This study aims to provide a coupled flow-deformation model for simulating land subsidence associated with groundwater extraction in aquifers. For this simulation, we have adopted the ELEMENT-FREE GALERKIN ((EFG)) method and considered the unsaturated effects in the aquifers based on the aquifer's hydrologic and geotechnical characteristics. This model gives us a better understanding of the aquifer's hydrogeological characteristics, enabling us to forecast changes in the hydraulic head and land subsidence. To ensure the credibility of our model and to verify the code, we modeled unsaturated hydromechanical benchmark problems. Then, using the (EFG) method as a numerical tool, we modeled an isotropic aquifer to investigate the effects of groundwater pumping on land subsidence and hydraulic changes in the aquifer. To ascertain the reliability of the modeling, we compared the results obtained from the (EFG) method with those from the Finite Element Method (FEM). The comparative analysis of (EFG) and FEM models demonstrates discrepancies of 5.51% in land subsidence and 13.35% in hydraulic head reduction, which are satisfying. The land subsidence and hydraulic head profiles demonstrate that the (EFG) method is capable of land subsidence simulation caused by water pumping. Furthermore, our findings highlight the nonlinear correlation between groundwater extraction and the subsequent decrease in hydraulic head and land subsidence augmentation. Finally, we conducted a parametric study to better understand the effect of various characteristics of aquifers and observe the effect of the aquifer's parameters, such as hydraulic conductivity, elastic modulus, and Poisson's ratio. We investigated the effect of each parameter on land subsidence increase and hydraulic head decline. The results show that elastic modulus and Poisson's ratio have the most significant effect on land subsidence. Although hydraulic conductivity controls the hydraulic decrement and land subsidence increase time, it slightly affects the ultimate hydraulic head and land subsidence at the steady-state stage. These results highlight the importance of in-situ measurement of elastic modulus and Poisson's ratio paraeters with acceptable accuracy for groundwater extraction projects, as these parameters play a significant role in the feasibility studies.

In this paper, the ELEMENT-FREE GALERKIN ((EFG)) method is employed to obtain three dimensional static behavior of thick functionally graded plates. The Poisson’s ratio is taken to be constant and the Young’s modulus is considered to be graded through the thickness of plate by an exponential function. The shape function is calculated using the 3D moving least squares (MLS) approximation. Because the MLS approximation lacks the Kronecker delta function property, therefore the constrained GALERKIN weak-form is used. The Lagrange multiplier method is employed to enforce the essential boundary condition. Effects of weight functions, nodal density and the dimensionless size of the support domain are investigated and favorable value for the dimensionless size of the support domain is calculated. Also a new trigonometric weight function is introduced. Effects of functionally grading index, dimensionless thickness and boundary conditions on the stress and deformation of the plate are investigated. Several examples are presented for thick functionally graded plates under static load. Also in order to verify the obtained results, they are compared with the results of other data reported in the literature. Numerical results indicate that the rate of convergence of the proposed method is higher than that of finite element method especially for stress calculation.

The ELEMENT-FREE GALERKIN ((EFG)) and the radial point interpolation (RPIM) methods are two meshless methods in the field of the computational mechanics. In the present study, a computational scheme using a variable domain and a fixed domain is presented based on the coupling of (EFG) and RPIM for analysis of two dimensional double free surface flows under radial gate for the computation of the free surface profiles, velocity and pressure distributions, and the flow rate of a 2D gravity fluid flow through the conduit. The coupling between (EFG) and RPIM is achieved by using the RPIM shape functions as the weight functions for (EFG) method. In this approach, contrary to (EFG) method, the imposition of the essential boundary conditions is straight forward and shape functions fulfill the Kronecker delta property. In this study, the fluid is assumed to be inviscid and incompressible and the obtained results are compared by conducting a hydraulic model test. The results are in agreement in terms of free surface profiles and pressure distributions.

This paper presents ELEMENT-FREE GALERKIN ((EFG)) method as a computational technique that can effectively avoid the disadvantage of mesh entanglement. The present method is used to analyze the static defelection of beams. The moving least squares (MLS) approximation has been used for constructing the shape function based on a set of nodes arbitrarily distributed in the analysis domain.

Many ranking methods have been proposed so far. However, there is not any method which can always give a satisfactory solution for every situation. In this paper, we propose a method for ranking fuzzy numbers based on the distance method and compare the results with other ranking methods in some examples.

 The ELEMENT-FREE GALERKIN method ((EFG)) and the natural element method (NEM) are two well know methods in the computational mechanics and meshless methods. In this paper, a computational scheme using a variable domain and a fixed domain is presented based on coupling of (EFG) and NEM for analysis of two dimensional spillway flow under radial gate for the computation of the free surface profile and the flow rate of a 2D gravity fluid f low through a conduit and under a radial gate. The coupling between (EFG) and NE is achieved by using the natural element shape functions as the weight functions for the element free GALERKIN method. In this method, contrary to (EFG) method, the imposition of the essential boundary conditions is straight forward and shape functions fulfill the Kronecker delta property. In this study, the fluid is assumed to be inviscid and incompressible. The validity of the proposed method is verified by comparing the results from (EFG)-NE simulation results with those obtained from finite element simulation and experimental results. It is concluded that the results obtained by (EFG)-NE method is in good agreement with those from FEM and experimental results. Therefore, the coupled (EFG)-NE method is capable to handle spillway flow simulation.

The ELEMENT-FREE GALERKIN method ((EFG)) and the natural element method (NEM) are two well know methods in the computational mechanics and meshless methods. In this paper, a computational technique is presented based on coupling of (EFG) and NEM for large plastic deformation simulation in the tensile test and forward extrusion process. The coupling between (EFG) and NE is achieved by using the natural element shape functions as the weight functions for the element free GALERKIN method. In this method, contrary to (EFG) method, the imposition of the essential boundary conditions is straight forward and shape functions fulfill the Kronecker delta property. The inspection cases are tensile test simulation in axi-symmetry state and forward extrusion simulation for circular shape components from round billets. In this method, the punch stroke value is divided to sub-steps whereas a new set of nodes become active at the end of each sub-step of deformation. Hollman-Ludwik law is selected to explain the material behavior after the yielding point. The validity of the proposed method is verified by comparing the results from (EFG)-NE simulation results with those obtained from finite element simulation (ANSYS result). It is concluded that the results obtained by (EFG)-NE method is in good agreement with those from FEM and therefore, the coupled (EFG)-NE method is capable to handle large plastic deformation simulation.

A formulation of the Element Free GALERKIN ((EFG)), one of the mesh-less methods, is developed for solving coupled problems and its validity for application to soil-water problems is examined through numerical analysis. The numerical approach is constructed to solve two governing partial differential equations of equilibrium and the continuity of pore water, simultaneously. Spatial variables in a weak form, the displacement increment and excess 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 to create the discretization of the time domain. Implementation of essential boundary conditions is based on penalty method. Examples are studied and the obtained results are compared with closed-form or finite element method solutions to demonstrate the capability of the developed model. The results indicate that the (EFG) method is capable of handling coupled problems in saturated porous media and can predict well, both soil deformation and the variation of pore water pressure, over time.

Electric field gradients ((EFG)) at in and Ce sites, electronic specific heat and the magnetic moments at Ce site have been calculated for CeIn3. The calculations were performed by increasing pressure gradually from -5 to +22 GPa, within the density functional theory (DFT) and using the augmented plane waves plus local orbital (APW+lo) method . The so-called PBE-GGA+U and WC-GGA+U schemes have been employed. Results show that the calculated (EFG)’s at the In site grow smoothly by imposing pressure. We have compared the (EFG)’s at zero pressure with theoretical and experimental results. It is shown that our simulation results for (EFG)’s are close to the results of the other study and in good agreement with experimental data at the ambient pressure. We show that with increasing the pressure, the electronic density of states at Fermi level decreases and causes an increase in (EFG). Results also indicate that by increasing the pressure, both f density of states at Fermi level and the magnetic moment of Ce decrease. An almost linear increase of magnetic moment versus Ce-4f density of states at Fermi level is observed for the certain range of parameters.