A meshless algorithm with the improved moving least square approximation for the nonlinear improved Boussinesq equation

2020 ◽  
Author(s):  
Yu Tan ◽  
Xiao-Lin Li
Keyword(s):  
Boussinesq Equation ◽  
Least Square ◽  
Moving Least Square ◽  
Moving Least Square Approximation

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.

Square Cracks in Three-Dimensional Transversely Isotropic Solids

2012 ◽  
Vol 487 ◽  
pp. 617-621
Author(s):  
Ya Dong Bian ◽  
Yu Zhou Sun
Keyword(s):  
Crack Opening ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Boundary Integral ◽  
Least Square ◽  
Weight Functions ◽  
Opening Displacement ◽  
Moving Least Square ◽  
Moving Least Square Approximation ◽  
Fracture Damage

This paper presents a study for the square crack in a three-dimensional infinite transversely isotropic medium, which can model the fracture damage of rock that displays transversely isotropic behavior. The study is based on a newly derived boundary integral equation. To carry out the numerical simulation, the crack opening displacement is first expressed as the product of the weight functions and the characteristic terms, and the unknown weight is approximated with the moving least-square approximation. A boundary type numerical scheme is established, and the effect of the orientation of the principle axis on the stress intensity factor is studied. The interaction between two coplanar square cracks are also modeled and discussed.

Numerical Simulation Based on Meshless Formulation: Application to 2D Solid Mechanics

2012 ◽  
Author(s):  
Y. Ghozzi ◽  
C. Labergere ◽  
P. Villon
Keyword(s):  
Weight Function ◽  
Solid Mechanics ◽  
Specific Weight ◽  
Least Square ◽  
Weight Functions ◽  
Boundary Line ◽  
Moving Least Square ◽  
Simulation Based ◽  
Moving Least Square Approximation ◽  
The Galerkin Method

This paper presents the development of Meshless Methods based on Moving Least Square Approximation (MLSA) [3][10][14]. In the case of solid mechanics, the shape displacement functions are computed for each node with a centered scheme approximation [3][12] associated with a specific weight function [10]. Both interpolated and approximated weight functions are studied [10][9][15]. We propose to build a new C1 weight function based on a 2d boundary line. The Galerkin Method is used to solve the mechanical equilibrium balance problems [14]. A 2-dimensional example is presented to validate the Meshless Method.

scholarly journals The Improved Moving Least-Square Ritz Method for the One-Dimensional Sine-Gordon Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Qi Wei ◽  
Rongjun Cheng
Keyword(s):  
Gordon Equation ◽  
Ritz Method ◽  
Least Square ◽  
Sine Gordon Equation ◽  
One Dimensional ◽  
Moving Least Square ◽  
Discrete Equations ◽  
Moving Least Square Approximation ◽  
Minimization Procedure ◽  
The One

Analysis of the one-dimensional sine-Gordon equation is performed using the improved moving least-square Ritz method (IMLS-Ritz method). The improved moving least-square approximation is employed to approximate the 1D displacement field. A system of discrete equations is obtained by application of the Ritz minimization procedure. The effectiveness and accuracy of the IMLS-Ritz method for the sine-Gordon equation are investigated by numerical examples in this paper.

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.

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