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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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Multi-scale methods
TL;DR: In this article, the meshless hierarchical partition of unity is used as a multiple scale basis for elastic-plastic one-dimensional problems and 2-D large deformation strain localization problems.
Journal ArticleDOI
A mass-redistributed finite element method (MR-FEM) for acoustic problems using triangular mesh
TL;DR: An improved finite element method for solving acoustic problems by re-distributing the mass in the mass matrix to "tune" the balance, aiming to minimize the dispersion errors.
Journal ArticleDOI
The finite element method enriched by interpolation covers
Jaehyung Kim,Klaus-Jürgen Bathe +1 more
TL;DR: This paper considers the 3-node triangular and 4-node tetrahedral displacement-based elements for two- and three-dimensional analyses, respectively, and evaluates the effectiveness of the method, and illustrates the power of the scheme through the solution of various problems.
Journal ArticleDOI
A meshfree weak-strong (MWS) form method for time dependent problems
TL;DR: In this paper, a mesh free weak-strong (MWS) form method is proposed for time dependent problems, which is based on a combination of both the strong form and the local weak form.
Journal ArticleDOI
Explicit and implicit meshless methods for linear advection–diffusion-type partial differential equations
TL;DR: These schemes use well distributed quasi-random points and approximate the solution using global radial basis functions to solve linear advection-diffusion problems with complex-shaped boundaries in higher dimensions with no need for complex mesh/grid structure and with no extra implementation difficulties.
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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