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 meshfree radial point interpolation method for analysis of functionally graded material (FGM) plates
TL;DR: In this article, a mesh-free model is presented for static and dynamic analyses of functionally graded material (FGM) plates based on the radial point interpolation method (PIM).
Journal ArticleDOI
A meshfree method for the solution of two-dimensional cubic nonlinear Schrödinger equation
TL;DR: In this paper, an efficient numerical technique is developed to approximate the solution of two-dimensional cubic nonlinear Schrodinger equations, which is based on the nonsymmetric radial basis function collocation method (Kansa's method), within an operator Newton algorithm.
Journal ArticleDOI
Multiscale numerical modeling of propagation and coalescence of multiple cracks in rock masses
TL;DR: In this paper, a multiscale numerical model based on the extended finite element method and global-local analysis is proposed to simulate the damage evolution of crack-weakened rock masses.
Journal ArticleDOI
An edge-based smoothed tetrahedron finite element method (ES-T-FEM) for 3D static and dynamic problems
TL;DR: A novel domain-based selective scheme is proposed leading to a combined ES-T-/NS-FEM model that is immune from volumetric locking and hence works well for nearly incompressible materials.
Journal ArticleDOI
Analysis of stiffened corrugated plates based on the FSDT via the mesh-free method
TL;DR: In this article, the elastic bending of unstiffened and stiffened corrugated plates is studied, and a mesh-free Galerkin method is presented for the analyses, where the stiffness matrix is obtained by superimposing the strain energy of the orthotropic plate and the beams.
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
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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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