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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Weighted Extended B-Spline Approximation of Dirichlet Problems
TL;DR: A new finite element method which uses weighted extended B-splines on a regular grid as basis functions for solving Dirichlet problems on bounded domains in arbitrary dimensions yields smooth, high order accurate approximations with relatively low dimensional subspaces.
Journal ArticleDOI
Free vibration analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method in thermal environment
TL;DR: In this article, a free vibration analysis of functionally graded nanocomposite plates reinforced by single-walled carbon nanotubes (SWCNTs), using the element-free kp-Ritz method, is presented.
Journal ArticleDOI
Meshless animation of fracturing solids
TL;DR: A new meshless animation framework for elastic and plastic materials that fracture is presented, with a highly dynamic surface and volume sampling method that supports arbitrary crack initiation, propagation, and termination, while avoiding many of the stability problems of traditional mesh-based techniques.
Journal ArticleDOI
New boundary condition treatments in meshfree computation of contact problems
Jiun-Shyan Chen,Hui-Ping Wang +1 more
TL;DR: In this paper, two boundary condition treatments are proposed to enhance the computational efficiency of mesh-free methods for contact problems by introducing singularities to the kernel functions of the essential and contact boundary nodes so that the corresponding coefficients of the singular kernel shape functions recover nodal values and consequently kinematic constraints can be imposed directly.
Journal ArticleDOI
An extended finite element method with higher-order elements for curved cracks
TL;DR: In this paper, a finite element method for linear elastic fracture mechanics using enriched quadratic interpolations is presented, which is enriched with the asymptotic near tip displacement solutions and the Heaviside function so that the finite element approximation is capable of resolving the singular stress field at the crack tip as well as the jump in the displacement field across the crack face.
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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