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    A unified approach to the mathematical analysis of generalized RKPM, gradient RKPM, and GMLS

    , Article Computer Methods in Applied Mechanics and Engineering ; Volume 200, Issue 5-8 , January , 2011 , Pages 540-576 ; 00457825 (ISSN) Behzadan, A ; Shodja, H. M ; Khezri, M ; Sharif University of Technology
    2011
    Abstract
    It is well-known that the conventional reproducing kernel particle method (RKPM) is unfavorable when dealing with the derivative type essential boundary conditions [1-3]. To remedy this issue a group of meshless methods in which the derivatives of a function can be incorporated in the formulation of the corresponding interpolation operator will be discussed. Formulation of generalized moving least squares (GMLS) on a domain and GMLS on a finite set of points will be presented. The generalized RKPM will be introduced as the discretized form of GMLS on a domain. Another method that helps to deal with derivative type essential boundary conditions is the gradient RKPM which incorporates the... 

    EFG mesh-less method for coupled hydro-mechanical analysis of unsaturated porous media

    , Article Unsaturated Soils: Research and Applications - Proceedings of the 6th International Conference on Unsaturated Soils, UNSAT 2014 ; Vol. 1, issue , July , 2014 , p. 581-587 ; 978-1-138-00150-3 Samimi, S ; Pak, A ; Sharif University of Technology
    Abstract
    Numerical modeling of the fully coupled phenomena of solid deformation-fluid flow in partially saturated porous media is of great interest in many branches of science and engineering. In this study, a new formulation based on one of the famous mesh-less methods, called Element-Free Galerkin (EFG), is developed to simulate the water and air movement through variably saturated soils. For this purpose, the governing partial differential equations including the equilibrium equation and mass conservation laws for each fluid phase are discretized in space using the same EFG shape functions. To enforce the essential boundary conditions, penalty method is employed. Temporal discretization is... 

    Three-dimensional free vibration of arbitrarily shaped laminated micro-plates with sliding interfaces within couple stress theory

    , Article Journal of Sound and Vibration ; Volume 339 , March , 2015 , Pages 176-195 ; 0022460X (ISSN) Kamali, M. T ; Shodja, H. M ; Forouzan, B ; Sharif University of Technology
    Academic Press  2015
    Abstract
    Free vibration of laminated micro-plates with arbitrary geometry and boundary conditions consisting of several micro-layers with free sliding/frictional sliding/perfect interfaces is of interest. The inter-layer bond in the direction normal to the interfaces is perfect, and thus the corresponding displacement component is continuous across the interfaces. The mentioned in-plane interface conditions may be realized by varying the stiffness of the sliding inter-layer spring of vanishing thickness. For free sliding and perfect interface conditions the stiffness→0 and a, respectively. Couple stress theory as a useful higher order continuum theory is utilized to formulate the problem.... 

    GRKPM: Theory and Applications in Laminated Composite Plates and Nonlinear Evolutionary Partial Differential Equations With Large Gradients

    , Ph.D. Dissertation Sharif University of Technology Hashemian, Alireza (Author) ; Mohammadi Shodja, Hossein (Supervisor)
    Abstract
    Reproducing kernel particle method (RKPM) is a meshfree method for solving various differential equations. RKPM is based on pure mathematics; therefore, it is in the center of attention of many scientists. One major problem in RKPM is satisfying the essential boundary conditions (EBCs) involving the derivative of the field function. This problem is considered herein and its solution is proposed. To this end, two actions should be undertaken. First, the concept of Hermitian interpolation is employed to add the derivative term to the reproducing equation of RKPM and a new meshless method called gradient RKPM (GRKPM) is introduced. Second, the corrected collocation method is modified so... 

    A coupled hydro-mechanical analysis for prediction of hydraulic fracture propagation in saturated porous media using EFG mesh-less method

    , Article Computers and Geotechnics ; Vol. 55, issue , January , 2014 , p. 254-266 Oliaei, M. N ; Pak, A ; Soga, K ; Sharif University of Technology
    Abstract
    The details of the Element Free Galerkin (EFG) method are presented with the method being applied to a study on hydraulic fracturing initiation and propagation process in a saturated porous medium using coupled hydro-mechanical numerical modelling. In this EFG method, interpolation (approximation) is based on nodes without using elements and hence an arbitrary discrete fracture path can be modelled.The numerical approach is based upon solving two governing partial differential equations of equilibrium and continuity of pore water simultaneously. Displacement increment and pore water pressure increment are discretized using the same EFG shape functions. An incremental constrained Galerkin... 

    A novel three-dimensional element free Galerkin (EFG) code for simulating two-phase fluid flow in porous materials

    , Article Engineering Analysis with Boundary Elements ; Vol. 39, issue. 1 , 2014 , pp. 53-63 ; ISSN: 09557997 Samimi, S ; Pak, A ; Sharif University of Technology
    Abstract
    In the past few decades, numerical simulation of multiphase flow systems has received increasing attention because of its importance in various fields of science and engineering. In this paper, a three-dimensional numerical model is developed for the analysis of simultaneous flow of two fluids through porous media. The numerical approach is fairly new based on the element-free Galerkin (EFG) method. The EFG is a type of mesh-less method which has rarely been used in the field of flow in porous media. The weak forms of the governing partial differential equations are derived by applying the weighted residual method and Galerkin technique. The penalty method is utilized for imposition of the... 

    RKPM with augmented corrected collocation method for treatment of material discontinuities

    , Article CMES - Computer Modeling in Engineering and Sciences ; Volume 62, Issue 2 , 2010 , Pages 171-204 ; 15261492 (ISSN) Shodja, H. M ; Khezri, M ; Hashemian, A ; Behzadan, A ; Sharif University of Technology
    2010
    Abstract
    An accurate numerical methodology for capturing the field quantities across the interfaces between material discontinuities, in the context of reproducing kernel particle method (RKPM), is of particular interest. For this purpose the innovative numerical technique, so-called augmented corrected collocation method is introduced; this technique is an extension of the corrected collocation method used for imposing essential boundary conditions (EBCs). The robustness of this methodology is shown by utilizing it to solve two benchmark problems of material discontinuities, namely the problem of circular inhomogeneity with uniform radial eigenstrain, and the problem of interaction between a crack... 

    A fully coupled element-free Galerkin model for hydro-mechanical analysis of advancement of fluid-driven fractures in porous media

    , Article International Journal for Numerical and Analytical Methods in Geomechanics ; Volume 40, Issue 16 , 2016 , Pages 2178-2206 ; 03639061 (ISSN) Samimi, S ; Pak, A ; Sharif University of Technology
    John Wiley and Sons Ltd 
    Abstract
    Hydraulic fracturing (HF) of underground formations has widely been used in different fields of engineering. Despite the technological advances in techniques of in situ HF, the industry uses semi-analytical tools to design HF treatment. This is due to the complex interaction among various mechanisms involved in this process, so that for thorough simulations of HF operations a fully coupled numerical model is required. In this study, using element-free Galerkin (EFG) mesh-less method, a new formulation for numerical modeling of hydraulic fracture propagation in porous media is developed. This numerical approach, which is based on the simultaneous solution of equilibrium and continuity... 

    A three-dimensional mesh-free model for analyzing multi-phase flow in deforming porous media

    , Article Meccanica ; Volume 51, Issue 3 , 2016 , Pages 517-536 ; 00256455 (ISSN) Samimi, S ; Pak, A ; Sharif University of Technology
    Springer Netherlands 
    Abstract
    Fully coupled flow-deformation analysis of deformable multiphase porous media saturated by several immiscible fluids has attracted the attention of researchers in widely different fields of engineering. This paper presents a new numerical tool to simulate the complicated process of two-phase fluid flow through deforming porous materials using a mesh-free technique, called element-free Galerkin (EFG) method. The numerical treatment of the governing partial differential equations involving the equilibrium and continuity equations of pore fluids is based on Galerkin’s weighted residual approach and employing the penalty method to introduce the essential boundary conditions into the weak forms.... 

    Non-isothermal simulation of the behavior of unsaturated soils using a novel EFG-based three dimensional model

    , Article Computers and Geotechnics ; Volume 99 , 2018 , Pages 93-103 ; 0266352X (ISSN) Iranmanesh, M. A ; Pak, A ; Samimi, S ; Sharif University of Technology
    Elsevier Ltd  2018
    Abstract
    In this paper, a three-dimensional simulation of fully coupled multiphase fluid flow and heat transfer through deforming porous media is presented in the context of EFG mesh-less method. Spatial discretization of the system of governing equations is performed using EFG and a fully implicit finite difference scheme is employed for temporal discretization. Penalty method is used for imposition of essential boundary conditions. The developed numerical tool is employed to simulate two problems of nuclear waste disposal and CO2 sequestration in deep underground strata. The obtained results demonstrate the capability and robustness of the developed EFG code. © 2018 Elsevier Ltd  

    Three-dimensional simulation of fully coupled hydro-mechanical behavior of saturated porous media using Element Free Galerkin (EFG) method

    , Article Computers and Geotechnics ; Volume 46 , 2012 , Pages 75-83 ; 0266352X (ISSN) Samimi, S ; Pak, A ; Sharif University of Technology
    2012
    Abstract
    Meshless methods are a relatively new type of numerical methods that have attracted the attention of many researchers over the past years. So far, a number of meshless methods have been developed and applied to solve problems in various fields of engineering, including solid mechanics and geotechnical problems. The Element-Free Galerkin (EFG) method is adopted in this study for solving the governing partial differential equations of equilibrium and continuity of pore fluid flow for numerical simulation of coupled hydro-mechanical problems. For this purpose, the weak form of the governing equations is derived by applying the weighted residual method and Galerkin technique. The penalty method... 

    Stabilized Meshless Local Petrov-Galerkin (MLPG) method for incompressible viscous fluid flows

    , Article CMES - Computer Modeling in Engineering and Sciences ; Volume 29, Issue 2 , 2008 , Pages 75-94 ; 15261492 (ISSN) Haji Mohammadi, M ; Sharif University of Technology
    2008
    Abstract
    In this paper, the truly Meshless Local Petrov-Galerkin (MLPG) method is extended for computation of steady incompressible flows, governed by the Navier-Stokes equations (NSE), in vorticity-stream function formulation. The present method is a truly meshless method based on only a number of randomly located nodes. The formulation is based on two equations including stream function Poisson equation and vorticity advection-dispersion-reaction equation (ADRE). The meshless method is based on a local weighted residual method with the Heaviside step function and quartic spline as the test functions respectively over a local subdomain. Radial basis functions (RBF) interpolation is employed in shape...