On the influence of far-field model reduction techniques using a coupled FEM-SBFEM approach in time domain

Marco Schauer

doi:10.33187/jmsm.435146

EN

On the influence of far-field model reduction techniques using a coupled FEM-SBFEM approach in time domain

Abstract

To analyse soil-structure-interaction problems, often unbounded domain has to be taken into account. Since the finite element method (FEM) does not provide open boundary itself the scaled boundary finite element method (SBFEM) which fulfils the radiation condition for wave propagation to infinity is used. The coupling of FEM and SBFEM in time domain is very time and memory consuming, due to the almost fully populated acceleration unit-impulse matrices and the convolution integral, which has to be solved at every time step. This paper studies ways to overcome this drawback and describes the influence of different model reduction techniques: like extrapolated acceleration unit-impulse response matrices, geometric far-field decoupling and sub-structured far-fields which can be applied to the far-field and also their combination. The different techniques for a FEM-SBFEM coupling in time domain are evaluated in terms of accuracy and computational effort.

Keywords

Finite element method,Geometrical decoupling,Model reduction,Scaled boundary finite element method,Soil-structure interaction,Sub-structuring,Unbounded domain

References

[1] Antes H, Spyrakos C. 1997 Soil-Structure Interaction, eds. Beskos DE, Anagnotopoulos SA. Computer Analysis and Design of Earthquake Resistant Structures Computational Mechanics Publications, Southampton.
[2] Astley RJ. 2000. Infinite elements for wave problems: a review of current formulations and a assessment of accuracy 49(7):951–976 International Journal for Numerical Methods in Engineering.
[3] Bazyar MH, Sing C. 2008. A continued fraction based high order transmitting boundary for wave propagation in unbounded domains of arbitrary geometry 74(2):209–237 International Journal for Numerical Methods in Engineering.
[4] Beer G. 2001. Programming the Boundary Element Method Wiley & Sons, Chichester, U.K.
[5] Birk C, Prempramote S, Song C. 2012. An improved continued-fraction-based high-order transmitting boundary for time-domain analyses in unbounded domains 89(3):269–298 International Journal for Numerical Methods in Engineering.
[6] Brebbia CA, Telles JCF, Wrobel LC. Boundary Element Techniques - Theory and Applications in Engineering Springer, Berlin, Heidelberg.
[7] Bettess P. 1992. Infinite Elements Penshaw Press, Sunderland, U.K.
[8] Borsutzky R. 2008. Seismic Risk Analysis of Buried Lifelines 63 Mechanik-Zentrum Technische Universit¨at Braunschweig.
[9] Chen D, Birk C, Song C, Du C. 2013 A high-order approach for modelling transient wave propagation problems using the scaled boundary finite element method 97(13):937–959 International Journal for Numerical Methods in Engineering.
[10] Chung J, Hulbert GM. 1993. A Time Integration Algorithm for Structural Dynamics with Improved Numerical Dissipation: The Generalized-a Method 60:371–375 Journal of Applied Mechanics.

[11] Cuthill E, McKee J. 1969. Reducing the Bandwidth of Sparse Symmetric Matrices 157–172, Proceedings of the 1969 24th National Conference. ACM.
[12] Engquist B, Majda A. 1977. Absorbing boundary conditions for the numerical simulation of waves 31(139):629–651 Mathematics of Computation.
[13] Givoli D, 1991 Non-reflecting Boundary Conditions 94:1–29 Journal of Computational Physics.
[14] Givoli D, 1992 Numerical Methods for Problems in Infinite Domains Elsevier Science Limited, Amsterdam.
[15] Harr ME. 1966. Foundations of Theoretical Soil Mechanics McGraw-Hill Book Company.
[16] Hilber H, Hughes T, Taylor R. 1977. Improved numerical dissipation for time integration algorithms in structural dynamics 5:283–292, Earthquake Engineering & Structural Dynamics.
[17] Lehmann L. 2003. Schnelles Verfahren zur Berechnung der Baugrund-Bauwerk-Interaktion im Zeitbereich 22:6–9, D-A-CH Mitteilungsblatt.
[18] Lehmann L, Antes H, Schanz M. 2004. Transient analysis of soil-structure interaction problems: An effective FEM/SBFEM approach 99–116, Advanced Numerical Analyses of Solids and Structures, and Beyond, Graz, Institute for Structural Analysis, Verlag der Technischen Universit¨at Graz.
[19] Lehmann L. 2005. An effective finite element approach for soil-structure analysis in the time-domain 21(4):37–50, Structural Engineering and Mechanics.
[20] Lehmann L. 2006. Wave Propagation in Infinite Domains, Springer, Berlin / Heidelberg.
[21] Liao ZP, Wong HL. 1984. A transmitting boundary for the numerical simulation of elastic wave propagation 3(4):174–183 Soil Dynamics and Earthquake Engineering.
[22] Lysmer J, Kuhlmeyer RL. 1969. Finite dynamic model for infinite media 95:859–875 Journal of Engineering Mechanics.
[23] Meskouris K, Hinzen KG, Butenweg C, Mistler M. 2007. Bauwerke und Erdbeben - Grundlagen - Anwendung - Beispiele, Vieweg+Teubner Verlag, Wiesbaden.
[24] Newmark N. 1959. A method of computation for structural dynamics 85:67–94, Journal of Engineering Mechanics Division.
[25] Petersen C. 2000. Dynamik der Baukonstruktionen Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden.
[26] Poulos HG, Davis EH. 1974. Elastic Solutions for Soil and Rock Mechanics John Wiley & Sons, INC.
[27] Radmanovic B, Katz C. 2010. A High Performance Scaled Boundary Finite Element Method 10 IOP Conf. Series: Material Science and Engineering.
[28] Schauer M, Lehmann L. 2009. Large Scale Simulation with Scaled Boundary Finite Element Method 9(4) 103–106, roceedings in Applied Mathematics and Mechanics
[29] Schauer M, Roman JE, Quintana-Ort´ı ES, Langer S. 2012. Parallel Computation of 3-D Soil-Structure Interaction in Time Domain with a Coupled FEM/SBFEM Approach 52:446–467, Journal of Scientific Computing.
[30] Schauer MM. 2015. Ein effizienter gekoppelter FEM-SBFEM Ansatz zur Analyse von Boden-Bauwerk-Interaktionen im Zeitbereich Dissertation, Technische Universit¨at Braunschweig.
[31] Wolf J, Song C. 1996. Finite-Element Modelling of Unbounded Media John Wiley & Sons, Chichester.
[32] Wolf J. 2003. The Scaled Boundary Finite Element Method John Wiley & Sons, Chichester.
[33] Yan J, Zhang C, Jin F. 2004. A coupling procedure of FE and SBFE for soil–structure interaction in the time domain 591453–1471, Int. J. Numer. Meth. Engng.
[34] Zhang X, Wegner JL, Haddow JB. 1999. Three-Dimensional Dynamic Soil-Structure Interaction Analysis in the Time Domain 28(10):1501–1524, Earthquake Engineering and Structural Dynamics.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Marco Schauer ^*
Germany

Publication Date

September 30, 2018

Submission Date

June 20, 2018

Acceptance Date

August 21, 2018

Published in Issue

Year 2018 Volume: 1 Number: 2

DOI

https://doi.org/10.33187/jmsm.435146

IZ

https://izlik.org/JA68BX46DU

APA

Schauer, M. (2018). On the influence of far-field model reduction techniques using a coupled FEM-SBFEM approach in time domain. Journal of Mathematical Sciences and Modelling, 1(2), 93-104. https://doi.org/10.33187/jmsm.435146

AMA

1.Schauer M. On the influence of far-field model reduction techniques using a coupled FEM-SBFEM approach in time domain. Journal of Mathematical Sciences and Modelling. 2018;1(2):93-104. doi:10.33187/jmsm.435146

Chicago

Schauer, Marco. 2018. “On the Influence of Far-Field Model Reduction Techniques Using a Coupled FEM-SBFEM Approach in Time Domain”. Journal of Mathematical Sciences and Modelling 1 (2): 93-104. https://doi.org/10.33187/jmsm.435146.

EndNote

Schauer M (September 1, 2018) On the influence of far-field model reduction techniques using a coupled FEM-SBFEM approach in time domain. Journal of Mathematical Sciences and Modelling 1 2 93–104.

IEEE

[1]M. Schauer, “On the influence of far-field model reduction techniques using a coupled FEM-SBFEM approach in time domain”, Journal of Mathematical Sciences and Modelling, vol. 1, no. 2, pp. 93–104, Sept. 2018, doi: 10.33187/jmsm.435146.

ISNAD

Schauer, Marco. “On the Influence of Far-Field Model Reduction Techniques Using a Coupled FEM-SBFEM Approach in Time Domain”. Journal of Mathematical Sciences and Modelling 1/2 (September 1, 2018): 93-104. https://doi.org/10.33187/jmsm.435146.

JAMA

1.Schauer M. On the influence of far-field model reduction techniques using a coupled FEM-SBFEM approach in time domain. Journal of Mathematical Sciences and Modelling. 2018;1:93–104.

MLA

Schauer, Marco. “On the Influence of Far-Field Model Reduction Techniques Using a Coupled FEM-SBFEM Approach in Time Domain”. Journal of Mathematical Sciences and Modelling, vol. 1, no. 2, Sept. 2018, pp. 93-104, doi:10.33187/jmsm.435146.

Vancouver

1.Marco Schauer. On the influence of far-field model reduction techniques using a coupled FEM-SBFEM approach in time domain. Journal of Mathematical Sciences and Modelling. 2018 Sep. 1;1(2):93-104. doi:10.33187/jmsm.435146