Meshfree Methods

Author (s): Huerta, A., Belytschko, T., Fernández-Méndez, S., Rabczuk, T., Zhuang, X., and Arroyo, M.
Journal: Encyclopedia of Computational Mechanics Second Edition

Volume: 2 Fundamentals, Chapter 3
Pages: 1 – 38
Date: 2017

Abstract:
The aim of this chapter is to provide an in-depth presentation and survey of meshfree particle methods. Several particle approximations are reviewed; the SPH method, corrected gradient methods, the moving least squares (MLS) approximation, and maximum-entropy approximations. The discrete equations are derived from a collocation scheme or a Galerkin method. Special attention is paid to the treatment of essential boundary conditions. Finally, different approaches for modelling discontinuities in meshfree methods are described, including peridynamics and phase-fields.

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Bibtex:

@incollection{AH-HBFRZA:17,
	Author = {Huerta, Antonio and Belytschko, Ted and Fernandez-Mendez, Sonia and Rabczuk, Timon and Zhuang, Xiaoying and Arroyo, Marino},
	Title = {Meshfree {M}ethods},
	Booktitle = {Encyclopedia of Computational Mechanics Second Edition},
	Chapter = {3},
	Volume = {Part 2 Fundamentals},
	Editor = {Erwin Stein and Rene de Borst and Thomas J. R. Hughes},
	Pages = {},
	Publisher = {John Wiley \& Sons, Ltd.},
	Address = {Chichester},
	Year = {2017},
        Doi={10.1002/9781119176817.ecm2005},
        Url={https://onlinelibrary.wiley.com/doi/pdf/10.1002/9781119176817.ecm2005}
}