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
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Mechanical and thermal buckling analysis of functionally graded plates
X. Zhao,Yiu-Yin Lee,K.M. Liew +2 more
TL;DR: In this article, the first-order shear deformation plate theory, in conjunction with the element-free kp-Ritz method, is employed in the current formulation, assuming that the material property of each plate varies exponentially through the thickness.
Journal ArticleDOI
Analysis of composite plates using higher-order shear deformation theory and a finite point formulation based on the multiquadric radial basis function method
TL;DR: In this article, the third-order theory of Reddy for composite laminated plates is discretized using a new type of meshless method, a finite point based on the multiquadric radial basis function method.
Journal ArticleDOI
Meshfree Methods: Progress Made after 20 Years
TL;DR: A large number of meshfree methods have emerged into a new class of computational methods with considerable success and a significant amount of progress has been made in ad-hoc methods over the past two decades.
Journal ArticleDOI
The element free galerkin method for dynamic propagation of arbitrary 3-d cracks
Petr Krysl,Ted Belytschko +1 more
TL;DR: In this article, a technique for modeling arbitrary three-dimensional dynamically propagating cracks in elastic bodies by the Element-Free Galerkin (EFG) method with explicit time integration is described.
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Crack propagation modelling using an advanced remeshing technique
TL;DR: In this paper, a fully automatic remesher is proposed to deal with multiple boundaries and multiple materials, and the propagation of the crack is achieved with both remeshing and nodal relaxation, and a maximal normal stress criterion is used to compute the crack direction.
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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