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
Citations
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An implicit gradient model by a reproducing kernel strain regularization in strain localization problems
TL;DR: In this paper, a reproducing kernel strain regularization (RKSR) is proposed for non-local strain localization. But it does not address the spectral properties of RKSR.
Journal ArticleDOI
Nonlinear analysis of corrugated plates using a FSDT and a meshfree method
TL;DR: In this paper, a geometrically nonlinear analysis of stiffened and un-stiffened corrugated plates using a mesh-free Galerkin method that is based on the first-order shear deformation theory is presented.
Journal ArticleDOI
A stabilized least-squares radial point collocation method (LS-RPCM) for adaptive analysis
TL;DR: In this paper, a stabilized radial point collocation method (RPCM) that uses locally supported nodes is proposed using least-squares stabilization technique, and the focus of this work is to stabilize the solution of the RPCM in order to perform adaptive analysis.
Journal ArticleDOI
A mesh-based partition of unity method for discontinuity modeling
TL;DR: This study explores a numerical analysis scheme, the manifold method, within the framework of the partition of unity method, which has been used in solving discrete-continuum interaction problems.
Journal ArticleDOI
Meshless method based on the local weak-forms for steady-state heat conduction problems
Xue-Hong Wu,Wen-Quan Tao +1 more
TL;DR: In this paper, the meshless local Petrov-Galerkin (MLPG) method is applied to compute two steady-state heat conduction problems of irregular complex domain in 2D space.
References
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Smoothed particle hydrodynamics: Theory and application to non-spherical stars
R. A. Gingold,Joseph J Monaghan +1 more
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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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