Enrichment and coupling of the finite element and meshless methods

By Antonio Huerta, S. Fernández‐Méndez. 2000

212 citations recorded by the source corpus.

A mixed hierarchical approximation based on finite elements and meshless methods is presented. Two cases are considered. The first one couples regions where finite elements or meshless methods are used to interpolate: continuity and consistency is preserved. The second one enriches a finite element mesh with particles. Thus, there is no need to remesh in adaptive refinement processes. In both cases the same formulation is used, convergence is studied and examples are shown. Copyright © 2000 John Wiley & Sons, Ltd.

Subfields: Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/35c3432207a84dd5d6f30314f4cec3a78726a8a9

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In Civil and Structural Engineering

In Mechanics of Materials

Citations in the corpus

A reproducing kernel method with nodal interpolation property (2003, methodology): “It is also noted that since piecewise linear nite element shape functions possess linear completeness, at least second-order basis functions are needed in the construction of the enrichment function I (x) in Reference [17].”
A coupled meshless-finite element method for fracture analysis of cracks (2001, unknown): “%; *<- & 2, * 22- 3 9!=; ' .”
Exact imposition of essential boundary condition and material interface continuity in Galerkin‐based meshless methods (2017, methodology): “They can be classified in three main groups: (1) methods based on a modification of the weak form, such as the Lagrange multiplier method [1], the penalty method [6], and the Nitsche method [7]; (2) methods coupling with finite element methods, see [8] and [9]; and (3) methods that can be interprete”
Positivity conditions in meshless collocation methods (2004, background): “In meshless approximations, there are various ways to satisfy the first positivity condition [23–26].”
A bridging domain and strain computation method for coupled atomistic–continuum modelling of solids (2007, unknown): “We note that the coefficient matrix of the left-hand side is the Gram matrix [20] Mkj (also called the moment matrix) given by Mkj = ∑ ∈SX pk p j w (52)”
Stability of incompressible formulations enriched with X-FEM (2008, methodology): “Apart from mixing meshless methods and finite elements [16] another alternative to overcome the re-meshing issue in finite elements is to use the eXtended Finite Element Method (X-FEM) based on the partition of unity framework introduced by Babuška and Melenk [17].”
Arbitrarily smooth generalized finite element approximations (2006, methodology): “One approach to reduce the computational cost of meshfree methods is to use these methods only in parts of the domain where they are strictly needed and use a finite element discretization elsewhere [8] [20] [34] [35] [49] [79].”
Imposing essential boundary conditions in mesh-free methods (2004, methodology): “A detailed comparison between the continuous blending method [12] and the bridging scale method [17], for the implementation of essential boundary conditions, can be found in [19].”
Consistent element‐free Galerkin method (2014, methodology): “Strategies developed for this purpose are the penalty method [11], coupling methods [12, 13], corrected collocation method [14] and so on.”
An improved stable XFEM (Is-XFEM) with a novel enrichment function for the computational modeling of cohesive cracks (2015, unknown): “4 The definition (29) corresponds to the bridging scale method [33, 69], whereas the one (33) dates back to the continuous blending method [18, 19].”