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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
Citations
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A meshless local Petrov-Galerkin scaled boundary method
Andrew Deeks,Charles E. Augarde +1 more
TL;DR: In this paper, a meshless method for determining the shape functions in the circumferential direction based on the local Petrov-Galerkin approach is presented, and the solution is shown to converge significantly faster than conventional scaled boundary finite elements when a comparable number of degrees of freedom are used.
Journal ArticleDOI
A temporal stable node-based smoothed finite element method for three-dimensional elasticity problems
TL;DR: In this article, a stabilized node-based smoothed finite element method (sNS-FEM) is formulated for three-dimensional (3-D) elastic-static analysis and free vibration analysis.
Journal ArticleDOI
Application of the element-free Galerkin meshless method to 3-D fracture mechanics problems
TL;DR: In this paper, a simple meshless method, known as element-free Galerkin method (EFG), is proposed for the solution of 3D elastic fracture mechanics problems.
Journal ArticleDOI
Modeling and simulation of bioheat transfer in the human eye using the 3D alpha finite element method (αFEM)
TL;DR: In this article, an alpha finite element method (αFEM) is proposed to compute two-dimensional and three-dimensional bioheat transfer in the human eyes, which can produce much more accurate results using triangular (2D) and tetrahedron (3D) elements.
Journal ArticleDOI
Conditions for locking-free elasto-plastic analyses in the Element-Free Galerkin method
TL;DR: In this article, it is shown that the finite element (FE) method can be conceived as a specialisation of the EFG method, and that for a specific choice of the FE shape functions are retrieved.
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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