Meshless methods in dual analysis: theoretical and implementation issues

This paper presents a meshless implementation of dual analysis for 2D linear elasticity problems. The derivation of the governing systems of equations for the discretized compatible and equilibrated models is detailed and crucial implementation issues of the proposed algorithm are discussed: (i) ari...

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Autores: Ivannikov, Vladimir, Tiago, C., Almeida, José Paulo Moitinho de, Díez, Pedro|||0000-0001-6464-6407
Tipo de recurso: artículo
Fecha de publicación:2013
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/78746
Acceso en línea:https://hdl.handle.net/2117/78746
https://dx.doi.org/10.1016/j.enganabound.2013.08.016
Access Level:acceso abierto
Palabra clave:Boundary element methods
Meshless methods
Dual analysis
Inf–sup condition
EBC enforcement
Anàlisi numèrica
Classificació AMS::65 Numerical analysis::65N Partial differential equations, boundary value problems
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics
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oai_identifier_str oai:upcommons.upc.edu:2117/78746
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repository_id_str
spelling Meshless methods in dual analysis: theoretical and implementation issuesIvannikov, VladimirTiago, C.Almeida, José Paulo Moitinho deDíez, Pedro|||0000-0001-6464-6407Boundary element methodsMeshless methodsDual analysisInf–sup conditionEBC enforcementAnàlisi numèricaClassificació AMS::65 Numerical analysis::65N Partial differential equations, boundary value problemsÀrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèricsThis paper presents a meshless implementation of dual analysis for 2D linear elasticity problems. The derivation of the governing systems of equations for the discretized compatible and equilibrated models is detailed and crucial implementation issues of the proposed algorithm are discussed: (i) arising of deficiencies associated with the independent approximation field used for the imposition of the essential boundary conditions (EBC) for the two parts of the boundary sharing a corner and (ii) determination of the Lagrange multipliers functional space used to impose EBC. An attempt to implement the latter resulted in an approximation which is nothing more than the trace on the essential boundary of the domain nodal functions. The difficulties posed by such approximation are explained using the inf-sup condition. Several examples of global (energy) and local (displacements) quantities of interest and theirs bounds determination are used to demonstrate the validity of the presented meshless approach to dual analysis. Numerical assessment of the convergence rates obtained for both models is made, for different polynomial basis degree.Award-winning20132013-12-0120152015-11-04journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/78746https://dx.doi.org/10.1016/j.enganabound.2013.08.016reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2http://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/787462026-05-27T15:37:01Z
dc.title.none.fl_str_mv Meshless methods in dual analysis: theoretical and implementation issues
title Meshless methods in dual analysis: theoretical and implementation issues
spellingShingle Meshless methods in dual analysis: theoretical and implementation issues
Ivannikov, Vladimir
Boundary element methods
Meshless methods
Dual analysis
Inf–sup condition
EBC enforcement
Anàlisi numèrica
Classificació AMS::65 Numerical analysis::65N Partial differential equations, boundary value problems
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics
title_short Meshless methods in dual analysis: theoretical and implementation issues
title_full Meshless methods in dual analysis: theoretical and implementation issues
title_fullStr Meshless methods in dual analysis: theoretical and implementation issues
title_full_unstemmed Meshless methods in dual analysis: theoretical and implementation issues
title_sort Meshless methods in dual analysis: theoretical and implementation issues
dc.creator.none.fl_str_mv Ivannikov, Vladimir
Tiago, C.
Almeida, José Paulo Moitinho de
Díez, Pedro|||0000-0001-6464-6407
author Ivannikov, Vladimir
author_facet Ivannikov, Vladimir
Tiago, C.
Almeida, José Paulo Moitinho de
Díez, Pedro|||0000-0001-6464-6407
author_role author
author2 Tiago, C.
Almeida, José Paulo Moitinho de
Díez, Pedro|||0000-0001-6464-6407
author2_role author
author
author
dc.subject.none.fl_str_mv Boundary element methods
Meshless methods
Dual analysis
Inf–sup condition
EBC enforcement
Anàlisi numèrica
Classificació AMS::65 Numerical analysis::65N Partial differential equations, boundary value problems
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics
topic Boundary element methods
Meshless methods
Dual analysis
Inf–sup condition
EBC enforcement
Anàlisi numèrica
Classificació AMS::65 Numerical analysis::65N Partial differential equations, boundary value problems
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics
description This paper presents a meshless implementation of dual analysis for 2D linear elasticity problems. The derivation of the governing systems of equations for the discretized compatible and equilibrated models is detailed and crucial implementation issues of the proposed algorithm are discussed: (i) arising of deficiencies associated with the independent approximation field used for the imposition of the essential boundary conditions (EBC) for the two parts of the boundary sharing a corner and (ii) determination of the Lagrange multipliers functional space used to impose EBC. An attempt to implement the latter resulted in an approximation which is nothing more than the trace on the essential boundary of the domain nodal functions. The difficulties posed by such approximation are explained using the inf-sup condition. Several examples of global (energy) and local (displacements) quantities of interest and theirs bounds determination are used to demonstrate the validity of the presented meshless approach to dual analysis. Numerical assessment of the convergence rates obtained for both models is made, for different polynomial basis degree.
publishDate 2013
dc.date.none.fl_str_mv 2013
2013-12-01
2015
2015-11-04
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/78746
https://dx.doi.org/10.1016/j.enganabound.2013.08.016
url https://hdl.handle.net/2117/78746
https://dx.doi.org/10.1016/j.enganabound.2013.08.016
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2

http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2

http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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