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A Comparison of Boundary Element Method and Finite Element Method Dynamic Solutions for Poroelastic Column

  • Leonid A. Igumnov
  • Aleksandr A. IpatovEmail author
  • Andrey N. Petrov
  • Svetlana Yu. Litvinchuk
  • Aron Pfaff
  • Victor A. Eremeyev
Chapter
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 120)

Abstract

Boundary element approach for solving boundary-value problems of saturated poroelastic solid dynamics is presented. Our boundary element approach is based on step scheme for numerical inversion of Laplace transform. Biot’s model of poroelastic media with four base functions is employed in order to describe wave propagation process, base functions are skeleton displacements and pore pressure of the fluid filler. The problem of the load acting on a poroelastic prismatic solid is solved by means of developed software based on boundary element approach. A comparison of obtained BEM solution with numerical-analytical solution and also with FEM solution from ANSYS is presented.

Keywords

Boundary element method Finite element method Dynamic solution Boundary integral equation Poroelastic column 

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Notes

Acknowledgements

This work was supported by a grant from the Government of the Russian Federation (contract No. 14.Y26.31.0031).

References

  1. Amenitsky AV, Belov AA, Igumnov LA, Karelin IS (2009) Granichnye integral’nye uravneniya dlya resheniya dinamicheskikh zadach trekhmernoi teorii porouprugosti (Boundary integral equations for analyzing dynamic problems of 3-D porouselasticity, in Russ.). Problems of Strength and Plasticity 71:164–171CrossRefGoogle Scholar
  2. Bazhenov VG, Igumnov LA (2008) Boundary Integral Equations and Boundary Element Methods in Treating the Problems of 3D Elastodynamics with Coupled Fields (in Russ.). Fizmatlet, MoscowGoogle Scholar
  3. Biot MA (1935) Le problème de la consolidation des matières argileuses sous une charge. Annales de la Société Scientifique de Bruxelles, série B 55:110–113Google Scholar
  4. Biot MA (1956a) Theory of propagation of elastic waves in a fluid-saturated porous solid. I. low-frequency range. The Journal of the Acoustical Society of America 28(2):168–178,  https://doi.org/10.1121/1.1908239CrossRefGoogle Scholar
  5. Biot MA (1956b) Theory of propagation of elastic waves in a fluid-saturated porous solid. II. higher frequency range. The Journal of the Acoustical Society of America 28(2):179–191,  https://doi.org/10.1121/1.1908241CrossRefGoogle Scholar
  6. Biot MA (1962) Generalized theory of acoustic propagation in porous dissipative media. The Journal of the Acoustical Society of America 34(9A):1254–1264,  https://doi.org/10.1121/1.1918315CrossRefGoogle Scholar
  7. Darcy H (1956) Les fontaines publiques de la ville de Dijon: Exposition et application des principes a suivre et des formules a employer dans les questions de distribution d’eau; ouvrage terminé par un appendice relatif aux fournitures d’eau de plusieurs villes au filtrage des eaux et a la fabrication des tuyaux de fonte, de plomb, de tole et de bitume. Dalmont, ParisGoogle Scholar
  8. Frenkel J (2005) On the theory of seismic and seismoelectric phenomena in a moist soil. Journal of Engineering Mechanics 131(9):879–887,  https://doi.org/10.1061/(asce)0733-9399(2005)131:9(879)
  9. Goldshteyn RV (1978) Boundary Integral Equations Method: Numerical Aspects and Application in Mechanics. Mir, MoskvaGoogle Scholar
  10. Igumnov LA, Petrov AN (2016) Modelirovanie dinamiki chastichno nasyshchennykh porouprugikh tel na osnove metoda granichno-vremennykh elementov (Dynamics of partially saturated poroelastic solids by boundary-element method (in Russ.). PNRPU Mechanics Bulletin 3:47–61,  https://doi.org/10.15593/perm.mech/2016.3.03CrossRefGoogle Scholar
  11. Igumnov LA, Litvinchuk SY, Petrov AN, Ipatov AA (2016) Numerically analytical modeling the dynamics of a prismatic body of two- and three-component materials. In: Advanced Materials, Springer Proceedings in Physics, vol 175, pp 505–516,  https://doi.org/10.1007/978-3-319-26324-3-35
  12. Lachat JC, Watson JO (1976) Effective numerical treatment of boundary integral equations: A formulation for three-dimensional elastostatics. International Journal for Numerical Methods in Engineering 10(5):991–1005,  https://doi.org/10.1002/nme.1620100503CrossRefGoogle Scholar
  13. Schanz M (2001) Wave Propagation in Viscoelastic and Poroelastic Continua: A Boundary Element Approach. Springer-Verlag, BerlinCrossRefGoogle Scholar
  14. Schanz M (2009) Poroelastodynamics: Linear models, analytical solutions, and numerical methods. Applied Mechanics Reviews 62(3):030,803,  https://doi.org/10.1115/1.3090831
  15. Terzaghi K (1923) Die Berechnung der Durchlassigkeitsziffer des Tones aus dem Verlauf der Hydrodynamichen Spannungserscheinungen. Akademie derWissenschaften inWien, Math Naturwiss Kl, Sitzungsberichte Abteilung II 132:125–138Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Leonid A. Igumnov
    • 1
  • Aleksandr A. Ipatov
    • 1
    Email author
  • Andrey N. Petrov
    • 1
  • Svetlana Yu. Litvinchuk
    • 1
  • Aron Pfaff
    • 2
  • Victor A. Eremeyev
    • 3
  1. 1.Research Institute for MechanicsNizhny Novgorod Lobachevsky State UniversityNizhny NovgorodRussia
  2. 2.Fraunhofer Institute for High-Speed Dynamics, Ernst-Mach-InstitutFreiburgGermany
  3. 3.Faculty of Civil and Environmental EngineeringGdańsk University of TechnologyGdańskPoland

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