Roots of Mesh-free methods go back to the seventies. The major difference to finite element methods is that the domain of interest is discretized only with nodes, often called particles. These particles interact via mesh-free shape functions in a continuum framework similar as finite elements do although particle "connectivity" can change over the course of a simulation. This flexibility of mesh-free methods has been exploited in applications with large deformations in fluid and solid mechanics, e.g. to name a few, free-surface flow, metal forming, fracture and fragmentation, to name a few.
Though there are a few publications on mesh-free methods formulated in an Eulerian (or ALE) description, e.g. Fries 2005, most mesh-free methods are pure Lagrangian in character. The non negligible advantages of mesh-free methods as compared to finite elements are: their higher order continuous shape functions that can be exploited e.g. for thin shells; higher smoothness; certain advantages in crack propagation problems. The most UN hidden drawback of mesh-free methods is probably their higher computational cost, regardless of some instabilities that certain mesh-free methods have. The paper deals with the basic methodology of mesh-free methods along with the mathematics involved.
By Vimalkumar P. Palsanawala" A Study on Mesh Free Methods: A Different Form of FEM"
Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-5 , August 2018,
Paper URL: http://www.ijtsrd.com/papers/ijtsrd18314.pdf
Direct URL: http://www.ijtsrd.com/engineering/mechanical-engineering/18314/a-study-on-mesh-free-methods-a-different-form-of-fem/vimalkumar-p-palsanawala
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