Journal ArticleDOI
Element‐free Galerkin methods
Ted Belytschko,Y. Y. Lu,L. Gu +2 more
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In this article, an element-free Galerkin method which is applicable to arbitrary shapes but requires only nodal data is applied to elasticity and heat conduction problems, where moving least-squares interpolants are used to construct the trial and test functions for the variational principle.Abstract:
An element-free Galerkin method which is applicable to arbitrary shapes but requires only nodal data is applied to elasticity and heat conduction problems. In this method, moving least-squares interpolants are used to construct the trial and test functions for the variational principle (weak form); the dependent variable and its gradient are continuous in the entire domain. In contrast to an earlier formulation by Nayroles and coworkers, certain key differences are introduced in the implementation to increase its accuracy. The numerical examples in this paper show that with these modifications, the method does not exhibit any volumetric locking, the rate of convergence can exceed that of finite elements significantly and a high resolution of localized steep gradients can be achieved. The moving least-squares interpolants and the choices of the weight function are also discussed in this paper.read more
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Improved element-free Galerkin method for two-dimensional potential problems
Zan Zhang,Peng Zhao,K.M. Liew +2 more
TL;DR: In this paper, the authors derived the formulae of an improved EFG (IEFG) method for two-dimensional potential problems by using the weighted orthogonal basis function to construct the MLS interpolants.
Journal ArticleDOI
Meshless local boundary integral equation method for 2D elastodynamic problems
TL;DR: In this article, a meshless method for solving transient elastodynamic boundary value problems, based on the local boundary integral equation (LBIE) method and the moving least squares approximation (MLS), is proposed.
Journal ArticleDOI
Numerical simulation of thermo-elastic fracture problems using element free Galerkin method
TL;DR: In this article, an element free Galerkin method (EFGM) has been extended to solve thermo-elastic fracture problems in homogeneous and inhomogeneous materials (bi-materials).
Journal ArticleDOI
Three-dimensional complex variable element-free Galerkin method
TL;DR: Numerical results reveal that the CVEFG method has better accuracy and higher computational efficiency than other methods such as the element-free Galerkin method.
Journal ArticleDOI
Further investigation of element-free galerkin method using moving kriging interpolation
TL;DR: Wang et al. as mentioned in this paper further scrutinized the new type of shape functions for Element-free Galerkin Method (EFGM) based on the Moving Kriging (MK) interpolation.
References
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Journal ArticleDOI
Smoothed particle hydrodynamics: Theory and application to non-spherical stars
R. A. Gingold,Joseph J Monaghan +1 more
Journal ArticleDOI
Theory of Elasticity (3rd ed.)
Journal ArticleDOI
Surfaces generated by moving least squares methods
Peter Lancaster,K. Salkauskas +1 more
TL;DR: In this article, an analysis of moving least squares (m.l.s.) methods for smoothing and interpolating scattered data is presented, in particular theorems concerning the smoothness of interpolants and the description of m. l.s. processes as projection methods.
Journal ArticleDOI
Generalizing the finite element method: Diffuse approximation and diffuse elements
TL;DR: The diffuse element method (DEM) as discussed by the authors is a generalization of the finite element approximation (FEM) method, which is used for generating smooth approximations of functions known at given sets of points and for accurately estimating their derivatives.
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