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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The rs‐method for material failure simulations
Rong Fan,Jacob Fish +1 more
TL;DR: In this paper, a new method for propagating arbitrary failure modes is presented, termed as the rs-version of the finite element method (or reduced order s-method), which has been integrated in ABAQUS and verified on several test problems.
Journal ArticleDOI
A natural neighbour meshless method with a 3D shell-like approach in the dynamic analysis of thin 3D structures
TL;DR: In this article, the authors presented the dynamic analysis of three-dimensional plate and shell structures based on an improved meshless method, the Natural Neighbour Radial Point Interpolation Method (NNRPIM) using a shell-like formulation.
Journal ArticleDOI
Simulation of the phase field Cahn–Hilliard and tumor growth models via a numerical scheme: Element-free Galerkin method
Vahid Mohammadi,Mehdi Dehghan +1 more
TL;DR: The temporal variable is discretized using a second-order method based on semi-implicit backward differential formula, and the stabilized term is added to the considered time discretization.
Journal ArticleDOI
Element free Galerkin approach based on the reproducing kernel particle method for solving 2D fractional Tricomi-type equation with Robin boundary condition
Mehdi Dehghan,Mostafa Abbaszadeh +1 more
TL;DR: A new version of the EFG method based on the shape functions of reproducing kernel particle method (RKPM) is proposed, which will solve the fractional Tricomi-type equation using the new technique.
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A thermodynamics-based cohesive model for discrete element modelling of fracture in cemented materials
TL;DR: In this paper, a discrete modeling approach employing a new cohesive model is proposed to investigate the failure response of cemented materials, based on a generic thermodynamic framework for coupling damage mechanics and plasticity theory.
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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