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BEM and FEM results of displacements in a poroelastic column

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Języki publikacji
EN
Abstrakty
EN
The dynamical investigation of two-component poroelastic media is important for practical applications. Analytic solution methods are often not available since they are too complicated for the complex governing sets of equations. For this reason, often some existing numerical methods are used. In this work results obtained with the finite element method are opposed to those obtained by Schanz using the boundary element method. Not only the influence of the number of elements and time steps on the simple example of a poroelastic column but also the impact of different values of the permeability coefficient is investigated.
Rocznik
Strony
883--896
Opis fizyczny
Bibliogr. 37 poz., rys., wykr.
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autor
autor
autor
  • Institute of Geotechnical Engineering and Soil Mechanics Berlin Institute of Technology, (TU Berlin), Sekr. TIB1-B7, Gustav-Meyer-Allee 25, D-13355 Berlin, Germany, albers@grundbau.tu-berlin.de
Bibliografia
  • [1] Albers, B. (2010). Modeling and Numerical Analysis of Wave Propagation in Saturated and Partially Saturated Porous Media, Postdoctoral thesis, Veröffentlichungen des Grundbauinstitutes der Technischen Universität Berlin, Vol. 48, Shaker, Aachen.
  • [2] Allard, J. F. (1993). Propagation of Sound in Porous Media. Modelling Sound Absorbing Materials, Elsevier, Essex.
  • [3] Atalla, N., Hamdi, A. M. and Panneton, R. (2001). Enhanced weak integral formulation for mixed (u,p) poroelastic equations, Journal of the Acoustical Society of America 109(6): 3065-3068.
  • [4] Atalla, N., Panneton, R. and Debergue, P. (1998). A mixed pressure-displacement formulation for poroelastic materials, Journal of the Acoustical Society of America 104(3): 1444-1452.
  • [5] Biot, M. A. (1941). General theory of three dimensional consolidation, Journal of Applied Physics 12(2): 155-164.
  • [6] Biot, M. A. (1956). Theory of propagation of elastic waves in a fluid saturated porous solid, I: Low frequency range, II: Higher frequency range, Journal of the Acoustical Society of America 28(2): 168-191.
  • [7] Bonnet, G. (1987). Basic singular solutions for a poroelastic medium in the dynamic range, Journal of the Acoustical Society of America 82(5): 1758-1762.
  • [8] Cheng, A. H.-D., Badmus, T. and Beskos, D. E. (1991). Integral equations for dynamic poroelasticity in frequency domain with BEM solution, Journal of Engineering Mechanics (ASCE) 117(5): 1136-1157.
  • [9] de Boer, R. and Ehlers, W. (1986). Theorie der Mehrkomponentenkontinua mit Anwendung auf bodenmechanische Probleme, Teil I, Technical Report 40, Forschungsberichte aus dem Fachbereich Bauwesen der Universität-GH Essen, Essen.
  • [10] Dominguez, J. (1992). Boundary element approach for dynamic poroelastic problems, International Journal for Numerical Methods in Engineering 35(2): 307-324.
  • [11] Eringen, A. C. and Suhubi, S. S. (1975). Elastodynamics, Vol. II, Academic Press, New York, NY.
  • [12] Fischer, M. (2004). The Fast Multipole Boundary Element Method and its Application to Structure-Acoustic Field Interaction, Ph.D. thesis, Universität Stuttgart, Stuttgart.
  • [13] Goodman, M. A. and Cowin, S. C. (1972). A continuum theory of granular materials, Archive for Rational Mechanics and Analysis 44(4): 249-266.
  • [14] Göransson, P. (1995). A weighted residual formulation of the acoustic wave propagation through a flexible porous material and comparison with a limp material model, Journal of Sound and Vibration 182(3): 479-494.
  • [15] Hild, P. (2011). A sign preserving mixed finite element approximation for contact problems, International Journal of Applied Mathematics and Computer Science 21(3): 487-498, DOI: 10.2478/v10006-011-0037-7.
  • [16] Holler, S. (2006). Dynamisches Mehrphasenmodell mit hypoplastischer Materialformulierung der Feststoffphase, Ph.D. thesis, RWTH Aachen, Aachen.
  • [17] Kelder, O. and Smeulders, D. M. J. (1997). Observation of the Biot slow wave in water-saturated Nivelsteiner sandstone, Geophysics 62(6): 1794-1796.
  • [18] Kogut, J. and Ciurej, H. (2010). A vehicle-track-soil dynamic interaction problem in sequential and parallel formulation, International Journal of Applied Mathematics and Computer Science 20(2): 295-303, DOI: 10.2478/v10006-010-0022-6.
  • [19] Korsawe, J. and Starke, G. (2005). A least-squares mixed finite element method for Biot's consolidation problem in porous media, SIAM Journal on Numerical Analysis 43(1): 318-339.
  • [20] Korsawe, J., Starke, G., Wang, W. and Kolditz, O. (2006). Finite element analysis of poro-elastic consolidation in porous media: Standard and mixed approaches, Computer Methods in Applied Mechanics and Engineering 195(9-12): 1096-1115.
  • [21] Lewis, R. W. and Schrefler, B. A. (1998). The Finite Element Method in the Static and Dynamic Deformation and Consolidation of Porous Media, Wiley, Chichester.
  • [22] Naumann, K. (2004). Implementierung eines Finiten Elementes in das FEM-Programmsystem ANSYS zur gekoppelten Fluid-Struktur Berechnung poröser Medien, Master's thesis, TU Berlin, Berlin.
  • [23] Panneton, R. and Atalla, N. (1997). An efficient finite element scheme for solving the threedimensional poroelasticity problem in acoustics, Journal of the Acoustical Society of America 101(6): 3287-3298.
  • [24] Plona, T. J. (1980). Observation of a second bulk compressional wave in a porous medium at ultrasonic frequencies, Applied Physics Letters 36(4): 259-261.
  • [25] Rackwitz, F., Naumann, K. and Savidis, S. A. (2005). Implementierung eines Finiten Elements zur Konsolidationsberechnung mit ANSYS, 23rd CADFEM Users' Meeting 2005, Bonn, Germany, (on CD-ROM/DVD).
  • [26] Savidis, S. A., Albers, B., Taşan, H. E. and Savvidis, G. (2011). Finite-Elemente-Berechnungen quasistatischer und dynamischer Probleme mit einem poroelastischen Zweikomponentenmodell, Bauingenieur 5: 241-249.
  • [27] Savvidis, G. (2009). Implementierung eines Finiten Elements in das FEM-Programmsystem ANSYS zur gekoppelten Fluid-Struktur Berechnung von wassergesättigten Böden, Master's thesis, TU Berlin, Berlin.
  • [28] Schanz, M. (2001). Application of 3d time domain boundary element formulation to wave propagation in poroelastic solids, Engineering Analysis with Boundary Elements 25(4-5): 363-376.
  • [29] Schanz, M. and Cheng, A. H.-D. (2000). Transient wave propagation in a one-dimensional poroelastic column, Acta Mechanica 145(1-4): 1-18.
  • [30] Schrefler, B. A. and Scotta, R. (2001). A fully coupled dynamic model for two-phase fluid flow in deformable porous media, Computer Methods in Applied Mechanics and Engineering 190(24-25): 3223-3246.
  • [31] Taşan, H. E. (2012). Zur Dimensionierung der Monopile-Gründungen von Offshore-Windenergieanlagen, Ph.D. thesis, Veröffentlichungen des Grundbauinstitutes der Technischen Universität Berlin, Vol. 52, Aachen.
  • [32] Taşan, H. E., Rackwitz, F. and Savidis, S. A. (2010). Behaviour of cyclic laterally loaded diameter monopiles in saturated sand, Proceedings of the 7th European Conference of Numerical Methods in Geotechnical Engineering, Trondheim, Norway, pp. 889-894.
  • [33] von Estorff, O. and Hagen, C. (2006). Iterative coupling of FEM and BEM in 3D transient elastodynamics, Engineering Analysis with Boundary Elements 30(7): 611-622.
  • [34] von Terzaghi, K. (1936). The shearing resistance of saturated soils and the angle between the planes of shear, 1st International Conference on Soil Mechanics and Foundation Engineering, Cambridge, MA, USA, Vol. 1, pp. 54-56.
  • [35] Wilmanski, K. (1996). Porous media at finite strains-The new model with the balance equation for porosity, Archives of Mechanics 48(4): 591-628.
  • [36] Zienkiewicz, O. C., Chan, A. H. C., Pastor, M., Schrefler, B. A. and Shiomi, T. (1999). Computational Geomechanics with Special Reference to Earthquake Engineering, John Wiley & Sons, West Sussex.
  • [37] Zienkiewicz, O. C. and Shiomi, T. (1984). Dynamic behaviour of saturated porous media: The generalized Biot formulation and its numerical solution, International Journal for Numerical and Analytical Methods in Geomechanics 8(1): 71-96.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPZ7-0008-0008
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