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Journal articles on the topic 'Spectral element modelling'

Author: Grafiati

Published: 25 May 2024

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1

Seriani, G. "3-D spectral element-by-element wave modelling on Cray T3E." Physics and Chemistry of the Earth, Part A: Solid Earth and Geodesy 24, no. 3 (January 1999): 241–45. http://dx.doi.org/10.1016/s1464-1895(99)00025-3.

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2

Griffith, M. D., K. Hourigan, and M. C. Thompson. "Modelling blockage effects using a spectral element method." ANZIAM Journal 46 (April 21, 2005): 167. http://dx.doi.org/10.21914/anziamj.v46i0.954.

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3

Fiborek, Piotr, Paweł H. Malinowski, Paweł Kudela, Tomasz Wandowski, and Wiesław M. Ostachowicz. "Time-domain spectral element method for modelling of the electromechanical impedance of disbonded composites." Journal of Intelligent Material Systems and Structures 29, no. 16 (February 27, 2018): 3214–21. http://dx.doi.org/10.1177/1045389x18758193.

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The research focuses on the electromechanical impedance method. The electromechanical impedance method can be treated as non-destructive testing or structural health monitoring approach. It is important to have a reliable tool that allows verifying the integrity of the investigated objects. The electromechanical impedance method was applied here to assess the carbon fibre–reinforced polymer samples. The single and adhesively bonded samples were investigated. In the reported research, the electromechanical impedance spectra up to 5 MHz were considered. The investigation comprised of modelling using spectral element method and experimental measurements. Numerical and experimental spectra were analysed. Differences in spectra caused by differences in considered samples were observed.

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4

Grabowska, Joanna, and Marek Krawczuk. "Identification of Discontinuities in Composite Rods and Beams Based on Lamb Wave Propagation." Key Engineering Materials 293-294 (September 2005): 517–24. http://dx.doi.org/10.4028/www.scientific.net/kem.293-294.517.

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The article presents a method of damage identification in composite rods and beams based on the analysis of changes in Lamb wave propagation. For modelling of the problem the spectral element method is used. Spectral elements of rod and beam suitable for modelling the composites are employed. In the presented paper the following discontinuities are analysed: the fatigue open and not propagating crack, changes in the cross-section area, material discontinuities, various fibres volume and angle. The influence of discontinuities on the Lamb wave propagation processes is analysed.

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5

Kudela, Pawel, and Wiesław M. Ostachowicz. "Wave Propagation Modelling in Composite Plates." Applied Mechanics and Materials 9 (October 2007): 89–104. http://dx.doi.org/10.4028/www.scientific.net/amm.9.89.

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The paper presents results of numerical simulation for transverse elastic waves corresponding to A0 mode of Lamb waves propagating in a composite plate. This problem is solved by using the Spectral Finite Element Method. Spectral plate elements with 36 nodes defined at Gauss-Lobatto-Legendre points are used. As a consequence of selecting Lagrange polynomials discrete orthogonality guaranteed leading to a diagonal mass matrix. This results in a crucial reduction of numerical operations required for a chosen time integration scheme. Numerical calculations have been carried out for various orientations of reinforcing fibres within the plate as well as for various fibre volumes fractions. The paper shows that the velocities of transverse elastic waves in composite materials are functions of the fibre orientation and the fibre volume fraction.

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6

Schulte, Rolf T., Ke Jia Xing, and Claus Peter Fritzen. "Spectral Element Modelling of Wave Propagation and Impedance Based SHM Systems." Key Engineering Materials 413-414 (June 2009): 683–90. http://dx.doi.org/10.4028/www.scientific.net/kem.413-414.683.

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In recent years many SHM approaches based on elastic waves that are generated and sensed by surface-bonded piezoelectric patches have been developed. Some of those utilize wave propagation phenomena; others use changes in the electromechanical impedance to detect structural damage. The capability of most approaches strongly depends on adequate choice of SHM system parameters like excitation signals and actuator/sensor types and positions. For this reason there is a growing interest in efficient and accurate simulation tools to shorten time and cost of the necessary tedious pretests. To detect small damage generally high frequency excitation signals have to be used. Because of this a very dense finite element mesh is required for an accurate simulation. As a consequence a conventional finite element simulation becomes computationally inefficient. A new approach that seems to be more promising is the time domain spectral element method. This contribution presents the theoretical background and some results of numerical calculations of the propagation of waves. The simulation is performed using the spectral element method (SEM), which leads to a diagonal mass matrix. Besides a significant saving of memory this leads to a crucial reduction of complexity of the time integration algorithm for the wave propagation calculation. A new approach to simulate the E/M impedance using time domain spectral elements is shown. An example demonstrates a good correlation of simulation and measurement data, so that the proposed simulation methodology seems to be a promising tool to make impedance based SHM systems more efficient, especially regarding the necessary parameter studies.

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7

von Winckel, G., S. Krishna, and E. A. Coutsias. "Spectral element modeling of semiconductor heterostructures." Mathematical and Computer Modelling 43, no. 5-6 (March 2006): 582–91. http://dx.doi.org/10.1016/j.mcm.2005.05.028.

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8

Kirby, Robert M., and Spencer J. Sherwin. "Stabilisation of spectral/hp element methods through spectral vanishing viscosity: Application to fluid mechanics modelling." Computer Methods in Applied Mechanics and Engineering 195, no. 23-24 (April 2006): 3128–44. http://dx.doi.org/10.1016/j.cma.2004.09.019.

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9

Żak, A., and M. Krawczuk. "Assessment of rod behaviour theories used in spectral finite element modelling." Journal of Sound and Vibration 329, no. 11 (May 2010): 2099–113. http://dx.doi.org/10.1016/j.jsv.2009.12.019.

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10

Eskilsson, C., and S. J. Sherwin. "Discontinuous Galerkin Spectral/hp Element Modelling of Dispersive Shallow Water Systems." Journal of Scientific Computing 22-23, no. 1-3 (June 2005): 269–88. http://dx.doi.org/10.1007/s10915-004-4140-x.

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11

Wasberg, Carl Erik, Thor Gjesdal, Bjørn Anders Pettersson Reif, and Øyvind Andreassen. "Variational multiscale turbulence modelling in a high order spectral element method." Journal of Computational Physics 228, no. 19 (October 2009): 7333–56. http://dx.doi.org/10.1016/j.jcp.2009.06.029.

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12

Schulte, R. T., and C. P. Fritzen. "Modelling of Wave-Based SHM Systems Using the Spectral Element Method." PAMM 10, no. 1 (November 16, 2010): 15–18. http://dx.doi.org/10.1002/pamm.201010005.

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13

Ostachowicz, Wiesław M., Marek Krawczuk, and Magdalena Palacz. "Experimental and Numerical Investigation of Wave Propagation in Composite Beam with an Additional Mass." Key Engineering Materials 293-294 (September 2005): 533–40. http://dx.doi.org/10.4028/www.scientific.net/kem.293-294.533.

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The article is to show results of numerical and experimental examination of changes in wave propagation in a composite rod with additional mass. For numerical modelling the spectral element method is used. For experimental verification the IFFM PAS laboratory equipment was used. As actuators and sensors PZT elements were utilised. The results obtained via numerical and experimental simulations are compared and discussed.

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14

Scott, Jennifer A. "Multilevel hybrid spectral element ordering algorithms." Communications in Numerical Methods in Engineering 21, no. 5 (March 14, 2005): 233–45. http://dx.doi.org/10.1002/cnm.740.

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15

Wang, Ying, and Hong Hao. "Modelling of Guided Wave Propagation with Spectral Element: Application in Structural Engineering." Applied Mechanics and Materials 553 (May 2014): 687–92. http://dx.doi.org/10.4028/www.scientific.net/amm.553.687.

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Among many structural health monitoring (SHM) methods, guided wave (GW) based method has been found as an effective and efficient way to detect incipient damages. In comparison with other widely used SHM methods, it can propagate in a relatively long range and be sensitive to small damages. Proper use of this technique requires good knowledge of the effects of damage on the wave characteristics. This needs accurate and computationally efficient modeling of guide wave propagation in structures. A number of different numerical computational techniques have been developed for the analysis of wave propagation in a structure. Among them, Spectral Element Method (SEM) has been proposed as an efficient simulation technique. This paper will focus on the application of GW method and SEM in structural health monitoring. The GW experiments on several typical structures will be introduced first. Then, the modeling techniques by using SEM are discussed.

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16

Afanasiev, Michael, Christian Boehm, Martin van Driel, Lion Krischer, Max Rietmann, Dave A. May, Matthew G. Knepley, and Andreas Fichtner. "Modular and flexible spectral-element waveform modelling in two and three dimensions." Geophysical Journal International 216, no. 3 (November 12, 2018): 1675–92. http://dx.doi.org/10.1093/gji/ggy469.

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17

Zou, Fangxin, and M. H. Aliabadi. "On modelling three-dimensional elastodynamic wave propagation with boundary spectral element method." European Journal of Computational Mechanics 27, no. 3 (May 4, 2018): 204–28. http://dx.doi.org/10.1080/17797179.2018.1485340.

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18

Haney, Matthew, Roel Snieder, Jean-Paul Ampuero, and Ronny Hofmann. "Spectral element modelling of fault-plane reflections arising from fluid pressure distributions." Geophysical Journal International 170, no. 2 (August 2007): 933–51. http://dx.doi.org/10.1111/j.1365-246x.2007.03437.x.

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19

Zou, Fangxin, and M. H. Aliabadi. "On modelling three-dimensional piezoelectric smart structures with boundary spectral element method." Smart Materials and Structures 26, no. 5 (April 13, 2017): 055015. http://dx.doi.org/10.1088/1361-665x/aa6664.

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20

Birgersson, F., S. Finnveden, and G. Robert. "Modelling turbulence-induced vibration of pipes with a spectral finite element method." Journal of Sound and Vibration 278, no. 4-5 (December 2004): 749–72. http://dx.doi.org/10.1016/j.jsv.2003.10.024.

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21

Sherwin, S. J., J. Peiró, O. Shah, G. S. Karamanos, and D. J. Doorly. "Computational haemodynamics: geometry and non-newtonian modelling using spectral/hp element methods." Computing and Visualization in Science 3, no. 1-2 (May 2000): 77–83. http://dx.doi.org/10.1007/s007910050054.

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22

Haidvogel, Dale B., Enrique Curchitser, Mohamed Iskandarani, Rowan Hughes, and Mark Taylor. "Global Modelling of the Ocean and Atmosphere Using the Spectral Element Method." Atmosphere-Ocean 35, sup1 (January 1997): 505–31. http://dx.doi.org/10.1080/07055900.1997.9687363.

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23

Wang, Ying, Hong Hao, Xinqun Zhu, and Jinping Ou. "Spectral Element Modelling of Wave Propagation with Boundary and Structural Discontinuity Reflections." Advances in Structural Engineering 15, no. 5 (May 2012): 855–70. http://dx.doi.org/10.1260/1369-4332.15.5.855.

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24

Sprague, M. A., and T. L. Geers. "A spectral-element method for modelling cavitation in transient fluid–structure interaction." International Journal for Numerical Methods in Engineering 60, no. 15 (August 3, 2004): 2467–99. http://dx.doi.org/10.1002/nme.1054.

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25

Lee, U., and J. Park. "Spectral element modelling and analysis of a pipeline conveying internal unsteady fluid." Journal of Fluids and Structures 22, no. 2 (February 2006): 273–92. http://dx.doi.org/10.1016/j.jfluidstructs.2005.09.003.

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26

DOUGLAS, CRAIG C., GUNDOLF HAASE, MOHAMED ISKANDARANI, and STEFAN REITZINGER. "SPECIAL SOLUTION STRATEGIES INSIDE A SPECTRAL ELEMENT OCEAN MODEL." Mathematical Models and Methods in Applied Sciences 13, no. 03 (March 2003): 309–22. http://dx.doi.org/10.1142/s0218202503002519.

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We present three ideas to accelerate the filtering process used in the multilayered Spectral Element Ocean Model (SEOM). We define and analyze a Schur complement preconditioner, a lumping of small entries and an algebraic multigrid (AMG) algorithm. and a algebraic multigrid with patch smoothing algorithm. Finally, we analyze the impact of variations of the Schur complement and AMG methods on memory and computer time.

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27

Virieux, Jean, Henri Calandra, and René-Édouard Plessix. "A review of the spectral, pseudo-spectral, finite-difference and finite-element modelling techniques for geophysical imaging." Geophysical Prospecting 59, no. 5 (August 22, 2011): 794–813. http://dx.doi.org/10.1111/j.1365-2478.2011.00967.x.

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28

Zhu, Jiao, Changchun Yin, Youshan Liu, Yunhe Liu, Ling Liu, Zhilong Yang, and Changkai Qiu. "3-D dc resistivity modelling based on spectral element method with unstructured tetrahedral grids." Geophysical Journal International 220, no. 3 (November 26, 2019): 1748–61. http://dx.doi.org/10.1093/gji/ggz534.

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SUMMARY In this paper, we propose a spectral element method (SEM) based on unstructured tetrahedral grids for direct current (dc) resistivity modelling. Unlike the tensor-product of 1-D Gauss–Lobatto–Legendre (GLL) quadrature in conventional SEM, we use Proriol–Koornwinder–Dubiner (PKD) polynomials to form the high-order basis polynomials on tetrahedral grids. The final basis functions are established by using Vandermonde matrix. Compared to traditional SEM, our method truly takes into account the high precision of spectral method and the flexibility of finite element method with unstructured grids for modelling the complex underground structures. After addressing the theory on the construction of basis functions and interpolation and integration nodes, we validate our algorithm using the analytical solutions for a layered earth model and the results from other methods for multiple geoelectrical models. We further investigate a dual-track scheme for improving the accuracy of our SEM by increasing the order of interpolation polynomials or by refining the grids.

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29

Sabouri, Mania, and Mehdi Dehghan. "Ahkmortar spectral element method for thep-Laplacian equation." Computers & Mathematics with Applications 76, no. 7 (October 2018): 1803–26. http://dx.doi.org/10.1016/j.camwa.2018.07.031.

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30

Bahrami, Saeed, Fatemeh Shirmohammadi, and Mohammad Mehdi Saadatpour. "Vibration analysis of thin shallow shells using spectral element method." Applied Mathematical Modelling 44 (April 2017): 470–80. http://dx.doi.org/10.1016/j.apm.2017.02.001.

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31

Birgersson, F., and S. Finnveden. "A spectral super element for modelling of plate vibration. Part 2: turbulence excitation." Journal of Sound and Vibration 287, no. 1-2 (October 2005): 315–28. http://dx.doi.org/10.1016/j.jsv.2004.11.011.

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32

Birgersson, F., S. Finnveden, and C. M. Nilsson. "A spectral super element for modelling of plate vibration. Part 1: general theory." Journal of Sound and Vibration 287, no. 1-2 (October 2005): 297–314. http://dx.doi.org/10.1016/j.jsv.2004.11.012.

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33

Lee, K. E., K. H. Parker, C. G. Caro, and S. J. Sherwin. "The spectral/hp element modelling of steady flow in non-planar double bends." International Journal for Numerical Methods in Fluids 57, no. 5 (2008): 519–29. http://dx.doi.org/10.1002/fld.1500.

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34

Belytschko, T., and Y. Y. Lu. "Global-local finite element-spectral-boundary element techniques for failure analysis." Computers & Structures 37, no. 2 (January 1990): 133–40. http://dx.doi.org/10.1016/0045-7949(90)90394-h.

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35

Mukherjee, Avisek, Soumyadipta Sarkar, and Arnab Banerjee. "Nonlinear eigenvalue analysis for spectral element method." Computers & Structures 242 (January 2021): 106367. http://dx.doi.org/10.1016/j.compstruc.2020.106367.

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36

Mitra, M., and S. Gopalakrishnan. "Wavelet based spectral finite element modelling and detection of de-lamination in composite beams." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2070 (February 15, 2006): 1721–40. http://dx.doi.org/10.1098/rspa.2005.1653.

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In this paper, a model for composite beam with embedded de-lamination is developed using the wavelet based spectral finite element (WSFE) method particularly for damage detection using wave propagation analysis. The simulated responses are used as surrogate experimental results for the inverse problem of detection of damage using wavelet filtering. The WSFE technique is very similar to the fast fourier transform (FFT) based spectral finite element (FSFE) except that it uses compactly supported Daubechies scaling function approximation in time. Unlike FSFE formulation with periodicity assumption, the wavelet-based method allows imposition of initial values and thus is free from wrap around problems. This helps in analysis of finite length undamped structures, where the FSFE method fails to simulate accurate response. First, numerical experiments are performed to study the effect of de-lamination on the wave propagation characteristics. The responses are simulated for different de-lamination configurations for both broad-band and narrow-band excitations. Next, simulated responses are used for damage detection using wavelet analysis.

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37

Liu, Z. L., T. Menouillard, and T. Belytschko. "An XFEM/Spectral element method for dynamic crack propagation." International Journal of Fracture 169, no. 2 (March 2, 2011): 183–98. http://dx.doi.org/10.1007/s10704-011-9593-y.

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38

Fernandino, M., and C. A. Dorao. "The least squares spectral element method for the Cahn–Hilliard equation." Applied Mathematical Modelling 35, no. 2 (February 2011): 797–806. http://dx.doi.org/10.1016/j.apm.2010.07.034.

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39

Zheng, Yong-Lai, Don Liu, Hui-Li Han, and Mohammad Ferdows. "Spectral element simulations of interactive particles in a fluid." Computers & Mathematics with Applications 77, no. 8 (April 2019): 2029–50. http://dx.doi.org/10.1016/j.camwa.2019.01.005.

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40

Sinclair, Catherine, Stewart Greenhalgh, and Bing Zhou. "2.5D modelling of elastic waves in transversely isotropic media using the spectral element method." Exploration Geophysics 38, no. 4 (December 1, 2007): 225–34. http://dx.doi.org/10.1071/eg07025.

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41

Kudela, Paweł, Arkadiusz Żak, Marek Krawczuk, and Wiesław Ostachowicz. "Modelling of wave propagation in composite plates using the time domain spectral element method." Journal of Sound and Vibration 302, no. 4-5 (May 2007): 728–45. http://dx.doi.org/10.1016/j.jsv.2006.12.016.

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42

Khasawneh, Firas A., and Brian P. Mann. "Stability of delay integro-differential equations using a spectral element method." Mathematical and Computer Modelling 54, no. 9-10 (November 2011): 2493–503. http://dx.doi.org/10.1016/j.mcm.2011.06.009.

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43

Hruby, Petr, Tomas Nahlik, and Dana Smetanova. "Mathematical Modelling of Shafts in Drives." Communications - Scientific letters of the University of Zilina 20, no. 4 (December 31, 2018): 36–40. http://dx.doi.org/10.26552/com.c.2018.4.36-40.

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Propeller shafts of the vehicle's drive transmit a torque to relatively large distances. The shafts are basically long and slender and must be dimensioned not only in terms of torsional stress, but it is also necessary to monitor their resistance to lateral vibration.In the paper, a simple model (of the solved problem) is constructed by the method of physical discretization, which is evident from the nature of the centrifugal force fields' influence on the spectral properties of the shaft. An analytical solving of speed resonances prop shafts test model (whose aim is to obtain values for verification subsequently processed models based on the transfer-matrix method and the finite element method) is performed.

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44

Tsuji, Paul, Jack Poulson, Björn Engquist, and Lexing Ying. "Sweeping preconditioners for elastic wave propagation with spectral element methods." ESAIM: Mathematical Modelling and Numerical Analysis 48, no. 2 (February 20, 2014): 433–47. http://dx.doi.org/10.1051/m2an/2013114.

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45

Xu, Hui, Chris D. Cantwell, Carlos Monteserin, Claes Eskilsson, Allan P. Engsig-Karup, and Spencer J. Sherwin. "Spectral/hp element methods: Recent developments, applications, and perspectives." Journal of Hydrodynamics 30, no. 1 (February 2018): 1–22. http://dx.doi.org/10.1007/s42241-018-0001-1.

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46

Shirmohammadi, Fatemeh, and Saeed Bahrami. "Dynamic response of circular and annular circular plates using spectral element method." Applied Mathematical Modelling 53 (January 2018): 156–66. http://dx.doi.org/10.1016/j.apm.2017.08.014.

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47

Cheng, Candong, Qing Huo Liu, Joon-Ho Lee, and Hisham Z. Massoud. "Spectral Element Method for the Schrödinger-Poisson System." Journal of Computational Electronics 3, no. 3-4 (October 2004): 417–21. http://dx.doi.org/10.1007/s10825-004-7088-z.

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48

Eibert, T. F., and J. L. Volakis. "Fast spectral domain algorithm for hybrid finite element/boundary integral modelling of doubly periodic structures." IEE Proceedings - Microwaves, Antennas and Propagation 147, no. 5 (2000): 329. http://dx.doi.org/10.1049/ip-map:20000706.

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49

Żak, A., and M. Krawczuk. "Certain numerical issues of wave propagation modelling in rods by the Spectral Finite Element Method." Finite Elements in Analysis and Design 47, no. 9 (September 2011): 1036–46. http://dx.doi.org/10.1016/j.finel.2011.03.019.

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50

Gao, Weimin, Lijing Wang, Jolanta K. Coffey, Hongren Wu, and Fugen Daver. "Finite Element Modelling and Experimental Validation of Scratches on Textured Polymer Surfaces." Polymers 13, no. 7 (March 25, 2021): 1022. http://dx.doi.org/10.3390/polym13071022.

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Surface texturing is a common modification method for altering the surface properties of a material. Predicting the response of a textured surface to scratching is significant in surface texturing and material design. In this study, scratches on a thermoplastic material with textured surface are simulated and experimentally tested. The effect of texture on scratch resistance, surface visual appearance, surface deformation and material damage are investigated. Bruise spot scratches on textured surfaces are found at low scratch forces (<3 N) and their size at different scratch forces is approximately the same. There is a critical point between the bruise spot damage and the texture pattern damage caused by continuous scratching. Scratch resistance coefficients and an indentation depth-force pattern are revealed for two textured surfaces. A texture named “Texture CB” exhibits high effectiveness in enhancing scratch visibility resistance and can increase the scratch resistance by more than 40% at low scratch forces. The simulation method and the analysis of the power spectral density of the textured surface enable an accurate prediction of scratches.

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