Analytische Chemie
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The Scaled Boundary Finite Element Method is known as an efficient method for the simulation of ultrasonic wave propagation. As to investigate acoustic wave behavior in case of fluid‐structure interaction, a fluid model is implemented in the SBFEM for prismatic structures. To omit coupling terms a displacement‐based formulation is used. Spurious modes, which occur in the solution, are suppressed using a penalty parameter. To verify this formulation dispersion curves obtained with Comsol Multiphysics are compared to results of SBFEM. The results of both methods are in very good agreement
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.
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.
Guided waves (GW) are of great interest for non-destructive testing (NDT) and structural health monitoring (SHM) of engineering structures such as for oil and gas pipelines, rails, aircraft components, adhesive bonds and possibly much more. Development of a technique based on GWs requires careful understanding obtained through modelling and analysis of wave propagation and mode-damage interaction due to the dispersion and multimodal character of GWs. The Scaled Boundary Finite Element Method (SBFEM) is a suitable numerical approach for this purpose allowing calculation of dispersion curves, mode shapes and GW propagation analysis. In this article, the SBFEM is used to analyse wave propagation in a plate consisting of an isotropic aluminium layer bonded as a hybrid to an anisotropic carbon fibre reinforced plastics layer. This hybrid Composite corresponds to one of those considered in a Type III composite pressure vessel used for storing gases, e.g., hydrogen in automotive and aerospace applications. The results show that most of the wave energy can be concentrated in a certain layer depending on the mode used, and by that damage present in this layer can be detected. The results obtained help to understand the wave propagation in multi-layered structures and are important for further development of NDT and SHM for Engineering structures consisting of multiple layers.
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.
In der Zerstörungsfreien Prüfung und der Zustandsüberwachung sind geführte Wellen von großem Interesse, um Fehlstellen zu finden und zu charakterisieren. Die Interaktion der Wellen mit den Fehlstellen kann dabei aufgrund ihrer Komplexität häufig nicht analytisch beschrieben werden. Dies macht numerische Programme neben Experimenten unabdingbar. Aufgrund der kleinen Wellenlänge im Verhältnis zur Bauteilgröße ist jedoch eine effiziente Simulation noch immer Teil der aktiven Forschung.
Um die Effizienz der Simulationsalgorithmen zu steigern, ist es möglich, analytische Annahmen in die Finite Elemente Methode (FEM) zu integrieren. Beispiele für solche Methoden sind die Scaled Boundary Finite Element Method als ein semi-analytisches Verfahren und eXtended Finite Element Method. Diese beiden Möglichkeiten erlauben es, die Wechselwirkungen effizient zu simulieren.
In diesem Beitrag werden verschiedene Wechselwirkungen und Auswertungsmöglichkeiten von geführten Wellen mit Fehlstellen vorgestellt. Hierbei liegt der Fokus auf linearen und nicht-linearen Effekten. Zunächst wird auf Modenkonversion eingegangen und der Frage nachgegangen, ob diese ausreicht, um einen Riss zu charakterisieren. Diese Untersuchungen motivieren dann ein inverses Verfahren, mit dem einige Parameter eines simulierten Risses in einer Folge von Simulationen wieder rekonstruiert werden. Ein zweiter Teil beschäftigt sich mit nicht-linearen Risseffekten. Diese Risseffekte erzeugen im allgemeinen höhere harmonische Wellen. Hier werden Ergebnisse und Filtermethoden zur Auswertung vorgestellt.
Damage Quantification in Aluminium-CFRP Composite Structures using Guided Wave Wavenumber Mapping
(2019)
The use of composite materials is associated not only with the advantages of weight reduction and improved structural performance but also with the risk of barely visible impacts or manufacturing damages. One of the promising techniques for the detection and characterisation of such damages is based on ultrasonic guided wave propagation and analysis. However, the multimodal nature and dispersive behaviour of these waves make their analysis difficult. Various signal processing techniques have been proposed for easier interpretation of guided wave signals and extraction of the necessary information about the damage. One of them is the wavenumber mapping which consists of creating a cartography of the wavenumber of a propagating mode over an inspected area, using a dense wavefield acquisition measured for example with a scanning laser Doppler vibrometer. This technique allows both the quantification of the in-plane size and the depth of damage, for example, impact-induced delamination in composite laminates.
In this contribution, wavenumber mapping is applied to a delaminated aluminium-CFRP composite structure which corresponds to composite-overwrapped pressure vessels used for storing gases in aerospace and automotive industries. The analysis of experimental data obtained from measurements of guided waves propagating in an aluminium-CFRP composite plate with impact-induced damage is performed. The output of the imaging is a three-dimensional representation of the delamination induced by the impact. Good agreement between conventional ultrasonic testing and guided wave damage mapping can be found.
Acoustic-structure interaction in the Scaled Boundary Finite Element Method for primsatic geometries
(2019)
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.
The Spectral Element Method (SEM) has been proven to be an efficient numerical method for solving the wave equation in linear elastic bodies. This efficiency is reduced if a stress singularity is present in the body. For example, re-entrant corners, material interfaces, fixed boundaries, and especially crack tips can cause stress singularities. To preserve the efficiency of the SEM, special solution strategies are required. There are many approaches which consider stress singularities, but comparisons are rare for dynamic problems. Finding an efficient model is an important step for many applications. In particular, applications for structural health monitoring and non-destructive evaluation rely on accurate and efficient crack models.
In this contribution, we present several models to capture singularities in combination with the SEM. The theory behind the models are shortly summarized and we show results for different benchmark problems in two dimensions. The first model deploys a new class of singular elements. For these singular elements, the crack tip approximation is computed based on the static Scaled Boundary Finite Element Method (SBFEM). The second model uses the continued‐fraction‐based SBFEM, while the third model uses an hp-refinement near the singularity. The models are compared among each other and evaluated in terms of their respective efficiency and accuracy.