The meshless finite element method

By Sergio R. Idelsohn, Eugenio Oñate, Néstor Calvo, Facundo Del Pin. 2003

269 citations recorded by the source corpus.

A meshless method is presented which has the advantages of the good meshless methods concerning the ease of introduction of node connectivity in a bounded time of order n, and the condition that the shape functions depend only on the node positions. Furthermore, the method proposed also shares several of the advantages of the finite element method such as: (a) the simplicity of the shape functions in a large part of the domain; (b) C0 continuity between elements, which allows the treatment of material discontinuities, and (c) ease of introduction of the boundary conditions. Copyright © 2003 John Wiley & Sons, Ltd.

Subfields: Civil and Structural Engineering, Mechanics of Materials, Safety, Risk, Reliability and Quality

View Paper: https://www.semanticscholar.org/paper/ff08c7a7af57dc886420e675a72c63bee4137f84

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Citations in the corpus

A Lagrangian meshless finite element method applied to fluid-structure interaction problems (2003, methodology): “[12].”
Meshfree Methods: Progress Made after 20 Years (2017, unknown): “…LS: least squares; (cid:129) MaxEnt: maximum entropy (Arroyo and Ortiz 2006; Sukumar 2004); (cid:129) MFEM: meshless finite element method (Idelsohn et al. 2003f); (cid:129) MFS: method of finite spheres (De and Bathe 2000); (cid:129) MLPG: meshless local Petrov-Galerkin (Atluri and Zhu…”
To mesh or not to mesh. That is the question (2006, background): “Lately, the meshless ideas were generalized to take into account the finite element type approximations in order to obtain the same computing time in mesh generation as in the evaluation of the meshless connectivity [9].”
Conforming polygonal finite elements (2004, methodology): “In a recent study, Idelsohn and co-workers [35, 36 ] used the Laplace shape function”
Possibilities of the particle finite element method for fluid–soil–structure interaction problems (2011, methodology): “We use a mesh regeneration procedure blending elements of different shapes using an extended Delaunay tesselation with special shape functions [17, 19].”
The particle finite element method. An overview (2004, unknown): “Details of the mesh generation procedure and the derivation of the MFEM shape functions can be found in [Idelsohn et al. (2003a; 2003c; 2004)].”
A displacement‐based finite element formulation for general polyhedra using harmonic shape functions (2014, methodology): “Shape functions derived from meshless methods have also been used to develop polyhedral finite elements [3, 5, 8].”
The natural neighbour radial point interpolation method: dynamic applications (2009, methodology): “) and the meshless finite element method (MFEM) ( Idelsohn et al. , 2003”
Interaction between an elastic structure and free-surface flows: experimental versus numerical comparisons using the PFEM (2008, methodology): “We use innovative mesh regeneration procedure blending elements of different shapes using an extended Delaunay tesselation [14,15].”
A complex variable meshless method for fracture problems (2006, methodology): “Now some meshless methods have been developed, such as diffuse element method (DEM)[3], element-free Galerkin method (EFG)[4], the finite point method (FPM)[5], meshless local Petrov-Galerkin method (MLPG)[6], multi-scale reproducing kernel particle method (MRKP)[7], wavelet particle method (WPM)[9]”
Meshfree and finite element nodal integration methods (2008, methodology): “The meshless finite element methods (FEMs) [16, 17] use extended Delaunay tesselations (EDT) to avoid these slivers and other degeneracies by forming polyhedra from the nodes common to the empty circumspheres.”