Journal ArticleDOI
Admissible approximations for essential boundary conditions in the reproducing kernel particle method
J. Gosz,Wing Kam Liu +1 more
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TLDR
In the reproducing kernel particle method (RKPM) and meshless methods in general, enforcement of essential boundary conditions is awkward as the approximations do not satisfy the Kronecker delta condition and are not admissible in the Galerkin formulation as they fail to vanish at essential boundaries as discussed by the authors.Abstract:
In the reproducing kernel particle method (RKPM), and meshless methods in general, enforcement of essential boundary conditions is awkward as the approximations do not satisfy the Kronecker delta condition and are not admissible in the Galerkin formulation as they fail to vanish at essential boundaries Typically, Lagrange multipliers, modified variational principles, or a coupling procedure with finite elements have been used to circumvent these shortcomingsread more
Citations
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Meshfree and particle methods and their applications
Shaofan Li,Wing Kam Liu +1 more
TL;DR: A survey of mesh-free and particle methods and their applications in applied mechanics can be found in this article, where the emphasis is placed on simulations of finite deformations, fracture, strain localization of solids; incompressible as well as compressible flows; and applications of multiscale methods and nano-scale mechanics.
Journal ArticleDOI
Imposing essential boundary conditions in mesh-free methods
TL;DR: This paper presents a general overview on the existing techniques to enforce essential boundary conditions in Galerkin based mesh-free methods and special attention is paid to the mesh- free coupling with finite elements for the imposition of prescribed values and to methods based on a modification of theGalerkin weak form.
Journal ArticleDOI
A review of meshless methods for laminated and functionally graded plates and shells
TL;DR: A review of meshless methods for composite structures is given in this paper, with main emphasis on the element-free Galerkin method and reproducing kernel particle method, including static and dynamic analysis, free vibration, buckling and nonlinear analysis.
Journal ArticleDOI
Meshfree Methods: Progress Made after 20 Years
TL;DR: A large number of meshfree methods have emerged into a new class of computational methods with considerable success and a significant amount of progress has been made in ad-hoc methods over the past two decades.
Journal ArticleDOI
Least‐squares collocation meshless method
TL;DR: In this article, a finite point method, least square collocation meshless method, is proposed, where the equilibrium conditions are satisfied not only at the collocation points but also at the auxiliary points in a least square sense.
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.
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
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.