Filtern
Dokumenttyp
- Beitrag zu einem Tagungsband (10)
- Vortrag (6)
- Zeitschriftenartikel (5)
Schlagworte
Organisationseinheit der BAM
This note studies the accuracy of Isogeometric Analysis (IGA) applied in the simulation of incompressible flows around a cylinder in two and three dimensions. Quantities of interest, like the drag coefficient, the lift coefficient, and the difference of the pressure between the front and the back of the cylinder are monitored. Results computed with standard finite element methods are used for comparison.
This paper addresses the computation of dispersion curves, mode shapes and propagation of elastic guided waves. It summarizes the approaches based on the Scaled Boundary Finite Element Method.
Descriptions for plates, rods, pipelines and waveguides with an arbitrary cross section are included. The important steps for the approximation of the displacement in bounded and unbounded domains are stated. The grid generation process is explained. It is highlighted that the Scaled Boundary Finite Element Method is very efficient, if large portions of the domain are either straight or with a constant curvature. The computation of dispersion curves for layered structures is presented.
The application of waveguides for acoustic measuring technologies and the development of non-destructive evaluation techniques with guided ultrasonic waves for plate like materials like carbon fiber reinforced plastic shells and layered structures require a good understanding of acoustic wave propagation inside the material. The well-known Finite Element Method can be used for simulations, however at least for higher frequencies, the ratio of wavelength and geometrical dimension demands a time-consuming fine grid. Using commercial simulation tools the computational costs increase considerably for ultrasonic frequencies.
In the recent years, the Federal Institute for Materials Research and Testing has developed a very efficient alternative for simulating acoustic wave propagation particularly in wave guides by extending the Scaled Boundary Finite Element Method (SBFEM). The SBFEM as a semi-analytical method has one main advantage over the classical Finite Element Method: It only demands a discretization of the boundary instead of the whole domain. This is pictured in the figures below. The method is still related to the Finite Element Method and uses their well-known solving strategies. SBFEM is shown to be highly efficient, especially in the frequency domain. Additionally, the efficiency can be increased by using higher-order spectral elements. In plates and cylinders, the SBFEM can be used to animate propagating modes and computes their wavenumber.
In this contribution, we present a short introduction into the basics of SBFEM formulation of the dynamic elastic wave equation. The applicability and efficiency of the approach is demonstrated by applying the method to layered structures and different wave guide geometries. As one example we present the wave propagation in a typical adhesive joint of different metal sheets as common in new designs in automotive industry. The analysis comprises the computation of dispersion curves as starting point of every development of non-destructive testing techniques for inspecting such structures as well as the analysis of the propagating modes. Additional examples presented handle special cases for axis-symmetric geometries, such as pipes and cylindrical rods which are common in various acoustic measurement applications.
The Scaled Boundary Finite Element Method (SBFEM) is a semi-analytical method that shows promising results in modelling of guided ultrasonic waves. Efficiency and low computational cost of the method are achieved by a discretisation of the boundary of a computational domain only, whereas for the domain itself the analytical solution is used. By means of the SBFEM different types of defects, e.g. cracks, pores, delamination, corrosion, integrated into a structure consisting of anisotropic and isotropic materials can be modelled.
In this contribution, the SBFEM is used to analyse the propagation of guided waves in a structure consisting of an isotropic metal bonded to anisotropic carbon fibre reinforced material. The method allows appropriate wave types (modes) to be identified and to analyse their interaction with different defects. Results obtained are used to develop a structural health monitoring system for composite pressure vessels used in automotive and aerospace industries.
In Non-Destructive Testing, ultrasonic waves are commonly used to identify flaws and cracks.
In plates, shells, pipes and other geometries guided waves can be used to test the whole structure at once. In these tests, the input and response signal can have a nonlinear relationship due to cracks. At least for higher deflections, the propagating wave excites each side of the crack in such a way that it hits the other side. This clapping generally leads to a generation of higher harmonic waves and is referred to Contact Acoustic Nonlinearity (CAN). To get a better insight into the salient physics of the effect numerical simulations are necessary.
In the recent years, the Scaled Boundary Finite Element Method (SBFEM) was introduced to efficiently simulate wave propagation. The main advantage of the method is an easy grid generation process because the domain is discretized with arbitrary polygons instead of the triangles and rectangles. Another advantage is the possibility to model crack tips elegantly without additional workload. The SBFEM approach is still related to the Finite Element Method and uses similar techniques. The method is very efficient using high-order-spectral elements.
In this contribution, we present a short introduction into the basics of SBFEM formulation of the dynamic elastic wave equation. The SBFEM is then extended for modeling the non-linear behavior of crack clapping. Different approaches with increasing complexity are presented and assessed with respect to numerical stability.
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
Damit eine Simulationsrechnung, beispielsweise mit einer FEM-Software, eine ausreichend hohe Genauigkeit erreicht, muss vorausgesetzt werden, dass die Modellparameter eine sehr hohe Güte aufweisen. Die genaue Kenntnis der Materialparameter ist dabei von besonderer Bedeutung. Um diese Parameter bestimmen zu können, müssen die verwendeten Werkstoffe messtechnisch charakterisiert werden. Neben anderen Ansätzen sind dafür akustische Verfahren im Ultraschallbereich geeignet. Für dünnwandige und plattenförmige Materialien können aus den sich ausbreitenden geführten Wellen messtechnisch Dispersionskurven bestimmt und aus diesen die Materialparameter abgeleitet werden.
Da für die Signalverarbeitung und für Optimierungsaufgaben aktuell zunehmend Machine Learning Tools zum Einsatz kommen, stellt sich die Frage, ob diese Werkzeuge auch für die Ermittlung der Materialparameter aus den gemessenen Dispersionskurven eingesetzt werden können.
In der vorgestellten Untersuchung soll ein Convolutional Neural Network aufgestellt werden, welches aus Dispersionsbildern Muster extrahiert und aus diesen eine Schätzung für die Materialparameter ermittelt. Um die Machbarkeit dieses Ansatzes zu prüfen, werden zunächst nur isotrope Materialien betrachtet. Für das Netz werden mit der Scaled-Boundary-Finite-Element-Methode synthetische Daten für das Trainieren und Validieren generiert. Zusätzlich werden die Hyperparameter des neuronalen Netzes variiert, um ein optimales Model für die Schätzung zu finden. Anschließend kann das Netz mit experimentellen Daten getestet und das Ergebnis hinsichtlich der Genauigkeit bewertet werden.
Die Scaled Boundary Finite Elemente Methode (SBFEM) ist eine semi-analytische Methode, die speziell für Modellierung von geführten Wellen weiterentwickelt und optimiert wurde. Da nur den Rand der Rechendomäne diskretisiert wird, hat die SBFEM einen geringen Rechenaufwand. In diesem Beitrag wird die SBFEM benutzt, um die Ausbreitung geführter Wellen in einer Metall-Faserverbund-Werkstoffstruktur zu analysieren. Mittels der SBFEM ist es möglich, verschiede Fehlertypen, z.B. Ermüdungsrisse, Poren, Delaminationen, Korrosion, in das numerische Modell zu integrieren und damit Defekt-Mode-Wechselwirkung zu analysieren. Die Ergebnisse wurden für die Entwicklung einer Methode zur Zustandsüberwachung von Composite-Druckbehältern verwendet.