TY - JOUR A1 - Gravenkamp, Hauke A1 - Man, H. A1 - Song, C. A1 - Prager, Jens T1 - The computation of dispersion relations for three-dimensional elastic waveguides using the scaled boundary finite element method JF - Journal of sound and vibration N2 - In this paper, a numerical approach for the computation of dispersion relations for three-dimensional waveguides with arbitrary cross-section is proposed. The formulation is based on the Scaled Boundary Finite Element Method (SBFEM). It is an extension of the approach previously derived for plate structures. It is shown that the wavenumbers of guided waves in a waveguide can be obtained as the eigenvalues of the Z matrix, which is well known in the SBFEM. The Hamiltonian properties of this matrix are utilized to derive an efficient way to compute the group velocities of propagating waves as eigenvalue derivatives. The cross-section of the waveguide is discretized using higher-order spectral elements. It is discussed in detail how symmetry axes can be utilized to reduce computational costs. In order to sort the solutions at different frequencies, a mode-tracking algorithm is proposed, based on the Padé expansion. KW - Guided waves KW - Simulation KW - Dispersion KW - Scaled boundary finite element method PY - 2013 DO - https://doi.org/10.1016/j.jsv.2013.02.007 SN - 0022-460X SN - 1095-8568 VL - 332 IS - 15 SP - 3756 EP - 3771 PB - Academic Press CY - London AN - OPUS4-28837 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Gravenkamp, Hauke A1 - Prager, Jens A1 - Man, H. A1 - Birk, C. A1 - Song, C. ED - Samali, ED - Attard, ED - Song, T1 - Numerical computation of dispersion relations in three-dimensional waveguides T2 - ACMSM 22 - Australasian conference on the mechanics of structures and materials - From materials to structures: advancement through innovation T2 - ACMSM 22 - Australasian conference on the mechanics of structures and materials CY - Sydney, Australia DA - 2012-12-11 KW - Guided waves KW - Dispersion KW - Scaled boundary finite element method KW - Non-destructive testing KW - Structural health monitoring PY - 2013 SN - 978-0-415-63318-5 SP - 897 EP - 902 PB - Taylor & Francis AN - OPUS4-27752 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Bulling, Jannis A1 - Gravenkamp, H. A1 - Birk, C. T1 - A high-order finite element technique with automatic treatment of stress singularities by semi-analytical enrichment JF - Computer Methods in Applied Mechanics and Engineering N2 - This paper presents an approach to the automatic enrichment of finite elements in the vicinity of a stress singularity. The enrichment consists of semi-analytical singular modes constructed using the Scaled Boundary Finite Element Method (SBFEM). In contrast to analytical methods, the SBFEM provides modes for inhomogeneous and anisotropic materials without additional effort. The finite element basis can be of arbitrary order and remains unaltered by the enrichment. The approach requires enrichment in only one layer of elements around a node. Due to the compatibility of SBFEM with FEM, there is no Need for transitional elements, and there are no parasitic terms. The approach is tested for several benchmark problems. The stress intensity factors are computed based on techniques inspired by the SBFEM. The proposed procedure is compared to a Standard finite element implementation and shows a significant improvement in the error of the displacement field for problems involving singular stresses. KW - Enriched finite element method KW - Scaled boundary finite element method KW - Stress intensity factors KW - Singular stress PY - 2019 DO - https://doi.org/10.1016/j.cma.2019.06.025 VL - 355 SP - 135 EP - 156 PB - Elsevier B.V. AN - OPUS4-48979 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Bulling, Jannis A1 - Gravenkamp, H. T1 - Comparison of different models for stress singularities in higher order finite element methods for elastic waves JF - PAMM - Publikationen der Proceedings der GAMM-Jahrestagungen N2 - In this contribution, we present three models to capture singularities in combination with the Spectral Element Method. The first model, the continued-fraction-based Scaled Boundary Finite Element Method, the second model, a new approach based on enrichment with static modes, and the third model, which uses an hp-refinement near the singularity, are compared among each other and evaluated in terms of their respective efficiency and accuracy. T2 - GAMM 2019 CY - Wien, Austria DA - 18.02.2019 KW - Enriched finite element method KW - Scaled boundary finite element method PY - 2019 DO - https://doi.org/10.1002/pamm.201900095 VL - 19 IS - 1 SP - 1 EP - 2 PB - Wiley-VHC AN - OPUS4-49794 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 - JOUR A1 - Krome, Fabian A1 - Gravenkamp, H. T1 - A semi-analytical curved element for linear elasticity based on the scaled boundary finite element method JF - INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING N2 - This work introduces a semi-analytical formulation for the simulation and modeling of curved structures based on the Scaled Boundary Finite Element Method (SBFEM). This approach adapts the fundamental idea of the SBFEM concept to scale a boundary to describe a geometry. Until now, scaling in SBFEM has exclusively been performed along a straight coordinate which enlarges, shrinks or shifts a given boundary. In this novel approach, scaling is based on a polar or cylindrical coordinate system such that a boundary is shifted along a curved scaling direction. The derived formulations are used to compute the static and dynamic stiffness matrices of homogeneous curved structures. The resulting elements can be coupled to general SBFEM or FEM domains. For elastodynamic problems computations are performed in the frequency domain. Results of this work are validated using the Global Matrix Method and Standard Finite Element analysis. KW - Scaled boundary finite element method KW - Elasticity KW - Curved structures PY - 2017 DO - https://doi.org/10.1002/nme.5306 SN - 0029-5981 SN - 1097-0207 VL - 109 IS - 6 SP - 790 EP - 808 PB - WILEY-BLACKWELL AN - OPUS4-40170 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Krome, Fabian A1 - Gravenkamp, H. A1 - Birk, C. T1 - Prismatic semi-analytical elements for the simulation of linear elastic JF - Computers and Structures N2 - This work addresses the computation of stiffness matrices for general prismatic structures with an arbitrary cross section. The presented approach is based on the scaled boundary finite element method (SBFEM), a semi-analytical method, which can be used to model structures by only discretizing the boundary of a domain. For prismatic structures, the process is further simplified, as only the cross section of the structure has to be discretized. Thus, a particular semi-analytical finite element is constructed for bounded and unbounded domains. The proposed approach leads to a frequency-dependent stiffness matrix. This stiffness matrix can easily be coupled to other prismatic SBFEM domains or general SBFEM domains. Necessary modifications to include forces along the scaling direction, such as body loads, are addressed. The results of the proposed approach are compared to those of traditional FEM models obtained using commercially available software. KW - Scaled boundary finite element method KW - Elasticity KW - Prismatic structures KW - Body-loads PY - 2017 DO - https://doi.org/10.1016/j.compstruc.2017.06.015 VL - 192 SP - 83 EP - 95 PB - Elsevier Ltd. AN - OPUS4-43415 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Lozano, Daniel A1 - Bulling, Jannis A1 - Asokkumar, A. A1 - Gravenkamp, H. A1 - Birk, C. T1 - 3D simulations of ultrasonic waves in plates using the scaled boundary finite element method and high-order transition elements JF - Wave Motion N2 - It can be difficult to efficiently model ultrasonic waves in 3D structures, especially when the computational model needs to account for complex geometries. This contribution presents a solution based on the Scaled Boundary Finite Element Method (SBFEM). It is a numerical tool suitable for elastodynamic problems. A space-tree discretisation, namely quad-trees, is used. This technique allows the decomposition of an image into quadrilaterals or quads, which are extruded to generate the 3D plate geometry. In particular, small quads resolve regions with discontinuities, allowing them to represent fine details in the structure. Moreover, this meshing technique allows for exploiting cell similarities, making the calculation procedure more efficient. The space-tree discretisations are generated from a high-resolution image containing all the information about damaged regions or boundary conditions. The resulting SBFEM polyhedral domains employ transition elements to ensure correct coupling between cells of different sizes. The analytical solution of a cylindrical scatterer serves as a reference to validate the proposed approach. Other examples also demonstrate the validity of the methodology and its flexibility. KW - High-order transition elements KW - Image-based models KW - Wave propagation KW - Scaled boundary finite element method PY - 2023 DO - https://doi.org/10.1016/j.wavemoti.2023.103158 VL - 120 SP - 1 EP - 20 PB - Elsevier B.V. AN - OPUS4-57768 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER -