A Variational Formulation of The Boundary Element Method in Transient Poroelasticity

  • E. Pan
  • G. Maier
  • B. Amadei
Conference paper

Abstract

Poroelasticity is concerned with heterogeneous media consisting of an elastic solid skeleton saturated by a diffusing pore fluid. Its range of application covers a variety of important real-life problems, such as design of nuclear reactor cores, exploitation of oil or gas deposits, simulation of living bone behaviour for orthopedical surgery, control of filtration leakage from reservoirs, and manufacturing process design for composite materials. Poroelasticity is now the subject of a fairly abundant literature, stemming from Terzaghi’s concept of effective stress and Biot’s linear consolidation theory. From a computational mechanics point of view, poroelastic analysis has been conducted using either the finite element method or the traditional (collocation) boundary element method [1–3].

Keywords

Filtration Boulder Biot Betti 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    A. H. D. Cheng and M. Predeleanu, Transient boundary element formulation for linear poroelasticity. Appl. Math. Mod., vol. 11 (1987), pp. 285–290MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    D. E. Beskos, Dynamics of saturated rocks, I: Equations of motion. J. Engrg. Mech., vol. 115 (1989), pp. 982–995.CrossRefGoogle Scholar
  3. [3]
    Y. J. Chiou and S. Y. Chi, Boundary element analysis of Biot consolidation in layered elastic soils. Int. J. Num. Anal. Meth. Geomech., vol. 18 (1994), pp. 377–396.MATHCrossRefGoogle Scholar
  4. [4]
    G. Maier and C. Polizzotto, A Galerkin approach to boundary elements elastoplastic analysis. Comp. Meth. Appl. Mech. Engng., vol. 60 (1987), pp. 175–194.MATHCrossRefGoogle Scholar
  5. [5]
    C. Polizzotto, An energy approach to the boundary element method, part I: elastic solids. Comp. Meth. Appl. Mech. Eng., vol. 69 (1988), pp. 167–184.MathSciNetMATHCrossRefGoogle Scholar
  6. [6]
    C. Polizzotto, An energy approach to the boundary element method, part II: elastic-plastic solids. Comp. Meth. Appl. Mech. Eng., vol. 69 (1988), pp. 263–276.MathSciNetMATHCrossRefGoogle Scholar
  7. [7]
    S. Sirtori, G. Maier, G. Novati and S. Miccoli, A Galerkin symmetric boundaryv element method in elasticity: formulation and implementation. Int. J. Num. Meth. Engng., vol. 35 (1992), pp. 255–282.MathSciNetMATHCrossRefGoogle Scholar
  8. [8]
    G. Maier, G. Novati and Z. Cen, Symmetric Galerkin boundary element method for quasi-brittle fracture and frictional contact problems. Comp. Mech., vol. 13 (1993), pp. 74–89.MATHGoogle Scholar
  9. [9]
    J. H. Kane and C. Balakrishna, Symmetric Galerkin boundary formulations employing curved elements. Int. J. Num. Meth. Eng., vol. 36 (1993), pp. 2157–2187.MathSciNetMATHCrossRefGoogle Scholar
  10. [10]
    G. Maier, M. Diligenti and A. Carini, A variational approach to boundary element elastodynamic analysis and extension to multidomain problems. Int. J. Comp. Meth. Appl. Mech. Engng., vol. 92 (1991), pp. 193–213.MathSciNetMATHCrossRefGoogle Scholar
  11. [11]
    A. Carini, M. Diligenti and G. Maier, Boundary integral equation analysis in linear viscoelasticity: variational and saddle-point formulations. Comp. Mech., vol. 8 (1991), pp. 87–98.MathSciNetMATHCrossRefGoogle Scholar
  12. [12]
    M. P. Cleary, Fundamental solutions for a fluid-saturated porous solid. Int. J. Sol. Str., vol. 13 (1977), pp. 785–806.MathSciNetMATHCrossRefGoogle Scholar
  13. [13]
    E. Detournay and A. H. D. Cheng, Poroelastic solution of a plane strain point displacement discontinuity. J. Appl. Mech., vol. 54 (1987), pp. 783–787.MATHCrossRefGoogle Scholar
  14. [14]
    E. Pan, Dislocation in an infinite poroelastic medium. Acta Mechanica, vol 87 (1991), pp. 105–115.MathSciNetMATHCrossRefGoogle Scholar
  15. [15]
    J. R. Rice and M. P. Cleary, Some basic stress-diffusion solutions for fluid-saturated elastic porous media with compressible consituents. Rev. Geophys. Space Phys., vol. 14 (1976), pp. 227–241.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • E. Pan
    • 1
  • G. Maier
    • 2
  • B. Amadei
    • 1
  1. 1.University of ColoradoBoulderUSA
  2. 2.Technical University (Politecnico)MilanItaly

Personalised recommendations