Huerta, A.Belytschko, T.Fernandez-Mendez, S.Rabczuk, T.2007-08-142007-08-142004Rabczuk, T., Belytschko, T., Fernandez-Mendez, S., & Huerta A. Meshfree Methods. In Encyclopedia of Computational Mechanics. John Wiley & Sons, Mississauga, 2004.978-0-470-84699-5http://hdl.handle.net/10092/354Aim of the present chapter is to provide an in-depth presentation and survey of mesh-free particle methods. Several particle approximation are reviewed; the SPH method, corrected gradient methods and the Moving least squares (MLS) approximation. The discrete equations are derived from a collocation scheme or as Galerkin method. Special attention is paid to the treatment of essential boundary conditions. A brief review over radial basis functions is given because they play a significant role in mesh-free methods. Finally, different approaches for modelling discontinuities in mesh-free methods are described.Element-free GalerkinMoving least squaresMeshlessSmooth particle hydrodynamicsFields of Research::290000 Engineering and Technology::290500 Mechanical and Industrial Engineering::290501 Mechanical engineering