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- Scaled boundary finite element method (10)
- Dispersion (9)
- Guided waves (8)
- Lamb waves (4)
- Scaled Boundary Finite Element Method (3)
- Simulation (3)
- Crack detection (2)
- Cracks (2)
- Cylinders (2)
- Non-destructive testing (2)
Organisationseinheit der BAM
The CCQM-K148.a comparison was coordinated by the BIPM on behalf of the CCQM Organic Analysis Working Group for NMIs and DIs which provide measurement services in organic analysis under the CIPM MRA. It was undertaken as a "Track A" comparison within the OAWG strategic plan. CCQM-K148.a demonstrates capabilities for assigning the mass fraction content of a solid organic compound having moderate molecular complexity, where the compound has a molar mass in the range (75 - 500) g/mol and is non-polar (pKow < −2), when present as the primary organic component in a neat organic solid and where the mass fraction content of the primary component in the material is in excess of 950 mg/g.
Participants were required to report the mass fraction of Bisphenol A present in one supplied unit of the comparison material. Participants using a mass balance method for the assignment were also required to report their assignments of the impurity components present in the material. Methods used by the seventeen participating NMIs or DIs were predominantly based on either stand-alone mass balance (summation of impurities) or qNMR approaches, or the combination of data obtained using both methods. The results obtained using thermal methods based on freezing-point depression methods were also reported by a limited number of participants. There was excellent agreement between assignments obtained using all three approaches to assign the BPA content.
The assignment of the values for the mass fraction content of BPA consistent with the KCRV was achieved by most of the comparison participants with an associated relative standard uncertainty in the assigned value in the range (0.1 - 0.5)%.
Numerical modelling of lamb waves in cracked plates using the scaled boundary finite element method
(2013)
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.
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.
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.
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.
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.
The primary crystallite size of titania powder relates to its properties in a number of applications. Transmission electron microscopy was used in this interlaboratory comparison (ILC) to measure primary crystallite size and shape distributions for a commercial aggregated titania powder. Data of four size descriptors and two shape descriptors were evaluated across nine laboratories. Data repeatability and reproducibility was evaluated by analysis of variance. One-third of the laboratory pairs had similar size descriptor data, but 83% of the pairs had similar aspect ratio data. Scale descriptor distributions were generally unimodal and were well-described by lognormal reference models. Shape descriptor distributions were multi-modal but data visualization plots demonstrated that the Weibull distribution was preferred to the normal distribution. For the equivalent circular diameter size descriptor, measurement uncertainties of the lognormal distribution scale and width parameters were 9.5% and 22%, respectively. For the aspect ratio shape descriptor, the measurement uncertainties of the Weibull distribution scale and width parameters were 7.0% and 26%, respectively. Both measurement uncertainty estimates and data visualizations should be used to analyze size and shape distributions of particles on the nanoscale.
In this paper, a method is presented for the numerical computation of dispersion properties and mode shapes of guided waves in plate structures. The formulation is based on the Scaled Boundary Finite Element Method. The through-thickness direction of the plate is discretized in the finite element sense, while the direction of propagation is described analytically. This leads to a standard eigenvalue problem for the calculation of wave numbers. The proposed method is not limited to homogeneous plates. Multi-layered composites as well as structures with continuously varying material parameters in the direction of thickness can be modeled without essential changes in the formulation. Higher-order elements have been employed for the finite element discretization, leading to excellent convergence for complex structures. It is shown by numerical examples that this method provides highly accurate results with a small number of nodes while avoiding numerical problems and instabilities.