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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To mesh or not to mesh. That is the question
Sergio Idelsohn,Eugenio Oñate +1 more
TL;DR: In this paper, the authors show that the choice between using a standard finite element mesh (such as those made of tetrahedra or hexahedra) and using a meshless method is not, in large majority of the cases, the right question.
Journal ArticleDOI
On numerical modeling of animal swimming and flight
TL;DR: A review of the recent progress in numerical techniques of solving animal swimming and flight problems can be found in this paper, where the authors classified numerical studies into five stages, of which the main characteristics and the numerical strategies are described and discussed.
Journal ArticleDOI
A complex variable meshless method for fracture problems
Yumin Cheng,Jiuhong Li +1 more
TL;DR: In this article, a complex variable moving least-square approximation (CVMLS) is proposed for fracture problems, and the formulae of the complex variable meshless method are obtained.
Journal ArticleDOI
Solving heat transfer problems with phase change via smoothed effective heat capacity and element-free Galerkin methods
Haitian Yang,Yiqian He +1 more
TL;DR: In this article, a smoothed effective heat capacity model that combines with element-free Galerkin (EFG) method is presented to solve heat transfer problems with phase change.
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The Improved Element-Free Galerkin Method Based on the Nonsingular Weight Functions for Inhomogeneous Swelling of Polymer Gels
Fengbin Liu,Yumin Cheng +1 more
TL;DR: In this paper, the interpolating moving least squares (IMLS) method based on a nonsingular weight function is used to construct the approximation function, the weak form of the problem of inhomogenization.
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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