The Element-Free Galerkin Method for the Unsteady Magnetohydrodynamic Flow in a Duct

2015 ◽  
Vol 723 ◽  
pp. 181-185
Author(s):  
Xing Hui Cai ◽  
Hong Fu Qiang ◽  
Jiang Ren Lu ◽  
Guo Liang Wang
Keyword(s):  
Galerkin Method ◽  
Numerical Solutions ◽  
Magnetohydrodynamic Flow ◽  
Least Square ◽  
Element Free Galerkin Method ◽  
Moving Least Square ◽  
Coupled Equations ◽  
Element Free Galerkin ◽  
Moving Least Square Approximation ◽  
Element Free

In this paper, a meshless global element-free Galerkin method is given to obtain the numerical solutions of the coupled equations in the velocity and magnetic field for the unsteady magnetohydrodynamic flow through a straight duct with arbitrary electrical conductivity, that is, from perfectly conducting to insulated duct walls. The moving least-square approximation scheme is employed to construct shape functions. A time stepping method is employed to deal with the time derivatives. Non-uniform background grids and nodes are applied for numerical simulations. Computations are performed for different Hartmann numbers and wall conductivities at different time.

Wrinkling Analysis of Pre-Stressed Rectangular Membranes Using Element-Free Galerkin Method

2020 ◽  
pp. 2041001
Author(s):  
K. R. Unnikrishnan ◽  
I. R. Praveen Krishna ◽  
C. O. Arun
Keyword(s):  
Galerkin Method ◽  
Degrees Of Freedom ◽  
Least Square ◽  
Element Free Galerkin Method ◽  
Moving Least Square ◽  
Element Free Galerkin ◽  
Wrinkling Analysis ◽  
Moving Least Square Approximation ◽  
Element Free ◽  
The Mathematical Model

In this study, element-free Galerkin method (EFGM), a meshless method, is proposed for wrinkling analysis of pre-stressed rectangular membranes. The mathematical model for studying wrinkling of pre-stressed membranes is derived by considering the bending stiffness, though it is negligible. Moving least-square approximation for deflection is constructed by considering three degrees of freedom per node. Essential boundary conditions are imposed using scaled transformation matrix method. Initially, compression-induced buckling of a homogeneous thin plate without pre-stress is solved to validate the method and then a pre-stressed homogeneous membrane is analyzed for both compression-induced and shear-induced wrinkling. Capabilities of the proposed method for membrane analysis are compared with that of the finite element method (FEM). Comparative study on wrinkling analysis using EFGM and different FEM element types in a commercial FEM package shows that in lower modes both methods show satisfying consistency in eigenvalues with respect to the total of number of nodes, while at higher modes EFGM shows better consistency than FEM. Further, the study is extended to wrinkling of nonhomogeneous membranes subjected to linearly-varying in-plane load. The results obtained from EFGM analysis is compared and found to be matching well with those available in the literature.

scholarly journals Behavior of beam on elastic foundation using element free Galerkin method

2021 ◽  
Vol 12 (4) ◽  
pp. 14-22
Author(s):  
H.T.T. Lan
Keyword(s):  
Galerkin Method ◽  
Elastic Foundation ◽  
Least Square ◽  
Element Free Galerkin Method ◽  
Moving Least Square ◽  
Beam On Elastic Foundation ◽  
Element Free Galerkin ◽  
Mesh Free ◽  
System Equations ◽  
Element Free

One of mesh free methods, element free Galerkin method, is presented to analyze the finite beam on elastic foundation. The shape functions are constructed by using the moving least square interpolation based on a set of nodes that are arbitrarily distributed in specified domain. Discrete system equations are derived from the variation form of system equations. Numerical examples of finite beam on elastic foundation are given by establishing Matlab code. The results of this paper demonstrate the effectiveness of the proposed method with small errors compared to analytical solutions. Keywords: mesh free method, element free Galerkin method, moving least square, finite beam, elastic foundation.

FURTHER INVESTIGATION OF ELEMENT-FREE GALERKIN METHOD USING MOVING KRIGING INTERPOLATION

2004 ◽  
Vol 01 (02) ◽  
pp. 345-365 ◽  
Author(s):  
P. TONGSUK ◽  
W. KANOK-NUKULCHAI
Keyword(s):  
Boundary Conditions ◽  
Galerkin Method ◽  
Least Square ◽  
Kriging Interpolation ◽  
Shape Functions ◽  
Element Free Galerkin Method ◽  
Basic Premise ◽  
Moving Least Square ◽  
Element Free Galerkin ◽  
Element Free

Following its first introduction, this study further scrutinizes the new type of shape functions for Element-free Galerkin Method (EFGM) based on the Moving Kriging (MK) interpolation. Kriging is a geostatistical method of spatial interpolation. Its basic premise is that every unknown point can be interpolated from known scattered points in its specified neighborhood. This property is ideal for EFGM. Previously, a shortcoming of EFGM based on Moving Least Square (MLS) approximation is associated with its limitation to satisfy essential boundary conditions exactly. With MK interpolation functions, EFGM solution can satisfy essential boundary conditions automatically. Numerical tests on one and two-dimensional elasticity problems have confirmed the effectiveness of MK in addressing this specific shortcoming of EFGM. Furthermore, the study also finds the accuracy of EFGM to be greatly enhanced with the use of MK shape functions.

Study of Static Fracture Propagation by Element-Free Galerkin Method With Singular Weight Function at Crack Tip

2005 ◽  
Vol 21 (2) ◽  
pp. 125-129 ◽  
Author(s):  
K.-J. Shen ◽  
J. P. Sheng ◽  
C.-Y. Wang
Keyword(s):  
Galerkin Method ◽  
Crack Growth ◽  
Initial Crack ◽  
Least Square ◽  
Bending Test ◽  
Element Free Galerkin Method ◽  
Three Point Bending ◽  
Moving Least Square ◽  
Element Free Galerkin ◽  
Element Free

AbstractElement-free Galerkin method (EFGM) based on moving least-square curve fitting concept is presented and applied to elastic fracture problems. Because no element connectivity data are needed, EFGM is very convenient and effective numerical method for crack growth analysis. This paper is intended as an investigation of crack trajectory for different notch locations under three-point bending test. The initial crack growth angles obtained by element-free Galerkin method in comparison with those obtained by lab test reveal that both results are very close. However, numerical results also show that the location of an original notch can stronger affect the variation of crack path for different increment. The stress intensity factors (SIF) of cracks under three-point bending test with different increment are also investigated by EFGM.

A New Meshless Simulated Method of Chloride Diffusion in Concrete

2014 ◽  
Vol 1051 ◽  
pp. 725-729
Author(s):  
Ling Yao ◽  
Ling Zhang ◽  
Ling Ling Zhang ◽  
Xin Yue Zhang ◽  
Yong Jing Wang
Keyword(s):  
Chloride Content ◽  
Chloride Ions ◽  
Least Square ◽  
Chloride Diffusion ◽  
Element Free Galerkin Method ◽  
Error Norm ◽  
Moving Least Square ◽  
Element Free Galerkin ◽  
Moving Least Square Approximation ◽  
Element Free

In this paper, θ-EFG(theθfamily of methods –Element Free Galerkin) method is developed and adopted for the simulation of chloride diffusion in concrete. Diffusion of chloride ions is generally assumed to follow the Fick’s second law and its solving process usually adopts finite element and finite difference method. θ-EFG is a meshless method which uses a moving least square approximation in space domain, then uses the θ family of methods in time domain. Some discussions and One dimensional examples are carried out. The computational results compared with the analytical solution are shown that the relative error norm that time=20years, chloride content of different depth and depth =45 mm, chloride content are about 0.5% and 1% respectively.

A modified method to determine the radius of influence domain in element-free Galerkin method

2014 ◽  
Vol 229 (5) ◽  
pp. 795-805 ◽  
Author(s):  
Mao Sheng ◽  
Gensheng Li ◽  
Subhash Shah
Keyword(s):  
Least Square ◽  
Patch Tests ◽  
Moving Least Square ◽  
Modified Method ◽  
Point Of Interest ◽  
Element Free Galerkin ◽  
Radius Of Influence ◽  
Moving Least Square Approximation ◽  
Random Node ◽  
Element Free

The radius of the influence domain is an important parameter in the weight function and plays an essential role in the accuracy of approximations. A modified method was proposed for determining the radius of influence domain. The modification is that the radius of influence domain is prescribed by the desired amount of support nodes for any point of interest. The advantages of this strategy are the regularity of matrix can be ensured in moving least square approximation and the algorithm is simple and practicable. The modified method was validated by thousands of patch tests in the case of regular and irregular node collocations and Timoshenko beam problem with using random node collocation. Results show that the proposed method performs more capability to handle the arbitrary node collocation than the pre-existing methods. This paper provides an alternative way to determine the radius of influence domain.

Application of an Element-free Galerkin Method to Water Wave Propagation Problems

2014 ◽  
Vol 60 (1-4) ◽  
pp. 87-105 ◽  
Author(s):  
Ryszard Staroszczyk
Keyword(s):  
Wave Propagation ◽  
Galerkin Method ◽  
Present Model ◽  
Free Surface Elevation ◽  
Element Free Galerkin Method ◽  
Plane Flow ◽  
Element Free Galerkin ◽  
Proposed Model ◽  
Sloping Bed ◽  
Element Free

Abstract The paper is concerned with the problem of gravitational wave propagation in water of variable depth. The problem is solved numerically by applying an element-free Galerkin method. First, the proposed model is validated by comparing its predictions with experimental data for the plane flow in water of uniform depth. Then, as illustrations, results of numerical simulations performed for plane gravity waves propagating through a region with a sloping bed are presented. These results show the evolution of the free-surface elevation, displaying progressive steepening of the wave over the sloping bed, followed by its attenuation in a region of uniform depth. In addition, some of the results of the present model are compared with those obtained earlier by using the conventional finite element method.

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