Continuous blending of SPH with finite elements

Fernández‐Méndez, Sonia; Bonet, Javier; Huerta, Antonio

doi:10.1016/j.compstruc.2004.10.019

Cited by 48 publications

(35 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A general overview on existing techniques is presented in [24]. Amongst the different techniques discussed in [24] the continuous blending method [25,26,27] (i.e. introduce standard finite elements along the boundary and adapt the meshfree interpolation functions to obtain completeness) and Nitsche's method [28,29,30] are the most suitable alternatives.…”

Section: Dirichlet Boundary Conditionsmentioning

confidence: 99%

Bounds for quantities of interest and adaptivity in the element‐free Galerkin method

Vidal

Mariné

Dı́ez

et al. 2008

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

1 of estimators ensuring bounds for the error. Classical residual type estimators, which provide upper bounds of the error, require flux-equilibration procedures (hybrid-flux techniques) to properly set boundary conditions for local problems [10, 2]. Flux-equilibration requires a domain decomposition, which is natural in finite elements but not in mesh-free methods. Moreover, it is performed by a complex algorithm, strongly dependent on the finite element type and requiring a data structure that is not natural in a standard finite element code.The idea of using flux-free estimators, based on the partition-of-the-unity concept and using local subdomains different than elements, has been already proposed in [11,12,13,14] for finite elements. The main advantage of the flux-free approach is the simplicity in the implementation. Obviously, this is especially important in the 3D case.From the mesh-free point of view, another advantage is the fact that the local subdomains where the error equation is solved are the support of the functions characterizing the partition of unity. This is a concept that also exists in mesh-free methods and thus the extension is possible. Moreover, boundary conditions of the local problems are natural and the usual data structure of a code is directly employed.In the last few years, some research has been devoted to develop error estimation procedures for mesh-free methods. To the authors knowledge implicit residual based estimators have not been proposed for mesh-free methods. However, in [19] a strategy to assess the energy norm of the error for the Generalized Finite Element Method (GFEM) is presented and the possible generalizations to mesh-free methods are also devised. Implicit residual error estimators are now standard in finite elements because they are mathematically sound, more accurate and allow computing upper and lower bounds for energy norms as well as for functional outputs. In this paper the implicit residual-type flux-free error estimator proposed in [14], which is comparable in effectivity to the standard hybrid-flux estimators, is extended to the Element Free Galerkin Method. In the present work, the difficulties found when extending the implicit residual methods to mesh-free are related with the fact that the refined discretization do not induce nested functional spaces. This is specially important for the error representation. Moreover, the bounds for the specific quantity of interest must be in this case carefully computed. In reference [19] these difficulties are not encountered because the error estimator is performed in terms of the energy norm and in the GFEM the refined subspaces are nested.Mesh-free methods are especially well suited for adaptivity. Enriching the mesh-free discretization is straightforward because the new particles are added without any connectivity restriction. Here, a refinement scheme based on inserting particles following a quadtree structure in a background rectangular grid is proposed. The refinement criterion uses the information provided...

show abstract

Section: Dirichlet Boundary Conditionsmentioning

confidence: 99%

Bounds for quantities of interest and adaptivity in the element‐free Galerkin method

Vidal

Mariné

Dı́ez

et al. 2008

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

“…Although SPH approaches can be applied to problems with severe distortions, they are generally not as good as the finite-element method (FEM) [23][24][25][26][27] -a mature scheme with a high efficiency, suitable for structural applications. Therefore, alongside the SPH approach, the FEM is applied here to model steel/SPS structures and analyse their damage response, considerable effort was dedicated to coupled SPH-FEM methods [28][29][30][31][32][33][34][35][36][37][38] by various researchers in the past years. Johnson et al [28,29] developed a master-slave method to describe a contact between SPH particles and finite elements and used it to simulate highvelocity impacts.…”

Section: Introductionmentioning

confidence: 99%

SPH-FEM simulation of shaped-charge jet penetration into double hull: A comparison study for steel and SPS

Zhang

Wang

Silberschmidt

et al. 2016

Composite Structures

View full text Add to dashboard Cite

“…KI φ I (X) (3.50) and has recovered the delta propertŷ Blending meshfree approximation functions with FEM shape functions [18] while preserving the properties of the original shape function. Note that this transformation is only necessary for the shape functions of those points that have one or more constrained nodes inside their support domain.…”

Section: Transformation Methodsmentioning

confidence: 99%

On the application of meshfree methods to the nonlinear dynamics of multibody systems

Ibáñez¹

View full text Add to dashboard Cite

Continuous blending of SPH with finite elements

Cited by 48 publications

References 27 publications

Bounds for quantities of interest and adaptivity in the element‐free Galerkin method

Bounds for quantities of interest and adaptivity in the element‐free Galerkin method

SPH-FEM simulation of shaped-charge jet penetration into double hull: A comparison study for steel and SPS

On the application of meshfree methods to the nonlinear dynamics of multibody systems

Contact Info

Product

Resources

About