Finite Element Method with the Mortar Method N2 - The simulation of ultrasonic waves in a linearly elastic body can be computationally intensive. The reason is the relatively short wavelength compared to the body size for high frequencies. One possible approach to counteract the high computational costs is to decompose the domain into small parts and strive for parallelization. The Mortar Method is a well-established approach for domain decomposition. A rather new approach to discretize the emerging subdomains is the Scaled Boundary Finite Element Method. This semi-analytical method has many attractive properties. Some of these properties are listed subsequently. The grid consists of polygonal elements, which leaves much freedom in the meshing process. A variety of material distributions, including anisotropic materials, can be considered. High-order shape functions can be used for optimal convergence properties. The approach treats singularities at crack tips and corners analytically. Especially in the frequency domain, the Scaled Boundary Finite Element Method reduces the dimension of the approximation because only degrees of freedom which are associated with the boundary of a polygonal element are necessary. Those desirable properties make the method particularly suitable for calculating the dynamic responses in bodies with cracks, as it is essential for many non-destructive testing and structural health monitoring applications. In this contribution, we present a combination of the Scaled Boundary Finite Element Method with the Mortar Method in two dimensions. The presentation starts with a theoretical overview of both approaches. Subsequently, numerical examples demonstrate the stability of the combination for the polygonal boundary of the elements. The numerical examples increase in complexity and are compared to results computed on non-divided domains with the Finite Element Method. T2 - WCCM-ECCOMAS CONGRESS CY - Online meeting DA - 11.01.2021 KW - Ultrasound KW - Numerical Simulation KW - Scaled Boundary Finite Element Method, Mortar Method PY - 2021 AN - OPUS4-52275 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Lozano, Daniel A1 - Bulling, Jannis A1 - Prager, Jens T1 - Modeling guided waves interacting with arbitrarily shaped inhomogeneities using SBFEM in combination with an extruded quadtree decomposition for 3D plates N2 - 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 wave interacts differently because of the 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 makes the approach very efficient. Examples show the scattering characteristics of different guided wave modes after interacting with inhomogeneities and discontinuities in a plate. T2 - DAGA 2023 CY - Hamburg, Germany DA - 06.03.2023 KW - SBFEM KW - Quadtree KW - Ultrasound PY - 2023 SP - 1035 EP - 1038 CY - Hamburg AN - OPUS4-59776 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Bulling, Jannis A1 - Jurgelucks, B. A1 - Prager, Jens A1 - Walther, A. T1 - Experimental validation of an inverse method for defect reconstruction in a two-dimensional waveguide model N2 - Defect reconstruction is essential in non-destructive testing and structural health monitoring with guided ultrasonic waves. This paper presents an algorithm for reconstructing notches in steel plates, which can be seen as artificial defects representing cracks by comparing measured results with those from a simulation model. The model contains a parameterized notch, and its geometrical parameters are to be reconstructed. While the algorithm is formulated and presented in a general notation, a special case of guided wave propagation is used to investigate one of the simplest possible simulation models that discretizes only the cross section of the steel plate. An efficient simulation model of the plate cross section is obtained by the semi-analytical scaled boundary finite element method. The reconstruction algorithm applied is gradient-based, and algorithmic differentiation calculates the gradient. The dedicated experimental setup excites nearly plane wave fronts propagating orthogonal to the notch. A scanning laser Doppler vibrometer records the velocity field at certain points on the plate surface as input to the reconstruction algorithm. Using two plates with notches of different depths, it is demonstrated that accurate geometry reconstruction is possible. KW - Ultrasound KW - Waveguides KW - Symbolic computation KW - Optimization problems PY - 2024 DO - https://doi.org/10.1121/10.0025469 SN - 0001-4966 VL - 155 IS - 6 SP - 3794 EP - 3806 PB - Acoustical Society of America (ASA) AN - OPUS4-60325 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER -