Propagation of in-plane waves in an isotropic panel with a crack

SUMMARYAn accurate and efficient simulation of wave propagation phenomena plays an important role in different engineering disciplines. In structural health monitoring, for example, ultrasonic guided waves are used to detect and localize damage and to assess the structural integrity of the component part under consideration. Because of the complexity of real structures, the numerical simulation of structural health monitoring systems is a computationally demanding task. Therefore, to facilitate the analysis of wave propagation phenomena, the authors propose to combine the finite cell method with the spectral element method. The ensuing novel method is referred to as the spectral cell method. Because it does not rely on body‐fitted meshes, the resulting approach eliminates all discretization difficulties encountered in conventional finite element methods. Moreover, with the aid of mass lumping, it paves the way for the use of explicit time‐integration algorithms. In the first part of the paper, we show that using a lumped mass matrix instead of the consistent one has no detrimental effect on the accuracy of the spectral element method. We introduce the spectral cell method in the second part, showing that, when applied to wave propagation analysis, the spectral cell method yields results comparable with other standard higher order finite element approaches.Copyright © 2014 John Wiley & Sons, Ltd.

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“…Spectral elements employing the GLL grid have been proposed by Komatitsch and Tromp , Cohen , Zak et al . , Kudela et al . , Peng et al .…”

Section: The Finite and The Spectral Element Methodsmentioning

confidence: 99%

“…This nodal distribution is generally referred to as a GLL grid. Spectral elements employing the GLL grid have been proposed by Komatitsch and Tromp [43], Cohen [73], Zak et al [74], Kudela et al [75], Peng et al [39], and Ha and Chang [76], to mention just a few.…”

Section: Spectral Element Methodsmentioning

confidence: 99%

Numerical analysis of Lamb waves using the finite and spectral cell methods

Duczek

Joulaian

Düster

et al. 2014

Int. J. Numer. Meth. Engng

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“…Lagrangian polynomials based on the GP-, GLL-and CGL-grid do not show such a behavior. The GLL-grid is quite popular in applications (see [12,13,14] and many more), since in conjunction with the GLL-quadrature rule it enables the possibility to diagonalize the mass matrix through a slight under-integration [13]. Moreover, one can easily see that at the GLL-distribution the shape function values are not only equal to one at their corresponding nodes, but also reach their maxima at these points.…”

Section: Lagrange Shape Functionsmentioning

confidence: 99%

“…Besides the trivial choice of an equispaced distribution of nodes, various other suggestions of nodal placements are proposed in the literature, such as the Gauss-LobattoLegendre points [12,14], the Gauss points [13] or the Chebyshev-Gauss-Lobatto points [11,15]. The aim of this paper is to figure out how the solution of a problem is altered by the underlying nodal distribution of the Lagrangian polynomials.…”

Section: Introductionmentioning

confidence: 99%

Testing of Higher Order Finite Elements Based on Lagrange Polynomials in Dependence of the Underlying Nodal Grid

Schmicker¹,

Vivar-Perez²,

Gabbert³

2014

Proceedings of 10th World Congress on Computational Mechanics

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Abstract. The paper deals with the investigation of a higher order finite element method utilizing Lagrangian interpolation polynomials as shape functions, also often referred to as spectral element method (SEM). The main concern is to analyze the influence of the underlying nodal distribution on the convergence, performance and stability properties of the solution. To this end four different nodal configurations are investigated, namely the equispaced grid (EQ), the Gauss point grid (GP), the Gauss-Lobatto-Legendre grid (GLL) and the

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“…Zak et al. [4] discussed a concept for crack identification based on numerical simulation of in‐plane wave propagation. As a result of research carried out by Chang and his co‐workers in this area [5, 6], a product named SMART Layer® has been commercialised and next successfully utilised for detection of growing fatigue cracks in aluminium [7, 8] and bolt loosening in composite [9, 10] panels.…”

Section: Introductionmentioning

confidence: 99%

Lamb Waves for Damage Localisation in Panels

Wandowski

Kudela

Malinowski

et al. 2011

Strain

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In this study, Lamb wave propagation phenomena have been used to localise discontinuities in aluminium and composite panels. For that purpose, piezoelectric transducers have been used to excite and register Lamb waves in the panels. Excited waves that propagate and reflect from the panel edges and discontinuities were registered by piezoelectric sensors as voltage changes in time. Three different experiments have been conducted to investigate the wave propagation phenomena. In the first experiment, the attenuation and dispersion of Lamb waves in the aluminium panel has been studied. The second experiment has been oriented to localise an additional mass attached to the same panel. A dedicated signal-processing algorithm has been developed to aid the localisation procedure that allowed to extract relevant features of the discontinuity. The algorithm has been tested on signals from the panel with and without the additional mass. The results obtained have been compared to find the position of the discontinuity. The third experiment concerned a more realistic damage scenario when piezoelectric transducers have been arranged as a clock-like array to find a crack in a composite panel.

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Propagation of in-plane waves in an isotropic panel with a crack

Cited by 63 publications

References 28 publications

Numerical analysis of Lamb waves using the finite and spectral cell methods

Numerical analysis of Lamb waves using the finite and spectral cell methods

Testing of Higher Order Finite Elements Based on Lagrange Polynomials in Dependence of the Underlying Nodal Grid

Lamb Waves for Damage Localisation in Panels

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