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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Meshfree methods and their comparisons
TL;DR: In this paper, several typical meshfree methods are introduced and compared with each others in terms of their accuracy, convergence and effectivity, and the major technical issues in mesh free methods are discussed.
Journal ArticleDOI
Consistent pseudo-derivatives in meshless methods
Y. Krongauz,Ted Belytschko +1 more
TL;DR: In this paper, a meshless Petrov-Galerkin formulation is developed in which derivatives of the trial functions are obtained as a linear combination of derivatives of Shepard functions, and conditions on test functions and trial functions for nonintegrable pseudo-derivatives for Petrov Galerkin method which pass the patch test.
Journal ArticleDOI
A Lagrangian meshless finite element method applied to fluid-structure interaction problems
TL;DR: In this article, a method for the solution of the incompressible fluid flow equations using a Lagrangian formulation is presented, which simplifies the connections with fixed or moving solid structures, thus providing a very easy way to solve fluid-structure interaction problems.
Journal ArticleDOI
Particle dynamics modeling methods for colloid suspensions
Dan S. Bolintineanu,Gary S. Grest,Jeremy B. Lechman,Flint Pierce,Steven J. Plimpton,P. Randall Schunk +5 more
TL;DR: In this article, the authors present a review and critique of several methods for the simulation of the dynamics of colloidal suspensions at the mesoscale, focusing particularly on simulation techniques for hydrodynamic interactions, including implicit solvents (Fast Lubrication Dynamics, an approximation to Stokesian Dynamics) and explicit/particle-based (Multi Particle Collision Dynamics and Dissipative Particle Dynamics).
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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