On the use of local max-ent shape functions for the simulation of forming processes

W. Quak, D. Gonzalez, E Cueto, Antonius H. van den Boogaard

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

1 Citation (Scopus)
16 Downloads (Pure)

Abstract

In this work we review the opportunities given by the use of local maximum- entropy approximants (LME) for the simulation of forming processes. This approximation can be considered as a meshless approximation scheme, and thus presents some appealing features for the numerical simulation of forming processes in a Galerkin framework. Especially the behavior of these shape functions at the boundary is interesting. At nodes on the boundary, the functions possess a weak Kronecker-delta property, hence simplifying the prescription of boundary conditions. Shape functions at the boundary do not overlap internal nodes, nor do internal shape functions overlap nodes at the boundary. Boundary integrals can be computed easily and efficiently compared to for instance moving least-squares approximations. Furthermore, LME shapes also present a controllable degree of smoothness. To test the performance of the LME shapes, an elastic and a elasto-plastic problem was analyzed. The results were compared with a meshless method based on a moving least-squares approximation.
Original languageUndefined
Title of host publicationX international conference on computational plasticity
EditorsE Onate, D.R.J Owen
Place of PublicationBarcelona
PublisherCIMNE
Pages-
Number of pages4
Publication statusPublished - 2 Sep 2009
EventX International Conference on Computational Plasticity. Fundamentals and Applications 2009 - Barcelona, Spain
Duration: 2 Sep 20094 Sep 2009
Conference number: 10
http://congress.cimne.com/complas09/frontal/default.asp

Publication series

Name
PublisherCIMNE

Conference

ConferenceX International Conference on Computational Plasticity. Fundamentals and Applications 2009
Abbreviated titleCOMPLAS 2009
CountrySpain
CityBarcelona
Period2/09/094/09/09
Internet address

Keywords

  • METIS-261649
  • elasto-plasticity
  • Local max-ent
  • Metal forming
  • Meshless Methods
  • IR-69123

Cite this

Quak, W., Gonzalez, D., Cueto, E., & van den Boogaard, A. H. (2009). On the use of local max-ent shape functions for the simulation of forming processes. In E. Onate, & D. R. J. Owen (Eds.), X international conference on computational plasticity (pp. -). Barcelona: CIMNE.
Quak, W. ; Gonzalez, D. ; Cueto, E ; van den Boogaard, Antonius H. / On the use of local max-ent shape functions for the simulation of forming processes. X international conference on computational plasticity. editor / E Onate ; D.R.J Owen. Barcelona : CIMNE, 2009. pp. -
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abstract = "In this work we review the opportunities given by the use of local maximum- entropy approximants (LME) for the simulation of forming processes. This approximation can be considered as a meshless approximation scheme, and thus presents some appealing features for the numerical simulation of forming processes in a Galerkin framework. Especially the behavior of these shape functions at the boundary is interesting. At nodes on the boundary, the functions possess a weak Kronecker-delta property, hence simplifying the prescription of boundary conditions. Shape functions at the boundary do not overlap internal nodes, nor do internal shape functions overlap nodes at the boundary. Boundary integrals can be computed easily and efficiently compared to for instance moving least-squares approximations. Furthermore, LME shapes also present a controllable degree of smoothness. To test the performance of the LME shapes, an elastic and a elasto-plastic problem was analyzed. The results were compared with a meshless method based on a moving least-squares approximation.",
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Quak, W, Gonzalez, D, Cueto, E & van den Boogaard, AH 2009, On the use of local max-ent shape functions for the simulation of forming processes. in E Onate & DRJ Owen (eds), X international conference on computational plasticity. CIMNE, Barcelona, pp. -, X International Conference on Computational Plasticity. Fundamentals and Applications 2009, Barcelona, Spain, 2/09/09.

On the use of local max-ent shape functions for the simulation of forming processes. / Quak, W.; Gonzalez, D.; Cueto, E; van den Boogaard, Antonius H.

X international conference on computational plasticity. ed. / E Onate; D.R.J Owen. Barcelona : CIMNE, 2009. p. -.

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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AU - van den Boogaard, Antonius H.

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N2 - In this work we review the opportunities given by the use of local maximum- entropy approximants (LME) for the simulation of forming processes. This approximation can be considered as a meshless approximation scheme, and thus presents some appealing features for the numerical simulation of forming processes in a Galerkin framework. Especially the behavior of these shape functions at the boundary is interesting. At nodes on the boundary, the functions possess a weak Kronecker-delta property, hence simplifying the prescription of boundary conditions. Shape functions at the boundary do not overlap internal nodes, nor do internal shape functions overlap nodes at the boundary. Boundary integrals can be computed easily and efficiently compared to for instance moving least-squares approximations. Furthermore, LME shapes also present a controllable degree of smoothness. To test the performance of the LME shapes, an elastic and a elasto-plastic problem was analyzed. The results were compared with a meshless method based on a moving least-squares approximation.

AB - In this work we review the opportunities given by the use of local maximum- entropy approximants (LME) for the simulation of forming processes. This approximation can be considered as a meshless approximation scheme, and thus presents some appealing features for the numerical simulation of forming processes in a Galerkin framework. Especially the behavior of these shape functions at the boundary is interesting. At nodes on the boundary, the functions possess a weak Kronecker-delta property, hence simplifying the prescription of boundary conditions. Shape functions at the boundary do not overlap internal nodes, nor do internal shape functions overlap nodes at the boundary. Boundary integrals can be computed easily and efficiently compared to for instance moving least-squares approximations. Furthermore, LME shapes also present a controllable degree of smoothness. To test the performance of the LME shapes, an elastic and a elasto-plastic problem was analyzed. The results were compared with a meshless method based on a moving least-squares approximation.

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KW - Metal forming

KW - Meshless Methods

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Quak W, Gonzalez D, Cueto E, van den Boogaard AH. On the use of local max-ent shape functions for the simulation of forming processes. In Onate E, Owen DRJ, editors, X international conference on computational plasticity. Barcelona: CIMNE. 2009. p. -