Journal ArticleDOI
An n-sided polygonal smoothed finite element method (nSFEM) for solid mechanics
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TLDR
In this paper, Liu et al. extended the smoothed finite element method (SFEM) to a more general case, where the problem domain can be discretized by a set of polygons, each with an arbitrary number of sides.About:
This article is published in Finite Elements in Analysis and Design.The article was published on 2007-08-01. It has received 280 citations till now. The article focuses on the topics: Smoothed finite element method & Mixed finite element method.read more
Citations
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Journal ArticleDOI
An edge-based smoothed finite element method (ES-FEM) for static, free and forced vibration analyses of solids
TL;DR: In this paper, an edge-based smoothed finite element method (ES-FEM) was proposed to improve the accuracy of the FEM without much changing to the standard FEM settings.
Journal ArticleDOI
A node-based smoothed finite element method (NS-FEM) for upper bound solutions to solid mechanics problems
TL;DR: The numerical results demonstrated that the NS-FEM possesses the following properties: upper bound in the strain energy of the exact solution when a reasonably fine mesh is used; well immune from the volumetric locking; and insensitive to element distortion.
Journal ArticleDOI
A smoothed finite element method for plate analysis
TL;DR: In this paper, a quadrilateral element with smoothed curvatures for Mindlin-Reissner plates is proposed, where the curvature at each point is obtained by a non-local approximation via a smoothing function.
Journal ArticleDOI
A generalized gradient smoothing technique and the smoothed bilinear form for galerkin formulation of a wide class of computational methods
Gui-Rong Liu,Gui-Rong Liu +1 more
TL;DR: This paper presents a generalized gradient smoothing technique, the corresponding smoothed bilinear forms, and the smoothed Galerkin weakform that is applicable to create a wide class of efficient numerical methods with special properties including the upper bound properties.
Journal ArticleDOI
On the Virtual Element Method for three-dimensional linear elasticity problems on arbitrary polyhedral meshes
TL;DR: This work focuses on the linear elasticity equations in three-dimensions and elaborate upon the key concepts underlying the first-order VEM, and presents several numerical studies in order to verify convergence of the VEM and evaluate its performance for various types of meshes.
References
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Book
Theory of elasticity
TL;DR: The theory of the slipline field is used in this article to solve the problem of stable and non-stressed problems in plane strains in a plane-strain scenario.
Book
The finite element method
TL;DR: In this article, the methodes are numeriques and the fonction de forme reference record created on 2005-11-18, modified on 2016-08-08.
Journal ArticleDOI
Element‐free Galerkin methods
Ted Belytschko,Y. Y. Lu,L. Gu +2 more
TL;DR: 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.
Book
Spatial Tessellations: Concepts and Applications of Voronoi Diagrams
TL;DR: In this article, the Voronoi diagram generalizations of the Voroni diagram algorithm for computing poisson Voroni diagrams are defined and basic properties of the generalization of Voroni's algorithm are discussed.