Comparative Study Between Viscous Boundaries and Perfectly Matched Layer Boundaries

Authors

  • Adriano Trono Universidad Nacional de Córdoba, Facultad de Ciencias Exactas Físicas y Naturales. Córdoba, Argentina.
  • Diego Turello Universidad Nacional de Córdoba, Facultad de Ciencias Exactas Físicas y Naturales & Instituto de Estudios Avanzados en Ingeniería y Tecnología, CONICET. Córdoba, Argentina.
  • Federico Pinto Universidad Nacional de Córdoba, Facultad de Ciencias Exactas Físicas y Naturales & Instituto de Estudios Avanzados en Ingeniería y Tecnología, CONICET. Córdoba, Argentina.
  • Marcelo A. Ceballos Universidad Nacional de Córdoba, Facultad de Ciencias Exactas Físicas y Naturales & Instituto de Estudios Avanzados en Ingeniería y Tecnología, CONICET. Córdoba, Argentina.

DOI:

https://doi.org/10.70567/mc.v41i9.47

Keywords:

Perfectly matched layer (PML), Standard viscous boundaries, Soil-structure interaction

Abstract

In the modeling of soil-structure interaction effects, it is important to adequately consider absorbing boundary conditions to simulate the infinite nature of the medium surrounding the structure. However, there are still deficiencies in absorbing boundaries when representing the radiation of outgoing waves, particularly when the analysis is performed in the time domain. ABAQUS and PLAXIS offer viscous absorbing boundaries, which are inadequate for absorbing waves that propagate at nonperpendicular angles to the boundary. This work compares the absorption performance of these absorbing boundaries with that of perfectly matched layers (PML). Using 2D finite elements, a rigid foundation subjected to different types of dynamic loads is modeled. The results of applying one type of absorbing boundary or the other are compared with reference solutions.

References

ABAQUS 6.12. Abaqus User's Manual. Volume V: Prescribed conditions, constraints and interactions. 2012.

Basu, U. y Chopra, A.K., Perfectly matched layers for time-harmonic elastodynamics of unbounded domains: theory and finite-element implementation, Computer methods in applied mechanics and engineering, 192, 1337-1375 (2003). https://doi.org/10.1016/S0045-7825(02)00642-4

Berenger J. P. A perfectly matched layer for the absorption of electromagnetic waves. Journal of Computational Physics, 114(2):185-200, 1994. https://doi.org/10.1006/jcph.1994.1159

Bielak, J. Loukakis, K., Yoshiaki, H. Yoshimura, C., Domain reduction method for threedimensional earthquake modeling in localized regions, part I: theory, Bulletin of the Seismological Society of America, Vol. 93, No.2 pp.817-824. 2003. https://doi.org/10.1785/0120010251

Fathi, A., Poursartip, B. Kallivokas, L. F.: Time domain hybrid formulations for wave simulation in three-dimensional PML-truncated heterogeneous media. International Journal for Numerical Methods in Engineering. DOI:10.1002/nme.4780, 2015. https://doi.org/10.1002/nme.4780

Gazetas G. Analysis of machine foundation vibrations: state of the art. Soil Dynamics and Earthquake Engineering, Vol.2. No 1, 0261-7277/83/010002-41. 1983. https://doi.org/10.1016/0261-7277(83)90025-6

Kramer, S.L.. Geotechnical Earthquake Engineering. Prentice Hall, 1996.

Kucukcoban S. y Kallivokas, L.F. A symmetric hybrid formulation for transient wave simulations in PML-truncated heterogeneous media. Wave Motion, 50, 57-79 (2013). https://doi.org/10.1016/j.wavemoti.2012.06.004

Lysmer J. Kuhlemeyer R. L.. Finite dynamic model for infinite media. Journal of Engineering Mechanics Division, 95:859-877, 1969. https://doi.org/10.1061/JMCEA3.0001144

Luco E. J., Westmann R. A. Dynamic response of a rigid footing bonded to an elastic half space. Journal of Applied Mechanics. 527-534. 1972. https://doi.org/10.1115/1.3422711

Meza-Fajardo, K. C., Papageorgiou, A. S.: A non-convolutional, Split-field, perfectly matched layer for wave propagation in isotropic and anisotropic elastic media: stability analysis. Bulletin of the Seismological Society of America 98(4), 1811-1836 (2008). https://doi.org/10.1785/0120070223

PLAXIS. Plaxis Scientific MANUAL. 2019.

Trono A., Brewer A.T., Pinto F., Ceballos M. A.: Bordes absorbentes de capas perfectamente acopladas mediante elementos finitos mixtos. Asociación Argentina de Mecánica Computacional, Vol XXXIX, 2022.

Trono A., Brewer A.T., Pinto F., Ceballos M. A.: Estabilización del medio de capa perfectamente acoplada mediante funciones de estiramiento multiaxiales. Asociación Argentina de Mecánica Computacional, Vol XXXX, 2023.

Wolf. J., P. Dynamic soil-structure interaction. International Series in Civil Engineening and Engineering mechanics, Prentice-Hall. 1985.

Zienkiewicz, O.C., Bicanic N. Earthquake input definition and the transmitting boundary conditions. Advances in Computational Nonlinear Mechanics. Springer-Verlag. Wien, 1989. https://doi.org/10.1007/978-3-7091-2828-2_3

Published

2024-11-08

Issue

Section

Conference Papers in MECOM 2024