Numerical analysis of Biot's consolidation process by radial point interpolation method

Wang, Jingguo; Liu, G.R; Lin, Pengzhi

doi:10.1016/s0020-7683(02)00005-7

Cited by 130 publications

(61 citation statements)

References 20 publications

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“…By applying the weighted residual method on Equation (19) and inserting Equations (22), (23) and (25) into Equation (19), the following constrained Galerkin weak form of the equilibrium …”

Section: Strong and Weak Formsmentioning

confidence: 99%

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Some numerical issues using element‐free Galerkin mesh‐less method for coupled hydro‐mechanical problems

Oliaei

Soga

Pak

2008

Num Anal Meth Geomechanics

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SUMMARYA new formulation of the element-free Galerkin (EFG) method is developed for solving coupled hydromechanical 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.

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“…By applying the weighted residual method on Equation (19) and inserting Equations (22), (23) and (25) into Equation (19), the following constrained Galerkin weak form of the equilibrium …”

Section: Strong and Weak Formsmentioning

confidence: 99%

“…The approximation is unconditionally stable when 0.5, but for any value of = 1 the numerical solution can exhibit a spurious rippling effect (Wang et al [25]). This time integration is applied to Equation (24).…”

Section: Strong and Weak Formsmentioning

confidence: 99%

Some numerical issues using element‐free Galerkin mesh‐less method for coupled hydro‐mechanical problems

Oliaei

Soga

Pak

2008

Num Anal Meth Geomechanics

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“…Quartic spline weight function (15) Exponential weight function (16) Conical weight function (17) where dm is the radius of the support in Fig. 2.…”

Section: Governing Equationsmentioning

confidence: 99%

Mesh-Free Method for Soil-Water Coupled Problem Within Finite Strain and Its Numerical Validity

Murakami

Setsuyasu

Arimoto

2005

SOILS AND FOUNDATIONS

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A formulation of the Element-Free Galerkin Method (EFG method), i.e., one of the mesh-free meshless methods developed in the field of computational mechanics for solving partial differential equations, is furnished for consolidation within finite strain and its validity for application to soil-water coupled problems is examined through a numerical analysis. The numerical strategy is constructed to solve a set of governing equations, e.g., the equilibrium for the nominal stress rate and the continuity of pore water, and the numerical discretization of the weakform of the governing equations leads to an updated Lagrangian scheme. The accuracy of the proposed numerical strategy is examined through an analysis of unconfined compression tests and simple shear tests under undrained and plane strain conditions through a comparison of stress paths integrated directly from the Cam-clay model within the framework of finite strain. It is also revealed that the particular type of weight function to be adopted in the moving least-squares (MLS) approximation, even in the same order, can determine the resultant shape functions of the EFG method for both the displacement and the pore water pressure field such that they are smoother than those of the usualFEM. The functions are advantageous in that they avoid spatial instability in the numerical solutions for pore water pressure under undrained conditions appearing in saturated soil column tests, where the shape function of the pore water pressure in the conventional FEM computation is adopted as a lower order than that of the displacement to remedy this type of numerical difficulty. To emphasize the applicability and the feasibility of the mesh-free computation, the consolidation phenomena are demonstrated in the analysis of a punch problem for a soft soil foundation which hasstress singularity under both ends of a rigid loading platen for the same problem which Yatomi et al. (1989) solved with FEM.

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“…Remarkable successes have been reported in applying these methods for analyzing challenging engineering problems, namely, fracture modelling [4][5][6], plate problems [7], finite deformation problem [8,9], consolidation problem [10], dynamic simulation [11], three-dimensional problems [12,13], topology-optimization of structures and thermodynamic analysis, where laborious preprocessing involved in the FEM is avoided.…”

Section: Introductionmentioning

confidence: 99%

An improved meshless Shepard and least squares method possessing the delta property and requiring no singular weight function

2013

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The nal publication is available at Springer via http://dx.doi.org/10.1007/s00466-013-0912-1. Additional information:Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractThe meshless Shepard and least squares (MSLS) method and the meshless Shepard (MS) method are Partition of Unity (PU) based meshless interpolations which eliminate the problems by other meshless methods such as the difficulty in direct imposition of the essential boundary conditions. However, singular weight functions have to be used in both methods to enforce the approximation interpolatory, which leads to the loss of smoothness in approximation and locally oscillatory results. In this paper, an improved MSLS interpolation is developed by using dually defined nodal supports such that no singular weight function is required. The proposed interpolation satisfies the delta property at boundary nodes and the compatibility condition throughout the domain, and is capable of exactly reproducing the basis function. The computational cost of the present interpolation is much lower than the Moving Least-Squares (MLS) approximation which is probably the most widely used meshless interpolation at present.

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Numerical analysis of Biot's consolidation process by radial point interpolation method

Cited by 130 publications

References 20 publications

Some numerical issues using element‐free Galerkin mesh‐less method for coupled hydro‐mechanical problems

Some numerical issues using element‐free Galerkin mesh‐less method for coupled hydro‐mechanical problems

Mesh-Free Method for Soil-Water Coupled Problem Within Finite Strain and Its Numerical Validity

An improved meshless Shepard and least squares method possessing the delta property and requiring no singular weight function

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