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BEM and FEM results of displacements in a poroelastic column Cover

BEM and FEM results of displacements in a poroelastic column

International Journal of Applied Mathematics and Computer Science
Volume 22 (2012): Issue 4 (December 2012)
By:
Open Access
|Dec 2012

References

  1. Albers, B. (2010). <em>Modeling and Numerical Analysis of Wave Propagation in Saturated and Partially Saturated Porous Media</em>, Postdoctoral thesis, Veröffentlichungen des Grundbauinstitutes der Technischen Universität Berlin, Vol. 48, Shaker, Aachen.
    Search in Google Scholar
  2. Allard, J.F. (1993). <em>Propagation of Sound in Porous Media. Modelling Sound Absorbing Materials</em>, Elsevier, Essex.<dgdoi:pub-id xmlns:dgdoi="http://degruyter.com/resources/doi-from-crossref" pub-id-type="doi"><a href="https://doi.org/10.1007/978-94-011-1866-8" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1007/978-94-011-1866-8</a></dgdoi:pub-id>
    Search in Google Scholar
  3. Atalla, N., Hamdi, A.M. and Panneton, R. (2001). Enhanced weak integral formulation for mixed (u,p) poroelastic equations, <em>Journal of the Acoustical Society of America </em><bold>109</bold>(6): 3065-3068.<dgdoi:pub-id xmlns:dgdoi="http://degruyter.com/resources/doi-from-crossref" pub-id-type="doi"><a href="https://doi.org/10.1121/1.1365423" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1121/1.1365423</a></dgdoi:pub-id>
    Search in Google Scholar
  4. Atalla, N., Panneton, R. and Debergue, P. (1998). A mixed pressure-displacement formulation for poroelastic materials, <em>Journal of the Acoustical Society of America </em><bold>104</bold>(3): 1444-1452.<dgdoi:pub-id xmlns:dgdoi="http://degruyter.com/resources/doi-from-crossref" pub-id-type="doi"><a href="https://doi.org/10.1121/1.424355" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1121/1.424355</a></dgdoi:pub-id>
    Search in Google Scholar
  5. Biot, M.A. (1941). General theory of three dimensional consolidation, <em>Journal of Applied Physics </em><bold>12</bold>(2): 155-164.<dgdoi:pub-id xmlns:dgdoi="http://degruyter.com/resources/doi-from-crossref" pub-id-type="doi"><a href="https://doi.org/10.1063/1.1712886" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1063/1.1712886</a></dgdoi:pub-id>
    Search in Google Scholar
  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, <em>Journal of the Acoustical Society of America </em><bold>28</bold>(2): 168-191.<dgdoi:pub-id xmlns:dgdoi="http://degruyter.com/resources/doi-from-crossref" pub-id-type="doi"><a href="https://doi.org/10.1121/1.1908241" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1121/1.1908241</a></dgdoi:pub-id>
    Search in Google Scholar
  7. Bonnet, G. (1987). Basic singular solutions for a poroelastic medium in the dynamic range, <em>Journal of the Acoustical Society of America </em><bold>82</bold>(5): 1758-1762.<dgdoi:pub-id xmlns:dgdoi="http://degruyter.com/resources/doi-from-crossref" pub-id-type="doi"><a href="https://doi.org/10.1121/1.395169" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1121/1.395169</a></dgdoi:pub-id>
    Search in Google Scholar
  8. Cheng, A.H.-D., Badmus, T. and Beskos, D.E. (1991). Integral equations for dynamic poroelasticity in frequency domain with BEM solution, <em>Journal of Engineering Mechanics (ASCE) </em><bold>117</bold>(5): 1136-1157.<dgdoi:pub-id xmlns:dgdoi="http://degruyter.com/resources/doi-from-crossref" pub-id-type="doi"><a href="https://doi.org/10.1061/(ASCE)0733-9399(1991)117:5(1136)" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1061/(ASCE)0733-9399(1991)117:5(1136)</a></dgdoi:pub-id>
    Search in Google Scholar
  9. de Boer, R. and Ehlers, W. (1986). Theorie der Mehrkomponentenkontinua mit Anwendung auf bodenmechanische Probleme, Teil I, <em>Technical Report 40</em>, Forschungsberichte aus dem Fachbereich Bauwesen der Universität-GH Essen, Essen.
    Search in Google Scholar
  10. Dominguez, J. (1992). Boundary element approach for dynamic poroelastic problems, <em>International Journal for Numerical Methods in Engineering </em><bold>35</bold>(2): 307-324.<dgdoi:pub-id xmlns:dgdoi="http://degruyter.com/resources/doi-from-crossref" pub-id-type="doi"><a href="https://doi.org/10.1002/nme.1620350206" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1002/nme.1620350206</a></dgdoi:pub-id>
    Search in Google Scholar
  11. Eringen, A.C. and Suhubi, S.S. (1975). <em>Elastodynamics</em>, Vol. II, Academic Press, New York, NY.
    Search in Google Scholar
  12. Fischer, M. (2004). <em>The Fast Multipole Boundary Element Method and its Application to Structure-Acoustic Field Interaction</em>, Ph.D. thesis, Universität Stuttgart, Stuttgart.
    Search in Google Scholar
  13. Goodman, M.A. and Cowin, S.C. (1972). A continuum theory of granular materials, <em>Archive for Rational Mechanics and Analysis </em><bold>44</bold>(4): 249-266.<dgdoi:pub-id xmlns:dgdoi="http://degruyter.com/resources/doi-from-crossref" pub-id-type="doi"><a href="https://doi.org/10.1007/BF00284326" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1007/BF00284326</a></dgdoi:pub-id>
    Search in Google Scholar
  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, <em>Journal of Sound and Vibration </em><bold>182</bold>(3): 479-494.<dgdoi:pub-id xmlns:dgdoi="http://degruyter.com/resources/doi-from-crossref" pub-id-type="doi"><a href="https://doi.org/10.1006/jsvi.1995.0211" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1006/jsvi.1995.0211</a></dgdoi:pub-id>
    Search in Google Scholar
  15. Hild, P. (2011). A sign preserving mixed finite element approximation for contact problems, <em>International Journal of Applied Mathematics and Computer Science </em><bold>21</bold>(3): 487-498, DOI: <a href="https://doi.org/10.2478/v10006-011-0037-7." target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.2478/v10006-011-0037-7.</a><dgdoi:pub-id xmlns:dgdoi="http://degruyter.com/resources/doi-from-crossref" pub-id-type="doi"><a href="https://doi.org/10.2478/v10006-011-0037-7" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.2478/v10006-011-0037-7</a></dgdoi:pub-id>
    Search in Google Scholar
  16. Holler, S. (2006). <em>Dynamisches Mehrphasenmodell mit hypoplastischer Materialformulierung der Feststoffphase, </em>Ph.D. thesis, RWTH Aachen, Aachen.
    Search in Google Scholar
  17. Kelder, O. and Smeulders, D.M.J. (1997). Observation of the Biot slow wave in water-saturated Nivelsteiner sandstone, <em>Geophysics </em><bold>62</bold>(6): 1794-1796.<dgdoi:pub-id xmlns:dgdoi="http://degruyter.com/resources/doi-from-crossref" pub-id-type="doi"><a href="https://doi.org/10.1190/1.1444279" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1190/1.1444279</a></dgdoi:pub-id>
    Search in Google Scholar
  18. Kogut, J. and Ciurej, H. (2010). A vehicle-track-soil dynamic interaction problem in sequential and parallel formulation, <em>International Journal of Applied Mathematics and Computer Science </em><bold>20</bold>(2): 295-303, DOI: <a href="https://doi.org/10.2478/v10006-010-0022-6." target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.2478/v10006-010-0022-6.</a><dgdoi:pub-id xmlns:dgdoi="http://degruyter.com/resources/doi-from-crossref" pub-id-type="doi"><a href="https://doi.org/10.2478/v10006-010-0022-6" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.2478/v10006-010-0022-6</a></dgdoi:pub-id>
    Search in Google Scholar
  19. Korsawe, J. and Starke, G. (2005). A least-squares mixed finite element method for Biot’s consolidation problem in porous media, <em>SIAM Journal on Numerical Analysis </em><bold>43</bold>(1): 318-339.<dgdoi:pub-id xmlns:dgdoi="http://degruyter.com/resources/doi-from-crossref" pub-id-type="doi"><a href="https://doi.org/10.1137/S0036142903432929" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1137/S0036142903432929</a></dgdoi:pub-id>
    Search in Google Scholar
  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, <em>Computer Methods in Applied Mechanics and Engineering </em><bold>195</bold>(9-12): 1096-1115.<dgdoi:pub-id xmlns:dgdoi="http://degruyter.com/resources/doi-from-crossref" pub-id-type="doi"><a href="https://doi.org/10.1016/j.cma.2005.04.011" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1016/j.cma.2005.04.011</a></dgdoi:pub-id>
    Search in Google Scholar
  21. Lewis, R.W. and Schrefler, BA. (1998). <em>The Finite Element Method in the Static and Dynamic Deformation and Consolidation of Porous Media, </em>Wiley, Chichester.
    Search in Google Scholar
  22. Naumann, K. (2004). <em>Implementierung eines Finiten Elementes in das FEM-Programmsystem ANSYS zur gekoppelten Fluid-Struktur Berechnung poröser Medien, </em>Master’s thesis, TU Berlin, Berlin.
    Search in Google Scholar
  23. Panneton, R. and Atalla, N. (1997). An efficient finite element scheme for solving the threedimensional poroelasticity problem in acoustics, <em>Journal of the Acoustical Society of America </em><bold>101</bold>(6): 3287-3298.<dgdoi:pub-id xmlns:dgdoi="http://degruyter.com/resources/doi-from-crossref" pub-id-type="doi"><a href="https://doi.org/10.1121/1.418345" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1121/1.418345</a></dgdoi:pub-id>
    Search in Google Scholar
  24. Plona, T. J. (1980). Observation of a second bulk compressional wave in a porous medium at ultrasonic frequencies, <em>Applied Physics Letters </em><bold>36</bold>(4): 259-261.<dgdoi:pub-id xmlns:dgdoi="http://degruyter.com/resources/doi-from-crossref" pub-id-type="doi"><a href="https://doi.org/10.1063/1.91445" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1063/1.91445</a></dgdoi:pub-id>
    Search in Google Scholar
  25. Rackwitz, F., Naumann, K. and Savidis, S.A. (2005). Implementierung eines Finiten Elements zur Konsolidationsberechnung mit ANSYS, <em>23rd CAD-FEM Users’ Meeting 2005, Bonn, Germany, </em>(on CD-ROM/DVD).
    Search in Google Scholar
  26. Savidis, S.A., Albers, B., Tas¸an, H.E. and Savvidis, G. (2011). Finite-Elemente-Berechnungen quasistatischer und dynamischer Probleme mit einem poroelastischen Zweikomponentenmodell, <em>Bauingenieur </em><bold>5</bold>: 241-249.
    Search in Google Scholar
  27. Savvidis, G. (2009). <em>Implementierung eines Finiten Elements in das FEM-Programmsystem ANSYS zur gekoppelten Fluid-Struktur Berechnung von wassergesättigten Böden, </em>Master’s thesis, TU Berlin, Berlin.
    Search in Google Scholar
  28. Schanz, M. (2001). Application of 3d time domain boundary element formulation to wave propagation in poroelastic solids, <em>Engineering Analysis with Boundary Elements </em><bold>25</bold>(4-5): 363-376.<dgdoi:pub-id xmlns:dgdoi="http://degruyter.com/resources/doi-from-crossref" pub-id-type="doi"><a href="https://doi.org/10.1016/S0955-7997(01)00022-4" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1016/S0955-7997(01)00022-4</a></dgdoi:pub-id>
    Search in Google Scholar
  29. Schanz, M. and Cheng, A.H.-D. (2000). Transient wave propagation in a one-dimensional poroelastic column, <em>Acta Mechanica </em><bold>145</bold>(1-4): 1-18.<dgdoi:pub-id xmlns:dgdoi="http://degruyter.com/resources/doi-from-crossref" pub-id-type="doi"><a href="https://doi.org/10.1007/BF01453641" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1007/BF01453641</a></dgdoi:pub-id>
    Search in Google Scholar
  30. Schrefler, B.A. and Scotta, R. (2001). A fully coupled dynamic model for two-phase fluid flow in deformable porous media, <em>Computer Methods in Applied Mechanics and Engineering </em><bold>190</bold>(24-25): 3223-3246.<dgdoi:pub-id xmlns:dgdoi="http://degruyter.com/resources/doi-from-crossref" pub-id-type="doi"><a href="https://doi.org/10.1016/S0045-7825(00)00390-X" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1016/S0045-7825(00)00390-X</a></dgdoi:pub-id>
    Search in Google Scholar
  31. Taşan, H.E. (2012). <em>Zur Dimensionierung der Monopile-Gründungen von Offshore-Windenergieanlagen</em>, Ph.D. thesis, Veröffentlichungen des Grundbauinstitutes der Technischen Universität Berlin, Vol. 52, Aachen.
    Search in Google Scholar
  32. Taşan, H.E., Rackwitz, F. and Savidis, S.A. (2010). Behaviour of cyclic laterally loaded diameter monopiles in saturated sand, <em>Proceedings of the 7th European Conference of Numerical Methods in Geotechnical Engineering, Trondheim, Norway, </em>pp. 889-894.
    Search in Google Scholar
  33. von Estorff, O. and Hagen, C. (2006). Iterative coupling of FEM and BEM in 3D transient elastodynamics, <em>Engineering Analysis with Boundary Elements </em><bold>30</bold>(7): 611-622.<dgdoi:pub-id xmlns:dgdoi="http://degruyter.com/resources/doi-from-crossref" pub-id-type="doi"><a href="https://doi.org/10.1016/j.enganabound.2006.01.007" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1016/j.enganabound.2006.01.007</a></dgdoi:pub-id>
    Search in Google Scholar
  34. von Terzaghi, K. (1936). The shearing resistance of saturated soils and the angle between the planes of shear, <em>1st International Conference on Soil Mechanics and Foundation Engineering, Cambridge, MA, USA, </em>Vol. 1, pp. 54-56.
    Search in Google Scholar
  35. Wilmanski, K. (1996). Porous media at finite strains-The new model with the balance equation for porosity, <em>Archives of Mechanics </em><bold>48</bold>(4): 591-628.
    Search in Google Scholar
  36. Zienkiewicz, O.C., Chan, A.H.C., Pastor, M., Schrefler, B.A. and Shiomi, T. (1999). <em>Computational Geomechanics with Special Reference to Earthquake Engineering</em>, John Wiley &amp; Sons, West Sussex.
    Search in Google Scholar
  37. Zienkiewicz, O.C. and Shiomi, T. (1984). Dynamic behaviour of saturated porous media: The generalized Biot formulation and its numerical solution, <em>International Journal for Numerical and Analytical Methods in Geomechanics </em><bold>8</bold>(1): 71-96.<dgdoi:pub-id xmlns:dgdoi="http://degruyter.com/resources/doi-from-crossref" pub-id-type="doi"><a href="https://doi.org/10.1002/nag.1610080106" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1002/nag.1610080106</a></dgdoi:pub-id>
    Search in Google Scholar
DOI: https://doi.org/10.2478/v10006-012-0065-y | Journal eISSN: 2083-8492 | Journal ISSN: 1641-876X
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Language: English
Page range: 883 - 896
Published on: Dec 28, 2012
Published by: Sciendo
In partnership with: Paradigm Publishing Services
Publication frequency: 4 times per year
Keywords:
finite element method,
boundary element method,
poroelastic media.
Related subjects:
Mathematics,
Applied mathematics

© 2012 Bettina Albers, Stavros A. Savidis, H. Ercan Taşan, Otto von Estorff, Malte Gehlken, published by Sciendo
This work is licensed under the Creative Commons License.

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