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.

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.

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.

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.

An Efficient Meshfree Method for Fracture Analysis of Cracks in Bi-Materials

2006 ◽  
Author(s):  
B. Nandulal ◽  
B. N. Rao ◽  
C. Lakshmana Rao
Keyword(s):  
Computational Efficiency ◽  
Basis Function ◽  
Meshfree Method ◽  
Fracture Analysis ◽  
Least Square ◽  
Moving Least Square ◽  
Linear Elastic ◽  
Moving Least Square Approximation ◽  
Material Fracture ◽  
Element Free

This paper presents an enriched meshless method based on an improved moving least-square approximation (IMLS) method for fracture analysis of cracks in homogeneous, isotropic, linear-elastic, two-dimensional bimaterial solids, subject to mixed-mode loading conditions. The method involves an element-free Galerkin formulation in conjunction with IMLS and a new enriched basis functions to capture the singularity field in linear-elastic bi-material fracture mechanics. In the IMLS method, the orthogonal function system with a weight function is used as the basis function. The IMLS has higher computational efficiency and precision than the MLS, and will not lead to an ill-conditioned system of equations. The proposed enriched basis function can be viewed as a generalized enriched basis function, which degenerates to a linear-elastic basis function when the bimaterial constant is zero. Numerical examples are presented to illustrate the computational efficiency and accuracy of the proposed method.

USE OF B-SPLINE FUNCTION IN ELEMENT FREE GALERKIN METHOD FOR NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATION

2009 ◽  
Vol 06 (03) ◽  
pp. 349-360
Author(s):  
K. SANDEEP ◽  
K. KAMAL KUMAR
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Spline Function ◽  
Least Square ◽  
Partial Differential ◽  
Order Continuity ◽  
B Spline ◽  
Moving Least Square ◽  
Element Free Galerkin ◽  
Element Free

The paper presents application of a B-spline function in place of a shape function obtained by using moving least square approximant with B-spline weight and linear basis. The piecewise polynomial function of B-spline with C2 and lower order continuity is efficiently used in element free Galerkin (EFG) method to generate a new fast algorithm for the solution of one-dimensional partial differential equation. The support of B-spline function is assumed as the domain of influence of EFG method. The results of bar deflection are compared with those obtained by other researchers.

The Improved Element-Free Galerkin Method for Diffusional Drug Release Problems

2020 ◽  
Vol 12 (08) ◽  
pp. 2050096
Author(s):  
Guodong Zheng ◽  
Yumin Cheng
Keyword(s):  
Drug Release ◽  
Weak Form ◽  
Equation System ◽  
Least Square ◽  
Moving Least Square ◽  
Scale Parameters ◽  
Element Free Galerkin ◽  
Penalty Factor ◽  
The Difference ◽  
Element Free

By using the improved moving least-square (IMLS) approximation to present the shape function, the improved element-free Galerkin (IEFG) method is investigated to solve diffusional drug release problems in this paper. In order to get the discretized equation system, Galerkin weak form of a diffusional drug release problem is used with applying essential boundary conditions using the penalty method. The difference method is applied for discretization of time domain. Then the formulae of IEFG method for solving diffusional drug release problems are presented. Three numerical example problems are given to study the convergence of solutions of IEFG method in this paper. The influences of scale parameters of influence domain, penalty factor and node distribution on the accuracy of the solutions of IEFG method are discussed. Compared with finite element method, the correctness of IEFG method in this paper is shown.

A MESHLESS ANALYSIS OF SHELLS BASED ON MOVING KRIGING INTERPOLATION

2007 ◽  
Vol 04 (04) ◽  
pp. 543-565 ◽  
Author(s):  
VILAYSAK SAYAKOUMMANE ◽  
WORSAK KANOK-NUKULCHAI
Keyword(s):  
Additional Treatment ◽  
Least Square ◽  
Shell Structures ◽  
Kriging Interpolation ◽  
Interpolation Function ◽  
Moving Least Square ◽  
Element Free Galerkin ◽  
Kronecker Delta ◽  
Mls Approximation ◽  
Element Free

An Element Free Galerkin Method (EFGM) for the analysis of degenerated shell structures is presented. The method is based on the Moving Kriging (MK) Interpolation function. The properties of the interpolation function possess the Kronecker delta property. With the MK Interpolation function no additional treatment required at the boundary conditions compared with that of using Moving Least Square (MLS) approximation. This deficiency of MLS at boundary condition has been definitely eradicated. The membrane and shear locking in the numerical analysis for degenerated shell problems has been alleviated by using higher order and removed by using quartic order of polynomials. Numerical benchmark examples for shell structures are presented to validate the proposed approach.

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.

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