An adaptive procedure based on background cells for meshless methods

Liu, G.R; Tu, Zecan

doi:10.1016/s0045-7825(01)00360-7

Cited by 111 publications

(63 citation statements)

References 9 publications

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“…Nodes can easily be added and removed without the need for complex manipulation of the data structures involved. Since error estimates for finite elements are not always directly transferable to meshfree methods, various approaches have been proposed [18][19][20][21][22][23]. Effective approaches to estimate the interpolation/approximation error were proposed in [20,21,24,25].…”

Section: Introductionmentioning

confidence: 99%

Adaptive element-free Galerkin method applied to the limit analysis of plates

Askes

Gilbert

2010

Computer Methods in Applied Mechanics and Engineering

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The implementation of an h-adaptive Element-Free Galerkin (EFG) method in the framework of limit analysis is described. The naturally conforming property of meshfree approximations (with no nodal connectivity required) facilitates the implementation of h-adaptivity. Nodes may be moved, discarded or introduced without the need for complex manipulation of the data structures involved. With the use of the Taylor expansion technique, the error in the computed displacement field and its derivatives can be estimated throughout the problem domain with high accuracy. A stabilized conforming nodal integration scheme is extended to error estimators and results in an efficient and truly meshfree adaptive method. To demonstrate its effectiveness the procedure is then applied to plates with various boundary conditions.

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Section: Introductionmentioning

confidence: 99%

Adaptive element-free Galerkin method applied to the limit analysis of plates

Askes

Gilbert

2010

Computer Methods in Applied Mechanics and Engineering

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“…[5]) and (most commonly) meshless methods (e.g. [6][7][8][9][10][11][12]). However, inspection of equations (1) to (5) shows the stresses to be smooth functions of position, with no stress concentrations or singularities.…”

Section: Problem Definitionmentioning

confidence: 99%

The use of Timoshenko's exact solution for a cantilever beam in adaptive analysis

Augarde

Deeks

2008

Finite Elements in Analysis and Design

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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-prot 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. ABSTRACTThe exact solution for the deflection and stresses in an end-loaded cantilever is widely used to demonstrate the capabilities of adaptive procedures, in finite elements, meshless methods and other numerical techniques. In many cases, however, the boundary conditions necessary to match the exact solution are not followed. Attempts to draw conclusions as to the effectivity of adaptive procedures is therefore compromised. In fact, the exact solution is unsuitable as a test problem for adaptive procedures as the perfect refined mesh is uniform.In this paper we discuss this problem, highlighting some errors that arise if boundary conditions are not matched exactly to the exact solution, and make comparisons with a more realistic model of a cantilever. Implications for code verification are also discussed.

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“…[75] describes an error estimate for the EFGM based on a Taylor series with a higher order derivative and a structured grid is used instead of a cloud of points, which makes the implementation very straightforward. Error estimation based on the gradient of strain energy density is proposed in [76] and an adaptive analysis for EFGM is proposed in [77] based on background cells, error being estimated based on two different integration orders and a refinement algorithm based on local Delaunay triangulation is also proposed. In [78], the approach from [70] is used for error estimation and adaptive analysis in crack propagation problems.…”

Section: Introductionmentioning

confidence: 99%

Finite deformation elasto-plastic modelling using an adaptive meshless method

Ullah

Augarde

2013

Computers & Structures

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'Finite deformation elasto-plastic modelling using an adaptive meshless method. ', Computers and structures., Further information on publisher's website:http://dx.doi.org/10. 1016/j.compstruc.2012.04.001 Publisher's copyright statement: NOTICE: this is the author's version of a work that was accepted for publication in Computers and structures. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reected in this document. Changes may have been made to this work since it was submitted for publication. A denitive version will be subsequently published in Computers and structures, 2012Computers and structures, , 10.1016Computers and structures, /j.compstruc.2012 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-prot 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. Problems including both material and geometric nonlinearities are of practical engineering importance in many applications. Efficient computational modelling of these problems with minimum computer resources remains challenging. Often these problems are modelled with the finite element method (FEM) with adaptive analysis, in which an error estimation procedure automatically determines regions for coarse and fine discretization. Meshless methods offer the attractive possibility of simpler adaptive procedures involving no remeshing, simply insertion or deletion of nodes. However, as meshless methods are computationally more expensive than the FEM, the use of the minimum possible number and proper distribution of nodes are important issues. In this study an adaptive meshless approach for nonlinear solid mechanics is developed based on the element free Galerkin method. An existing error estimation procedure for linear elasto-static problems, is extended here for nonlinear problems including finite deformation and elasto-plasticity, and a new adaptive procedure is described and demonstrated.

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An adaptive procedure based on background cells for meshless methods

Cited by 111 publications

References 9 publications

Adaptive element-free Galerkin method applied to the limit analysis of plates

Adaptive element-free Galerkin method applied to the limit analysis of plates

The use of Timoshenko's exact solution for a cantilever beam in adaptive analysis

Finite deformation elasto-plastic modelling using an adaptive meshless method

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