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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A coupled SPH-DEM model for micro-scale structural deformations of plant cells during drying☆
TL;DR: In this paper, a single plant cell was modeled with smoothed particle hydrodynamics (SPH) and a discrete element method (DEM) to study the basic micromechanics that govern the cellular structural deformations during drying.
Journal ArticleDOI
A double-layer interpolation method for implementation of BEM analysis of problems in potential theory
TL;DR: The DLIM keeps the main advantages of MLS, such as significantly alleviating the meshing task, while providing much better accuracy than the traditional BEM, and established additional constraint equations between source and virtual nodes using a moving least-squares approximation (second-layer interpolation).
Journal ArticleDOI
Vibration of Plate with Curvilinear Stiffeners Using Mesh-Free Method
TL;DR: In this article, the element-free Galerkin method was used for vibration analysis of unitized structures (e.g., a plate with curvilinear stiffeners) using the first-order shear deformation theory and Timoshenko beam theory, respectively.
Journal ArticleDOI
Moving particle finite element method with superconvergence: Nodal integration formulation and applications
Su Hao,Wing Kam Liu +1 more
TL;DR: In this article, a nodal-based moving particle finite element method, inconjunction with the proposed superconvergence approach, provides an optimized combination in numerical accuracy and computation efficiency.
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A localized collocation meshless method (LCMM) for incompressible flows CFD modeling with applications to transient hemodynamics
TL;DR: In this article, a localized collocation meshless method (LCMM) was proposed to model laminar incompressible flows and a high order upwinding scheme was devised to dampen the numerical oscillations arising in convection-dominated flows.
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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