An unequal-order radial interpolation meshless method for Biot's consolidation theory

Computers and Geotechnics

Volumn 34, Issue 2, 2007, Pages 61-70

  Wang, W D ^a   Wang, J G ^a   Wang, Z L ^b   Nogami, T ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^b UNIVERSITY OF SCIENCE AND TECHNOLOGY OF CHINA   (China)

Author keywords

Biot's consolidation theory; Pore water pressure; Radial PIM; Spurious oscillation; Unequal order approximation

Indexed keywords

APPROXIMATION THEORY; FINITE ELEMENT METHOD; INTERPOLATION; POLYNOMIALS; PORE PRESSURE;

BIOT'S CONSOLIDATION THEORY; RADIAL POINT INTERPOLATION MESHLESS TECHNIQUE; SPURIOUS OSCILLATION; UNEQUAL-ORDER APPROXIMATION;

CONSOLIDATION;

ALGORITHM; BIOT THEORY; CONSOLIDATION; INTERPOLATION; POREWATER; PRESSURE EFFECT; RADIAL FLOW;

EID: 33947150546     PISSN: 0266352X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compgeo.2006.10.010     Document Type: Article

References (29)

1. Biot M.A. General theory of three-dimensional consolidation. J Appl Phys 12 (1941) 155-164
2. Sandhu R.S., and Wilson E.L. Finite element analysis of seepage in elastic media. Proc ASCE EM 95 (1969) 641-651
3. Gaspar F.J., Lisbona F.J., and Vabishchevich P.N. Staggered grid discretizations for the quasi-static Biot's consolidation problem. Appl Numer Math 56 (2006) 888-898
4. Borja R. Finite element formulation for transient pore pressure dissipation: a variational approach. Int J Solid Struct 22 11 (1986) 1201-1211
5. Ghassemi A., Cheng A.H.D., Diek A., and Roegiers J.C. A complete plane strain fictitious stress boundary element method for poro-elastic media. Eng Anal Bound Elem 25 1 (2001) 41-48
6. Modaressi H., and Aubert P. Element-free Galerkin method for deforming multiphase porous media. Int J Numer Meth Eng 42 (1998) 313-340
7. Wang J.G., Liu G.R., and Wu Y.G. A point interpolation method for simulating dissipation process of consolidation. Comput Method Appl Mech Eng 190 45 (2001) 5907-5922
8. Onate E., Idelsohn S., Zienkiewicz O.C., and Taylor R.L. A finite point method in computational mechanics. Applications to convective transport and fluid flow. Int J Numer Meth Eng 39 (1996) 3839-3866
9. Wang J.G., Liu G.R., and Lin P. Numerical analysis of Biot's consolidation process by radial point interpolation method. Int J Solid Struct 39 6 (2002) 1557-1573
10. Vanlangen H., and Vermeer P.A. Automatic step size correction for non-associated plasticity problems. Int J Numer Meth Eng 29 3 (1990) 579-598
11. Sloan S.W., and Abbo A.J. Biot consolidation analysis with automatic time stepping and error control, part 1: theory and implementation. Int J Numer Anal Method Geomech 23 (1999) 467-492
12. Sloan S.W., and Abbo A.J. Biot consolidation analysis with automatic time stepping and error control, part 2: application. Int J Numer Anal Method Geomech 23 (1999) 493-529
13. Sheng D., and Sloan S.W. Time stepping schemes for coupled displacement and pore water pressure analysis. Comput Mech 31 (2003) 122-134
14. Vermeer P.A., and Van Langen H. An accuracy condition for consolidation by finite elements. Int J Numer Anal Method Geomech 5 (1981) 1-14
15. Sandhu R.S., and Lee S.C. Special finite elements for analysis of soil consolidation. Int J Numer Anal Method Geomech 9 (1985) 125-147
16. Bai M., Roegiers J.C., Zaman M., and Elsworth D. Minimizing numerical oscillation in the consolidation analysis. In: Pietruszczak, and Pande (Eds). Numerical models in geomechanics (1997), Balkema 359-364
17. Pastor M., Li T., Liu X., and Zienkiewicz O.C. Stabilized low-order finite elements for failure and localization problems in undrained soils and foundations. Comput Method Appl Mech Eng 174 (1999) 219-234
18. Miga M.I., Paulsen K.D., and Kennedy F.E. Von Neumann stability analysis of Biot's general two-dimensional theory of consolidation. Int J Numer Meth Eng 43 (1998) 955-974
19. Wood W.L. Practical time-stepping schemes (1990), Clarendon Press, Oxford
20. Murad M.A., and Loula A. On stability and convergence of finite element approximation of Biot's consolidation problem. Int J Numer Math Eng 37 (1994) 645-667
21. Chen X., Toh K.C., and Phoon K.K. A modified SSOR preconditioner for sparse symmetric indefinite linear systems of equations. Int J Numer Method Eng 65 (2006) 785-807
22. Zienkiewicz O.C., Huang M., and Pastor M. Localization problems in plasticity using finite elements with adaptive remeshing. Int J Numer Anal Method Geomech 19 (1995) 127-148
23. Johannes K., Gerhard S., Wenqing W., and Olaf K. Finite element analysis of poro-elastic consolidation in porous media: standard and mixed approaches. Comput Method Appl Mech Eng 195 (2006) 1096-1115
24. Wang J.G., Leung C.F., and Chow Y.K. Numerical solutions for flow in porous media. Int J Numer Anal Method Geomech 27 7 (2003) 565-583
25. Hughes T.J.R., Franca L.P., and Balestra. A new finite element formulation for computational fluid dynamics: v circumenting the Babuska-Brezzi condition: a stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolation. Comput Method Appl Mech Eng 59 (1986) 85-99
26. Wang J.G., and Liu G.R. A point interpolation meshless method based on radial basis functions. Int J Numer Method Eng 54 (2002) 1623-1648
27. Smolinski P., and Palmer T. Procedures for multi-time step integration of element-free Galerkin methods for diffusion problems. Comput Struct 77 (2000) 171-183
28. Zienkiewicz O.C., Qu S., Taylor R.L., and Nakazawa S. The patch test for mixed formulations. Int J Numer Method Eng 23 (1986) 1873-1883
29. PLAXIS manual: finite element code for soil and rock analysis (Version 7); 1998.