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Some numerical issues using element‐free Galerkin mesh‐less method for coupled hydro‐mechanical problems
Author(s) -
Oliaei Mohammad Norouz,
Soga Kenichi,
Pak Ali
Publication year - 2009
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.747
Subject(s) - discretization , galerkin method , finite element method , partial differential equation , mathematics , boundary value problem , displacement (psychology) , stability (learning theory) , weak formulation , discontinuous galerkin method , penalty method , boundary (topology) , domain (mathematical analysis) , mathematical analysis , mathematical optimization , computer science , structural engineering , engineering , psychology , machine learning , psychotherapist
A new formulation of the element‐free Galerkin (EFG) method is developed for solving coupled hydro‐mechanical problems. The numerical approach is based on solving the two governing partial differential equations of equilibrium and continuity of pore water simultaneously. Spatial variables in the weak form, i.e. displacement increment and pore water pressure increment, are discretized using the same EFG shape functions. An incremental constrained Galerkin weak form is used to create the discrete system equations and a fully implicit scheme is used for discretization in the time domain. Implementation of essential boundary conditions is based on a penalty method. Numerical stability of the developed formulation is examined in order to achieve appropriate accuracy of the EFG solution for coupled hydro‐mechanical problems. Examples are studied and compared with closed‐form or finite element method solutions to demonstrate the validity of the developed model and its capabilities. The results indicate that the EFG method is capable of handling coupled problems in saturated porous media and can predict well both the soil deformation and variation of pore water pressure over time. Some guidelines are proposed to guarantee the accuracy of the EFG solution for coupled hydro‐mechanical problems. Copyright © 2008 John Wiley & Sons, Ltd.