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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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Optimal shape profiles for cooling fins of high and low conductivity.
TL;DR: In this article, the authors present a numerical approach able to capture the dependence of the optimal shape profiles of thermal fins on the conductivity parameters, and obtain the optimal shapes similar to the shapes of intestinal villi and stegosaurus plates.
Journal ArticleDOI
Error analysis in Sobolev spaces for the improved moving least-square approximation and the improved element-free Galerkin method
Xiaolin Li,Hao Chen,Yan Wang +2 more
TL;DR: Under appropriate assumption on weight functions, error estimates for the IMLS approximation are then established in Sobolev spaces in multiple dimensions and numerical examples are presented to prove the theoretical error results.
Journal ArticleDOI
Studies on ballistic impact of the composite panels
TL;DR: In this paper, a composite plate made of woven fabric CFRP, E-glass/epoxy, and Kevlar/E-epoxy composites is considered for high velocity impact.
Journal ArticleDOI
Meshfree Simulations of Ductile Crack Propagations
Shaofan Li,Cerup B. Simonsen +1 more
TL;DR: In this paper, a mesh-free method is used to simulate ductile crack growth and propagation under finite deformation and large scale yielding conditions, and a so-called parametric visibility condition and its related particle splitting procedure have been developed to automatically adapt the evolving strong continuity or fracture configuration due to an arbitrary crack growth in ductile materials.
Journal ArticleDOI
High rock slope stability analysis using the enriched meshless shepard and least squares method
TL;DR: In this article, the meshless Shepard and least squares (MSLS) method is extended for modeling jointed rock mass and the joint is modeled as discontinuity governing the near-field stress.
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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