TY - CONF A1 - Saputra, A. A. A1 - Birk, C. A1 - Song, C. A1 - Gravenkamp, Hauke ED - Samali, ED - Attard, ED - Song, T1 - Numerical modelling of lamb waves in cracked plates using the scaled boundary finite element method 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 - Lamb waves KW - Scaled boundary finite element method KW - Crack detection KW - Continued fractions PY - 2013 SN - 978-0-415-63318-5 SP - 927 EP - 932 PB - Taylor & Francis AN - OPUS4-27751 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 - Gravenkamp, Hauke A1 - Birk, C. A1 - Song, C. T1 - Computation of dispersion curves for embedded waveguides using a dashpot boundary condition JF - The journal of the Acoustical Society of America N2 - In this paper a numerical approach is presented to compute dispersion curves for solid waveguides coupled to an infinite medium. The derivation is based on the scaled boundary finite element method that has been developed previously for waveguides with stress-free surfaces. The effect of the surrounding medium is accounted for by introducing a dashpot boundary condition at the interface between the waveguide and the adjoining medium. The damping coefficients are derived from the acoustic impedances of the surrounding medium. Results are validated using an improved implementation of an absorbing region. Since no discretization of the surrounding medium is required for the dashpot approach, the required number of degrees of freedom is typically 10 to 50 times smaller compared to the absorbing region. When compared to other finite element based results presented in the literature, the number of degrees of freedom can be reduced by as much as a factor of 4000. PY - 2014 DO - https://doi.org/10.1121/1.4864303 SN - 0001-4966 SN - 1520-8524 VL - 135 IS - 3 SP - 1127 EP - 1138 PB - American Institute of Physics CY - Melville, NY AN - OPUS4-30324 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Gravenkamp, Hauke A1 - Birk, C. A1 - Song, C. T1 - The computation of dispersion relations for axisymmetric waveguides using the Scaled Boundary Finite Element Method JF - Ultrasonics N2 - This paper addresses the computation of dispersion curves and mode shapes of elastic guided waves in axisymmetric waveguides. The approach is based on a Scaled Boundary Finite Element formulation, that has previously been presented for plate structures and general three-dimensional waveguides with complex cross-section. The formulation leads to a Hamiltonian eigenvalue problem for the computation of wavenumbers and displacement amplitudes, that can be solved very efficiently. In the axisymmetric representation, only the radial direction in a cylindrical coordinate system has to be discretized, while the circumferential direction as well as the direction of propagation are described analytically. It is demonstrated, how the computational costs can drastically be reduced by employing spectral elements of extremely high order. Additionally, an alternative formulation is presented, that leads to real coefficient matrices. It is discussed, how these two approaches affect the computational efficiency, depending on the elasticity matrix. In the case of solid cylinders, the singularity of the governing equations that occurs in the center of the cross-section is avoided by changing the quadrature scheme. Numerical examples show the applicability of the approach to homogeneous as well as layered structures with isotropic or anisotropic material behavior. KW - Guided waves KW - Numerical methods KW - Scaled Boundary Finite Element Method KW - Dispersion KW - Cylinders PY - 2014 DO - https://doi.org/10.1016/j.ultras.2014.02.004 SN - 0041-624x VL - 54 IS - 5 SP - 1373 EP - 1385 PB - Elsevier B.V. CY - Amsterdam AN - OPUS4-30491 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Gravenkamp, Hauke A1 - Birk, C. A1 - Song, C. T1 - Numerical modeling of elastic waveguides coupled to infinite fluid media using exact boundary conditions JF - Computers & structures N2 - The simulation of guided waves in plate structures and cylinders coupled to infinite fluids is addressed. The approach is based on the Scaled Boundary Finite Element Method. Only a straight line is discretized that represents the through-thickness direction or the radial direction. The surrounding fluid is accounted for by employing a damping boundary condition that is based on the analytical description of the radiation impedance. Since the radiation impedance is a function of the wavenumber in the waveguide, an iterative solution procedure is applied. The algorithm is highly efficient while the results are in agreement with the Global Matrix Method. KW - Guided waves KW - Embedded KW - Fluid KW - Ultrasound KW - Scaled boundary finite element method PY - 2014 DO - https://doi.org/10.1016/j.compstruc.2014.05.010 SN - 0045-7949 SN - 0366-7138 VL - 141 SP - 36 EP - 45 PB - Pergamon Press CY - Oxford AN - OPUS4-30896 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Gravenkamp, Hauke A1 - Birk, C. A1 - Song, C. T1 - Simulation of elastic guided waves interacting with defects in arbitrarily long structures using the scaled boundary finite element method JF - Journal of computational physics N2 - In this paper, an approach is presented to model the propagation of elastic waves and their interaction with defects in plate structures. The formulation is based on the Scaled Boundary Finite Element Method (SBFEM), a general semi-analytical method requiring the discretization of boundaries only. For a homogeneous finite or infinite plate section, only the through-thickness direction of the plate is discretized. To describe a defect, the full boundary of a short plate section of irregular shape is discretized. High-order spectral elements are employed for the discretization. The formulation for infinite plates can model the transmission into an unbounded domain exactly. Results are compared with conventional Finite Element Analyses in both time domain and frequency domain. The presented approach allows for the simulation of complex reflection and scattering phenomena using a very small number of degrees of freedom while the mesh consists of one-dimensional elements only. KW - Scaled Boundary Finite Element Method KW - Guided waves KW - Unbounded domains KW - Cracks PY - 2015 DO - https://doi.org/10.1016/j.jcp.2015.04.032 SN - 0021-9991 SN - 1090-2716 VL - 295 SP - 438 EP - 455 PB - Elsevier Inc. CY - Amsterdam AN - OPUS4-33207 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Gravenkamp, Hauke A1 - Song, C. A1 - Birk, C. T1 - Numerical modeling of waveguides embedded in infinite media T2 - ICSV22 - 22nd International congress on sound and vibration (Proceedings) N2 - This paper presents recently developed approaches for the numerical simulation of guided elastic waves in structures that are embedded in infinite fluid or solid media. The waveguide is described by the Scaled Boundary Finite Element Method, which is a general semi-analytical method that requires discretization of the boundary only. The influence of the surrounding medium on the wave propagation inside the waveguide is accounted for by appropriate boundary conditions. It is demonstrated that for many practical applications a formulation based on simple dashpot boundary conditions yields sufficiently accurate results. To increase accuracy for fluids, an alternative formulation based on exact boundary conditions and inverse iteration is proposed. This approach is of use particularly if the acoustic properties of the waveguide and surrounding material are similar. T2 - ICSV22 - 22nd International congress on sound and vibration CY - Florence, Italy DA - 12.07.2015 PY - 2015 SN - 978-88-88942-48-3 SN - 2329-3675 SP - 1 EP - 5 AN - OPUS4-33829 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Gravenkamp, Hauke A1 - Birk, C. A1 - Van, J. T1 - Modeling ultrasonic waves in elastic waveguides of arbitrary cross-section embedded in infinite solid medium JF - Computers & structures N2 - An approach is presented to model elastic waveguides of arbitrary cross-section coupled to infinite solid media. The formulation is based on the scaled boundary-finite element method. The surrounding medium is approximately accounted for by a dashpot boundary condition derived from the acoustic impedances of the infinite medium. It is discussed under which circumstances this approximation leads to sufficiently accurate results. Computational costs are very low, since the surrounding medium does not require discretization and the number of degrees of freedom on the cross-section is significantly reduced by utilizing higher-order spectral elements. KW - Guided waves KW - Scaled boundary finite element method KW - Leaky waves KW - Ultrasound PY - 2015 DO - https://doi.org/10.1016/j.compstruc.2014.11.007 SN - 0045-7949 SN - 0366-7138 VL - 149 SP - 61 EP - 71 PB - Pergamon Press CY - Oxford AN - OPUS4-32348 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 - 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 -