TY - CONF A1 - Bulling, Jannis A1 - Gravenkamp, Hauke 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 - Wasmer, Paul A1 - Bulling, Jannis A1 - Prager, Jens T1 - Ultrasonic sensor based on phononic crystals T2 - Proceedings of the ICA 2019 AND EAA EUROREGIO N2 - An essential task in many industries, e.g. food, petrol or chemical industry, is the precise and accurate characterization of liquids. Therefore, the development of innovative in-line sensors is of great interest. New concepts based on periodic structures, so-called phononic crystals (PnCs), are an interesting idea for the design of innovative sensors. A PnC-based sensor can be designed by introducing a resonance inside a bandgap, a frequency region where no wave propagation is allowed. High-Q measurement systems using PnCs are already reported in the literature. However, existing designs cannot be implemented into a piping system directly, but need special fittings, openings or by-passes to be in contact with the liquid. To circumvent this issue, we develop a new sensor based on PnCs, which can be directly implemented as part of the piping system. For this purpose, we use a PnC consisting of hollow cylinders with a periodic change of the outer diameter. A bandgap could be found for the described geometry without fluid in simulation and measurement. However, simulations show, that a bandgap for fluid-filled cylinders can only be obtained for quasi-longitudinal modes. Hence, we propose a mode selective excitation for the sensor. T2 - ICA 2019 CY - Aachen, Germany DA - 09.09.2019 KW - Phononic crystal KW - Ultrasound PY - 2019 SN - 978-3-939296-15-7 SN - 2226-7808 SN - 2415-1599 SP - 969 EP - 976 AN - OPUS4-48860 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Wasmer, Paul A1 - Bulling, Jannis A1 - Gravenkamp, H. A1 - Prager, Jens T1 - Acoustic-structure interaction in the Scaled Boundary Finite Element Method for primsatic geometries T2 - 8th GACM Colloquium on Computational Mechanics for Young Scientist from Academia and Industry - Proceedings N2 - Due to the short wavelength compared to the dimensions of the structure, the simulation of ultrasonic waves is still a challenging task. A numerical method well suited for this purpose is the semi-analytical Scaled Boundary Finite Element Method (SBFEM). When applying this method, only the boundary of a computational domain is discretized using finite elements, while the interior is described by an analytical ansatz. Hence, the number of degrees of freedom is reduced significantly compared to the classical Finite Element Method (FEM). In recent years, a particular formulation of the SBFEM for the simulation of ultrasonic guided waves was developed. The method constitutes an efficient algorithm for prismatic structures of arbitrary length, such as plates, pipes, or beams. Wave propagation phenomena in such structures can be modeled for isotropic and anisotropic inhomogeneous waveguides. Even though the method is an efficient tool for the simulation of guided waves in solid media, a reliable model for the simulation of acoustic wave propagation in fluids as well as acoustic-structure interaction in terms of SBFEM is still missing. In principle, the fluid can be described by a displacement-based formulation and thus be implemented in existing SBFEM algorithms for solid bodies. However, due to the discretization with classical finite elements, spurious modes occur, which cannot be separated from the physical modes straightforwardly. The spurious modes can be suppressed using a penalty parameter. Although very accurate results were achieved for some problems, this procedure has been proven unreliable for certain cases. For this reason, we propose a different approach in this contribution. We employ a pressure model to simulate the acoustic behavior of fluids. The implementation of the pressure model results in a higher effort due to the necessity of incorporating coupling terms, but it presents a stable alternative without spurious modes. The accuracy of the method is demonstrated in comparison with analytical solutions and results obtained using the FEM. T2 - GACM 2019 CY - Kassel, Germany DA - 28.08.2019 KW - Scaled Boundary Finite Element Method KW - Guided Waves KW - Ultrasound KW - Acoustic-Structure Interaction PY - 2019 UR - https://nbn-resolving.org/urn:nbn:de:kobv:b43-497364 UR - https://www.upress.uni-kassel.de/katalog/abstract.php?978-3-7376-5093-9 SN - 978-3-86219-5093-9 DO - https://doi.org/10.19211/KUP9783737650939 SP - 347 EP - 350 AN - OPUS4-49736 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 -