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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Transient thermoelastic deformations of a thick functionally graded plate
L. F. Qian,Romesh C. Batra +1 more
TL;DR: In this paper, the authors studied the transient thermoelastic deformations of a thick functionally graded plate with edges held at a uniform temperature and either simply supported or clamped.
Journal ArticleDOI
Volumetric locking in the element free Galerkin method
John E. Dolbow,Ted Belytschko +1 more
TL;DR: A new formulation of the Element Free Galerkin (EFG) method is developed for the modelling of incompressible materials and a selective reduced integration procedure is developed by implementing nodal quadrature.
Journal ArticleDOI
A meshfree unification: reproducing kernel peridynamics
TL;DR: This paper is the first investigation establishing the link between the meshfree state-based peridynamics method and other meshfree methods, in particular with the moving least squares reproducing kernel particle method (RKPM).
Journal ArticleDOI
Numerical simulation of functionally graded cracked plates using NURBS based XIGA under different loads and boundary conditions
TL;DR: In this paper, extended isogeometric analysis (XIGA) is performed to simulate the cracked functionally graded material (FGM) plates using first order shear deformation theory (FSDT) under different types of loading and boundary conditions.
Journal ArticleDOI
An isogeometric boundary element method for elastostatic analysis: 2D implementation aspects
TL;DR: In this article, an isogeometric boundary element method (IGABEM) is proposed for elastostatic analysis, which only requires a representation of the geometry of the domain for analysis, fitting neatly with the boundary representation provided completely by CAD.
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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