A Posteriori Error Estimation And Three-dimensional Adaptive Remeshing: Application To Error Control Of Non-Steady Metal Forming Simulations

Boussetta, Ramzy

doi:10.1063/1.1766869

Cited by 3 publications

(4 citation statements)

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“…Dealing with problems of metal forming process and mechanical structure, the element error is generally given, according to the norm of energy [18,19]. It expresses the difference between the exact stress σ and the FE one σ h :…”

Section: A Posteriori Error Estimationmentioning

confidence: 99%

“…Usually, this relation can be established with the using either of the following two strategies: The first allows us to calculate an optimal mesh for a prescribed accuracy, while the second seeks to optimize a mesh under the constraint of a number of degrees of freedom attached. One may refer to [18,19] for more details, which used a combination of them. The first strategy is used to compute an optimized new mesh.…”

Section: Size Map For Adaptive Strategiesmentioning

confidence: 99%

“…Particularly, the superconvergent patch recovery (SPR) technique is often preferred by several authors because it is robust and simple to use [18,19]. However, for borders nodes Fig.…”

Section: Super-convergent Patch Recovery (Spr) Techniquementioning

confidence: 99%

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Numerical simulation of metal forming processes with 3D adaptive Remeshing strategy based on a posteriori error estimation

et al. 2018

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In this work, a fully automated adaptive remeshing strategy, based on a tetrahedral element for 3D metal forming processes, was proposed in order to solve problems associated with the severe mesh distortion that occurs during the computation. The main idea is to use the h-type adaptive mesh in combination with an a-posteriori error estimator measured (by the energy norm) on each finite elements to locally control the mesh modification-as-needed. Once a new mesh is generated, all history-dependent variables must be carefully transferred between subsequent meshes. Therefore, several transfer techniques are described and compared. A special attention is given to restore the local mechanical equilibrium of the system with a new methodology. After presenting the necessary adaptive remeshing steps, some 3D analytic and numerical results using the proposed adaptive strategy are given to demonstrate the capabilities of the proposed equilibrated approach and to illustrate some practical characteristics of our remeshing process.

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Section: A Posteriori Error Estimationmentioning

confidence: 99%

Section: Size Map For Adaptive Strategiesmentioning

confidence: 99%

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Numerical simulation of metal forming processes with 3D adaptive Remeshing strategy based on a posteriori error estimation

et al. 2018

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“…Tetrahedral elements were used in the analysis, and different polynomials were used in the least squares fitting for the SPR method, possessing C 0 , C 1 and C 2 continuity. In [56], an improvement of the SPR method, i.e. minimal patch recovery (MPR), was introduced in which there was no need to calculate the nodal stresses.…”

Section: Error Estimationmentioning

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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Three-dimensional data transfer operators in large plasticity deformations using modified-SPR technique

Khoei

Gharehbaghi

2009

Applied Mathematical Modelling

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A Posteriori Error Estimation And Three-dimensional Adaptive Remeshing: Application To Error Control Of Non-Steady Metal Forming Simulations

Cited by 3 publications

References 0 publications

Numerical simulation of metal forming processes with 3D adaptive Remeshing strategy based on a posteriori error estimation

Numerical simulation of metal forming processes with 3D adaptive Remeshing strategy based on a posteriori error estimation

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

Three-dimensional data transfer operators in large plasticity deformations using modified-SPR technique

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