Element-free Galerkin methods in combination with finite element approaches

Hegen, Dries

doi:10.1016/0045-7825(96)00994-2

Cited by 185 publications

(93 citation statements)

References 8 publications

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“…After substitution of (15) in (16) the expression for L a is obtained, which exactly coincides with (12). However, this approach does not require the computation of vector ε a .…”

Section: Coupled Approximation Of Derivativesmentioning

confidence: 76%

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Continuous blending of SPH with finite elements

Fernández‐Méndez

Bonet²,

Huerta

2005

Computers & Structures

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This paper proposes a methodology for the continuous blending of the finite element method and Smooth Particle Hydrodynamics. The coupled approximation with finite elements and particles, and the discretization of the boundary value problem with a coupled integration, are described. An integration correction is also proposed to stabilize the solution. Some numerical examples demonstrate the applicability of the method.

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“…After substitution of (15) in (16) the expression for L a is obtained, which exactly coincides with (12). However, this approach does not require the computation of vector ε a .…”

Section: Coupled Approximation Of Derivativesmentioning

confidence: 76%

“…An important effort has been dedicated to the coupling of FE and meshless methods in the last years. Most of the literature is devoted to the coupling of FE with EFG or RKPM, see for instance [11][12][13][14][15][16]. However, the attention paid to the development of formulations linking FE with SPH methods is more modest [17,18].…”

Section: Introductionmentioning

confidence: 99%

Continuous blending of SPH with finite elements

Fernández‐Méndez

Bonet²,

Huerta

2005

Computers & Structures

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“…A coupling approach where no ramp functions are needed was first proposed by Hegen et al [21]. Rabczuk and Belytschko [44] used this approach to couple EFG nodes and finite elements to model the bond behavior in reinforced concrete beams in statics.…”

Section: Compatibility Coupling:coupling With Lagrange Multipliersmentioning

confidence: 99%

“…In this method, relative displacements between the particles and the elements are allowed. Xiao [51] developed an explicit method based on Lagrange multipliers (similar to the approach of Hegen et al [21]) which is a simplified version of the bridging domain coupling. He called this method edge-to-edge coupling.…”

Section: Compatibility Coupling:coupling With Lagrange Multipliersmentioning

confidence: 99%

Coupling of mesh-free methods with finite elements: basic concepts and test results

Rabczuk

Xiao

Sauer

2006

Commun. Numer. Meth. Engng.

179

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SUMMARYThis paper reviews several novel and older methods for coupling meshfree particle methods, particularly the elementfree Galerkin (EFG) method and the Smooth Particle Hydrodynamics (SPH), with finite elements. We study master slave couplings where particles are fixed across the finite element boundary, coupling via interface shape functions such that consistency conditions are satisfied, bridging domain coupling, compatibility coupling with Lagrange multipliers and hybrid coupling methods where forces from the particles are applied via their shape functions on the FE nodes and vice versa. The hybrid coupling methods are well suited for large deformations and adaptivity and the coupling procedure is independent from the particle distance and nodal arrangement. We will study the methods for several static and dynamic applications, compare the results to analytical and experimental data and show advantages and drawbacks of the methods.

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“…In that procedure moving least squares (MLS) shape functions are used in the EFG region of the problem domain, while hybrid shape functions, combining both MLS and FE shape functions, are used in the interface region. Other commonly used methods for FE-EFGM coupling are the continuous blending method in [14,15], methods based on Lagrange multipliers [16,17], on transition or bridge regions [18] and methods based on a collocation approach [19]. A comprehensive review of different FE-EFGM coupling procedures up to 2005 can be found in [20].…”

Section: Introductionmentioning

confidence: 99%

An adaptive finite element/meshless coupled method based on local maximum entropy shape functions for linear and nonlinear problems

Ullah

Coombs

Augarde

2013

Computer Methods in Applied Mechanics and Engineering

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'An adaptive nite element/meshless coupled method based on local maximum entropy shape functions for linear and nonlinear problems.', Computer methods in applied mechanics and engineering., 267 . pp. 111-132. Further information on publisher's website:http://dx.doi.org/10.1016/j.cma.2013.07.018Publisher's copyright statement: NOTICE: this is the author's version of a work that was accepted for publication in Computer Methods in Applied Mechanics and Engineering. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be re ected in this document. Changes may have been made to this work since it was submitted for publication. A de nitive version was subsequently published in Computer Methods in Applied Mechanics and Engineering, 267, 2013, 10.1016/j.cma.2013.07.018. Additional information:Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractIn this paper, an automatic adaptive coupling procedure is proposed for the finite element method (FEM) and the element-free Galerkin method (EFGM) for linear elasticity and for problems with both material and geometrical nonlinearities. In this new procedure, initially the whole of the problem domain is modelled using the FEM. During an analysis, those finite elements which violate a predefined error measure are automatically converted to an EFG zone. This EFG zone can be further refined by adding nodes, thus avoiding computationally expensive FE remeshing. Local maximum entropy shape functions are used in the EFG zone of the problem domain for two reasons: their weak Kronecker delta property at the boundaries allows straightforward imposition of essential boundary conditions and also provides a natural way to couple the EFG and FE regions compared to the use of moving least squares basis functions. The Zienkiewicz & Zhu error estimation procedure with the superconvergent patch method for strains and stresses recovery is used in the FE region of the problem domain, while the Chung & Belytschko error estimation procedure is used in the EFG region.

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Element-free Galerkin methods in combination with finite element approaches

Cited by 185 publications

References 8 publications

Continuous blending of SPH with finite elements

Continuous blending of SPH with finite elements

Coupling of mesh-free methods with finite elements: basic concepts and test results

An adaptive finite element/meshless coupled method based on local maximum entropy shape functions for linear and nonlinear problems

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