nach oben

Computational Mechanics

Erschienen in:

16.03.2019 | Original Paper

A stochastic spectral finite element method for solution of faulting-induced wave propagation in materially random continua without explicitly modeled discontinuities

verfasst von: P. Zakian, N. Khaji

Erschienen in: Computational Mechanics | Ausgabe 4/2019

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

This paper proposes a new efficient stochastically adapted spectral finite element method to simulate fault dislocation and its wave propagation consequences. For this purpose, a dynamic form of the split node technique is formulated and developed to stochastic spectral finite element method in order to model fault dislocation happening within a random media without increasing computational demand caused by discontinuities. As discontinuities are not modeled explicitly herein, no additional degrees of freedom are implemented in the proposed method due to the discontinuities, while effects of these discontinuities are preserved. Therefore, the present method simultaneously includes merits of stochastic finite element method, spectral finite element method and the spilt node technique, thereby providing a new numerical tool for analysis of wave propagation under fault dislocation in random media. Several numerical simulations are solved by the proposed method, which present stochastic analysis of fault slip-induced wave propagation in layered random media. Formulations and numerical results demonstrate capability, application and efficiency of this novel method.

Vorheriger Artikel A wavelet multiresolution interpolation Galerkin method for targeted local solution enrichment

Nächster Artikel An integrated approach for the conformal discretization of complex inclusion-based microstructures

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Ghanem RG, Spanos PD (2003) Stochastic Finite elements: a spectral approach. Courier Dover Publications, MineolaMATH

Kaminski M (2013) The stochastic perturbation method for computational mechanics. Wiley, HobokenCrossRefMATH

Stefanou G (2009) The stochastic finite element method: past, present and future. Comput Methods Appl Mech Eng 198(9–12):1031–1051. https://doi.org/10.1016/j.cma.2008.11.007 CrossRefMATH

Xiu D (2010) Numerical methods for stochastic computations: a spectral method approach. Princeton University Press, PrincetonCrossRefMATH

Anders M, Hori M (1999) Stochastic finite element method for elasto-plastic body. Int J Numer Methods Eng 46(11):1897–1916. https://doi.org/10.1002/(SICI)1097-0207(19991220)46:11%3c1897:AID-NME758%3e3.0.CO;2-3 CrossRefMATH

Kamiński M (2015) On the dual iterative stochastic perturbation-based finite element method in solid mechanics with Gaussian uncertainties. Int J Numer Methods Eng 104(11):1038–1060. https://doi.org/10.1002/nme.4976 MathSciNetCrossRefMATH

Papadopoulos V, Kalogeris I (2016) A Galerkin-based formulation of the probability density evolution method for general stochastic finite element systems. Comput Mech 57(5):701–716. https://doi.org/10.1007/s00466-015-1256-9 MathSciNetCrossRefMATH

Kamiński MM (2009) A generalized stochastic perturbation technique for plasticity problems. Comput Mech 45(4):349. https://doi.org/10.1007/s00466-009-0455-7 MathSciNetCrossRefMATH

van den Ende MPA, Chen J, Ampuero JP, Niemeijer AR (2018) A comparison between rate-and-state friction and microphysical models, based on numerical simulations of fault slip. Tectonophysics 733:273–295. https://doi.org/10.1016/j.tecto.2017.11.040 CrossRef

10.

Volterra V Sur l’équilibre des corps élastiques multiplement connexes. In: Annales scientifiques de l’Ecole Normale superieure, 1907. Société mathématique de France, pp 401–517

11.

van Zwieten GJ, Hanssen RF, Gutiérrez MA (2013) Overview of a range of solution methods for elastic dislocation problems in geophysics. J Geophys Res Solid Earth 118(4):1721–1732. https://doi.org/10.1029/2012JB009278 CrossRef

12.

Melosh HJ, Raefsky A (1983) Anelastic response of the Earth to a dip slip earthquake. J Geophys Res Solid Earth 88(B1):515–526. https://doi.org/10.1029/JB088iB01p00515 CrossRef

13.

Melosh HJ, Raefsky A (1981) A simple and efficient method for introducing faults into finite element computations. Bull Seismol Soc Am 71(5):1391–1400

14.

Dalguer LA, Day SM (2007) Staggered-grid split-node method for spontaneous rupture simulation. J Geophys Res Solid Earth 112(B2):B02302. https://doi.org/10.1029/2006JB004467 CrossRef

15.

Dalguer LA, Day SM (2006) Comparison of fault representation methods in finite difference simulations of dynamic rupture. Bull Seismol Soc Am 96(5):1764–1778. https://doi.org/10.1785/0120060024 CrossRef

16.

Andrews DJ (1999) Test of two methods for faulting in finite-difference calculations. Bull Seismol Soc Am 89(4):931–937

17.

van Zwieten GJ, van Brummelen EH, van der Zee KG, Gutiérrez MA, Hanssen RF (2014) Discontinuities without discontinuity: the weakly-enforced slip method. Comput Methods Appl Mech Eng 271:144–166. https://doi.org/10.1016/j.cma.2013.12.004 MathSciNetCrossRefMATH

18.

Soares D Jr, Mansur WJ (2009) An efficient time-truncated boundary element formulation applied to the solution of the two-dimensional scalar wave equation. Eng Anal Bound Elem 33(1):43–53. https://doi.org/10.1016/j.enganabound.2008.04.002 MathSciNetCrossRefMATH

19.

Hamzeh Javaran S, Khaji N, Moharrami H (2011) A dual reciprocity BEM approach using new Fourier radial basis functions applied to 2D elastodynamic transient analysis. Eng Anal Bound Elem 35(1):85–95. https://doi.org/10.1016/j.enganabound.2010.05.014 MathSciNetCrossRefMATH

20.

Javaran SH, Khaji N, Noorzad A (2010) First kind Bessel function (J-Bessel) as radial basis function for plane dynamic analysis using dual reciprocity boundary element method. Acta Mech 218(3):247–258. https://doi.org/10.1007/s00707-010-0421-7 MATH

21.

Romero A, Tadeu A, Galvín P, António J (2015) 2.5D coupled BEM–FEM used to model fluid and solid scattering wave. Int J Numer Methods Eng 101(2):148–164. https://doi.org/10.1002/nme.4801 MathSciNetCrossRefMATH

22.

Shi F, Lowe MJS, Skelton EA, Craster RV (2018) A time-domain finite element boundary integral approach for elastic wave scattering. Comput Mech 61(4):471–483. https://doi.org/10.1007/s00466-017-1471-7 MathSciNetCrossRefMATH

23.

Idesman A, Pham D, Foley JR, Schmidt M (2014) Accurate solutions of wave propagation problems under impact loading by the standard, spectral and isogeometric high-order finite elements. Comparative study of accuracy of different space-discretization techniques. Finite Elem Anal Des 88:67–89. https://doi.org/10.1016/j.finel.2014.05.007 MathSciNetCrossRef

24.

Noh G, Bathe K-J (2013) An explicit time integration scheme for the analysis of wave propagations. Comput Struct 129:178–193. https://doi.org/10.1016/j.compstruc.2013.06.007 CrossRef

25.

Ham S, Bathe K-J (2012) A finite element method enriched for wave propagation problems. Comput Struct 94–95:1–12. https://doi.org/10.1016/j.compstruc.2012.01.001 CrossRef

26.

Kim K-T, Zhang L, Bathe K-J (2018) Transient implicit wave propagation dynamics with overlapping finite elements. Comput Struct 199:18–33. https://doi.org/10.1016/j.compstruc.2018.01.007 CrossRef

27.

Żak A, Krawczuk M, Skarbek Ł, Palacz M (2014) Numerical analysis of elastic wave propagation in unbounded structures. Finite Elem Anal Des 90:1–10. https://doi.org/10.1016/j.finel.2014.06.001 CrossRef

28.

Song C (2009) The scaled boundary finite element method in structural dynamics. Int J Numer Methods Eng 77(8):1139–1171. https://doi.org/10.1002/nme.2454 MathSciNetCrossRefMATH

29.

Yang ZJ, Deeks AJ (2006) A frequency-domain approach for modelling transient elastodynamics using scaled boundary finite element method. Comput Mech 40(4):725–738. https://doi.org/10.1007/s00466-006-0135-9 CrossRefMATH

30.

Khodakarami MI, Khaji N (2014) Wave propagation in semi-infinite media with topographical irregularities using decoupled equations method. Soil Dyn Earthq Eng 65:102–112. https://doi.org/10.1016/j.soildyn.2014.06.006 CrossRef

31.

Khodakarami MI, Khaji N, Ahmadi MT (2012) Modeling transient elastodynamic problems using a novel semi-analytical method yielding decoupled partial differential equations. Comput Methods Appl Mech Eng 213–216:183–195. https://doi.org/10.1016/j.cma.2011.11.016 MathSciNetCrossRefMATH

32.

Toki K, Sawada S, Okashige Y (1987) Simulation of fault rupture process by the stochastic finite element method. Probab Eng Mech 2(3):129–137. https://doi.org/10.1016/0266-8920(87)90003-8 CrossRef

33.

Hori M (2011) Introduction to computational earthquake engineering. World Scientific, SingaporeCrossRefMATH

34.

Hori M, Ichimura T, Nakagawa H (2003) Analysis methods of stochastic model: application to strong motion and fault problems. Struct Eng Earthq Eng 20(2):105s–118sCrossRef

35.

Giraldo D, Restrepo D (2017) The spectral cell method in nonlinear earthquake modeling. Comput Mech 60(6):883–903. https://doi.org/10.1007/s00466-017-1454-8 MathSciNetCrossRefMATH

36.

Hainzl S, Zöller G, Brietzke GB, Hinzen K-G (2013) Comparison of deterministic and stochastic earthquake simulators for fault interactions in the Lower Rhine Embayment, Germany. Geophys J Int 195(1):684–694. https://doi.org/10.1093/gji/ggt271 CrossRef

37.

Korn M (1993) Seismic waves in random media. J Appl Geophys 29(3–4):247–269. https://doi.org/10.1016/0926-9851(93)90007-L CrossRef

38.

Manolis GD, Bagtzoglou AC (1992) A numerical comparative study of wave propagation in inhomogeneous and random media. Comput Mech 10(6):397–413. https://doi.org/10.1007/BF00363995 CrossRefMATH

39.

Ripperger J, Ampuero JP, Mai PM, Giardini D (2007) Earthquake source characteristics from dynamic rupture with constrained stochastic fault stress. J Geophys Res Solid Earth 112(B4):B04311. https://doi.org/10.1029/2006JB004515 CrossRef

40.

Zak A, Krawczuk M, Ostachowicz W (2006) Propagation of in-plane waves in an isotropic panel with a crack. Finite Elem Anal Des 42(11):929–941. https://doi.org/10.1016/j.finel.2006.01.013 CrossRef

41.

Ham S, Lai B, Bathe K-J (2014) The method of finite spheres for wave propagation problems. Comput Struct 142:1–14. https://doi.org/10.1016/j.compstruc.2014.05.012 CrossRef

42.

Noh G, Ham S, Bathe K-J (2013) Performance of an implicit time integration scheme in the analysis of wave propagations. Comput Struct 123:93–105. https://doi.org/10.1016/j.compstruc.2013.02.006 CrossRef

43.

Igel H, Käser M, Stupazzini M (2014) Simulation of seismic wave propagation in media with complex geometries. In: Meyers RA (ed) Encyclopedia of complexity and systems science. Springer, Berlin, pp 1–32. https://doi.org/10.1007/978-3-642-27737-5_468-2

44.

Sawada M, Haba K, Hori M (2018) Estimation of surface fault displacement by high performance computing. J Earthq Tsunami (article in press)

45.

Hennings B, Lammering R, Gabbert U (2013) Numerical simulation of wave propagation using spectral finite elements. CEAS Aeronaut J 4(1):3–10. https://doi.org/10.1007/s13272-012-0053-9 CrossRef

46.

Kudela P, Krawczuk M, Ostachowicz W (2007) Wave propagation modelling in 1D structures using spectral finite elements. J Sound Vib 300(1–2):88–100. https://doi.org/10.1016/j.jsv.2006.07.031 CrossRefMATH

47.

Priolo E, Carcione JM, Seriani G (1994) Numerical simulation of interface waves by high-order spectral modeling techniques. J Acoust Soc Am 95(2):681–693CrossRef

48.

Witkowski W, Rucka M, Chróścielewski J, Wilde K (2012) On some properties of 2D spectral finite elements in problems of wave propagation. Finite Elem Anal Des 55:31–41. https://doi.org/10.1016/j.finel.2012.02.001 CrossRef

49.

Komatitsch D, Tromp J (1999) Introduction to the spectral element method for three-dimensional seismic wave propagation. Geophys J Int 139(3):806–822. https://doi.org/10.1046/j.1365-246x.1999.00967.x CrossRef

50.

Zakian P, Khaji N (2016) A novel stochastic-spectral finite element method for analysis of elastodynamic problems in the time domain. Meccanica 51(4):893–920. https://doi.org/10.1007/s11012-015-0242-9 MathSciNetCrossRefMATH

51.

Khaji N, Zakian P (2017) Uncertainty analysis of elastostatic problems incorporating a new hybrid stochastic-spectral finite element method. Mech Adv Mater Struct 24(12):1030–1042. https://doi.org/10.1080/15376494.2016.1202359 CrossRef

52.

Haskell NA (1969) Elastic displacements in the near-field of a propagating fault. Bull Seismol Soc Am 59(2):865–908

53.

Zakian P, Khaji N, Kaveh A (2017) Graph theoretical methods for efficient stochastic finite element analysis of structures. Comput Struct 178:29–46. https://doi.org/10.1016/j.compstruc.2016.10.009 CrossRef

54.

Mohammadi S (2012) XFEM fracture analysis of composites. Wiley, HobokenCrossRef

55.

Gracie R, Ventura G, Belytschko T (2007) A new fast finite element method for dislocations based on interior discontinuities. Int J Numer Methods Eng 69(2):423–441. https://doi.org/10.1002/nme.1896 CrossRefMATH

Titel: A stochastic spectral finite element method for solution of faulting-induced wave propagation in materially random continua without explicitly modeled discontinuities
verfasst von: P. Zakian
N. Khaji
Publikationsdatum: 16.03.2019
Verlag: Springer Berlin Heidelberg
Erschienen in: Computational Mechanics / Ausgabe 4/2019
Print ISSN: 0178-7675
Elektronische ISSN: 1432-0924
DOI: https://doi.org/10.1007/s00466-019-01692-5

Neuer Inhalt

Bildnachweise

VDI-Icon, Profil Icon, inhalt2, Springer Professional Modul/© Springer Fachmedien Wiesbaden GmbH, Internationaler Motorenkongress/© [M] ATZlive | Chisnikov / Fotolia.com, Search Icon, Banner Hanser, Benedikt Bonnmann von Adesso/© Adesso, Teilzeit/© Fokussiert / stock.adobe.com, Hans-Joachim Lefeld/© Lucht Probst Associates GmbH, Zeitschrift Wissensmanagement Cover, PatentFit-Logo/© Springer Fachmedien Wiesbaden GmbH, 2023_Antrieb/© supervisuell, ATZ-Webinar: Prototypenfreie Entwicklung durch Offline- und Driver-in-the-Loop-HiL-Tests /© (c) VI-grade, chassis.tech plus 2023/© [M] ATZlive / TÜV SÜD PRODUCT SERVICE GMBH

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Weitere Artikel der Ausgabe 4/2019

Constrained stability of conservative static equilibrium

A wavelet multiresolution interpolation Galerkin method for targeted local solution enrichment

Computational analysis of performance deterioration of a wind turbine blade strip subjected to environmental erosion

Algorithmic aspects and finite element solutions for advanced phase field approach to martensitic phase transformation under large strains

Shape gradients for the failure probability of a mechanic component under cyclic loading: a discrete adjoint approach

On polarization-based schemes for the FFT-based computational homogenization of inelastic materials

Neuer Inhalt

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.