Journal ArticleDOI
A local point interpolation method for static and dynamic analysis of thin beams
YuanTong Gu,Gui-Rong Liu +1 more
TLDR
In this article, a new LPIM formulation is proposed to deal with fourth-order boundary-value and initial-value problems for static and dynamic analysis (stability, free vibration and forced vibration) of beams.About:
This article is published in Computer Methods in Applied Mechanics and Engineering.The article was published on 2001-08-03. It has received 152 citations till now. The article focuses on the topics: Interpolation & Polynomial interpolation.read more
Citations
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Journal ArticleDOI
A local radial point interpolation method (lrpim) for free vibration analyses of 2-d solids
Gui-Rong Liu,YuanTong Gu +1 more
TL;DR: In this article, a local radial point interpolation method (LRPIM) is presented to deal with boundary value problems for free vibration analyses of two-dimensional solids, where local weak forms are developed using weighted residual method locally from the partial differential equation of free vibration.
Journal ArticleDOI
A meshfree radial point interpolation method (RPIM) for three-dimensional solids
TL;DR: In this paper, a mesh-free radial point interpolation method (RPIM) is developed for stress analysis of 3D solids, based on the Galerkin weak form formulation using 3D meshfree shape functions constructed using radial basis functions.
Journal ArticleDOI
Numerical simulation of two-dimensional sine-Gordon solitons via a local weak meshless technique based on the radial point interpolation method (RPIM)
Mehdi Dehghan,Arezou Ghesmati +1 more
TL;DR: The meshless local radial point interpolation method (LRPIM) is adopted to simulate the two-dimensional nonlinear sine-Gordon (S-G) equation and a simple predictor–corrector scheme is performed to eliminate the nonlinearity.
Journal ArticleDOI
Meshfree methods and their comparisons
TL;DR: In this paper, several typical meshfree methods are introduced and compared with each others in terms of their accuracy, convergence and effectivity, and the major technical issues in mesh free methods are discussed.
Journal ArticleDOI
An Overview on Meshfree Methods: For Computational Solid Mechanics
TL;DR: This review paper presents a methodological study on possible and existing meshfree methods for solving the partial differential equations (PDEs) governing solid mechanics problems, based mainly on the research work in the past two decades at the authors group.
References
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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
An Introduction to the Finite Element Method
TL;DR: Second-order Differential Equations in One Dimension: Finite Element Models (FEM) as discussed by the authors is a generalization of the second-order differential equation in two dimensions.
Journal ArticleDOI
Reproducing kernel particle methods
TL;DR: A new continuous reproducing kernel interpolation function which explores the attractive features of the flexible time-frequency and space-wave number localization of a window function is developed and is called the reproducingkernel particle method (RKPM).
Journal ArticleDOI
A new Meshless Local Petrov-Galerkin (MLPG) approach in computational mechanics
Satya N. Atluri,T. Zhu +1 more
TL;DR: In this article, a local symmetric weak form (LSWF) for linear potential problems is developed, and a truly meshless method, based on the LSWF and the moving least squares approximation, is presented for solving potential problems with high accuracy.
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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A new Meshless Local Petrov-Galerkin (MLPG) approach in computational mechanics
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