Topological Derivative for an Anisotropic and Heterogeneous Heat Diffusion Problem

Autores
Giusti, Sebastian Miguel; Novotny, Antonio André
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The topological derivative measures the sensitivity of a given shape functional with respect to an infinitesimal singular domain perturbation. According to the literature, the topological derivative has been fully developed for a wide range of physical phenomenon modeled by partial differential equations, considering homogeneous and isotropic constitutive behavior. In fact, only a few works dealing with heterogeneous and anisotropic material behavior can be found in the literature, and, in general, the derived formulas are given in an abstract form. In this work, we derive the topological derivative in its closed form for the total potential energy associated to an anisotropic and heterogeneous heat diffusion problem, when a small circular inclusion of the same nature of the bulk phase is introduced at an arbitrary point of the domain. In addition, we provide a full mathematical justification for the derived formula and develop precise estimates for the remainders of the topological asymptotic expansion. Finally, the influence of the heterogeneity and anisotropy are shown through some numerical examples of heat conductors topology optimization.
Fil: Giusti, Sebastian Miguel. Universidad Tecnológica Nacional. Facultad Regional Córdoba. Departamento de Ingeniería Civil; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina
Fil: Novotny, Antonio André. No especifíca;
Materia
HEAT CONDUCTOR TOPOLOGY OPTIMIZATION
HETEROGENEOUS AND ANISOTROPIC HEAT DIFFUSION
TOPOLOGICAL ASYMPTOTIC ANALYSIS
TOPOLOGICAL DERIVATIVE
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/199135

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spelling Topological Derivative for an Anisotropic and Heterogeneous Heat Diffusion ProblemGiusti, Sebastian MiguelNovotny, Antonio AndréHEAT CONDUCTOR TOPOLOGY OPTIMIZATIONHETEROGENEOUS AND ANISOTROPIC HEAT DIFFUSIONTOPOLOGICAL ASYMPTOTIC ANALYSISTOPOLOGICAL DERIVATIVEhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The topological derivative measures the sensitivity of a given shape functional with respect to an infinitesimal singular domain perturbation. According to the literature, the topological derivative has been fully developed for a wide range of physical phenomenon modeled by partial differential equations, considering homogeneous and isotropic constitutive behavior. In fact, only a few works dealing with heterogeneous and anisotropic material behavior can be found in the literature, and, in general, the derived formulas are given in an abstract form. In this work, we derive the topological derivative in its closed form for the total potential energy associated to an anisotropic and heterogeneous heat diffusion problem, when a small circular inclusion of the same nature of the bulk phase is introduced at an arbitrary point of the domain. In addition, we provide a full mathematical justification for the derived formula and develop precise estimates for the remainders of the topological asymptotic expansion. Finally, the influence of the heterogeneity and anisotropy are shown through some numerical examples of heat conductors topology optimization.Fil: Giusti, Sebastian Miguel. Universidad Tecnológica Nacional. Facultad Regional Córdoba. Departamento de Ingeniería Civil; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; ArgentinaFil: Novotny, Antonio André. No especifíca;Pergamon-Elsevier Science Ltd2012-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/199135Giusti, Sebastian Miguel; Novotny, Antonio André; Topological Derivative for an Anisotropic and Heterogeneous Heat Diffusion Problem; Pergamon-Elsevier Science Ltd; Mechanics Research Communications; 46; 12-2012; 26-330093-6413CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0093641312001401info:eu-repo/semantics/altIdentifier/doi/10.1016/j.mechrescom.2012.08.005info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:38:18Zoai:ri.conicet.gov.ar:11336/199135instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:38:18.438CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Topological Derivative for an Anisotropic and Heterogeneous Heat Diffusion Problem
title Topological Derivative for an Anisotropic and Heterogeneous Heat Diffusion Problem
spellingShingle Topological Derivative for an Anisotropic and Heterogeneous Heat Diffusion Problem
Giusti, Sebastian Miguel
HEAT CONDUCTOR TOPOLOGY OPTIMIZATION
HETEROGENEOUS AND ANISOTROPIC HEAT DIFFUSION
TOPOLOGICAL ASYMPTOTIC ANALYSIS
TOPOLOGICAL DERIVATIVE
title_short Topological Derivative for an Anisotropic and Heterogeneous Heat Diffusion Problem
title_full Topological Derivative for an Anisotropic and Heterogeneous Heat Diffusion Problem
title_fullStr Topological Derivative for an Anisotropic and Heterogeneous Heat Diffusion Problem
title_full_unstemmed Topological Derivative for an Anisotropic and Heterogeneous Heat Diffusion Problem
title_sort Topological Derivative for an Anisotropic and Heterogeneous Heat Diffusion Problem
dc.creator.none.fl_str_mv Giusti, Sebastian Miguel
Novotny, Antonio André
author Giusti, Sebastian Miguel
author_facet Giusti, Sebastian Miguel
Novotny, Antonio André
author_role author
author2 Novotny, Antonio André
author2_role author
dc.subject.none.fl_str_mv HEAT CONDUCTOR TOPOLOGY OPTIMIZATION
HETEROGENEOUS AND ANISOTROPIC HEAT DIFFUSION
TOPOLOGICAL ASYMPTOTIC ANALYSIS
TOPOLOGICAL DERIVATIVE
topic HEAT CONDUCTOR TOPOLOGY OPTIMIZATION
HETEROGENEOUS AND ANISOTROPIC HEAT DIFFUSION
TOPOLOGICAL ASYMPTOTIC ANALYSIS
TOPOLOGICAL DERIVATIVE
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The topological derivative measures the sensitivity of a given shape functional with respect to an infinitesimal singular domain perturbation. According to the literature, the topological derivative has been fully developed for a wide range of physical phenomenon modeled by partial differential equations, considering homogeneous and isotropic constitutive behavior. In fact, only a few works dealing with heterogeneous and anisotropic material behavior can be found in the literature, and, in general, the derived formulas are given in an abstract form. In this work, we derive the topological derivative in its closed form for the total potential energy associated to an anisotropic and heterogeneous heat diffusion problem, when a small circular inclusion of the same nature of the bulk phase is introduced at an arbitrary point of the domain. In addition, we provide a full mathematical justification for the derived formula and develop precise estimates for the remainders of the topological asymptotic expansion. Finally, the influence of the heterogeneity and anisotropy are shown through some numerical examples of heat conductors topology optimization.
Fil: Giusti, Sebastian Miguel. Universidad Tecnológica Nacional. Facultad Regional Córdoba. Departamento de Ingeniería Civil; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina
Fil: Novotny, Antonio André. No especifíca;
description The topological derivative measures the sensitivity of a given shape functional with respect to an infinitesimal singular domain perturbation. According to the literature, the topological derivative has been fully developed for a wide range of physical phenomenon modeled by partial differential equations, considering homogeneous and isotropic constitutive behavior. In fact, only a few works dealing with heterogeneous and anisotropic material behavior can be found in the literature, and, in general, the derived formulas are given in an abstract form. In this work, we derive the topological derivative in its closed form for the total potential energy associated to an anisotropic and heterogeneous heat diffusion problem, when a small circular inclusion of the same nature of the bulk phase is introduced at an arbitrary point of the domain. In addition, we provide a full mathematical justification for the derived formula and develop precise estimates for the remainders of the topological asymptotic expansion. Finally, the influence of the heterogeneity and anisotropy are shown through some numerical examples of heat conductors topology optimization.
publishDate 2012
dc.date.none.fl_str_mv 2012-12
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/199135
Giusti, Sebastian Miguel; Novotny, Antonio André; Topological Derivative for an Anisotropic and Heterogeneous Heat Diffusion Problem; Pergamon-Elsevier Science Ltd; Mechanics Research Communications; 46; 12-2012; 26-33
0093-6413
CONICET Digital
CONICET
url http://hdl.handle.net/11336/199135
identifier_str_mv Giusti, Sebastian Miguel; Novotny, Antonio André; Topological Derivative for an Anisotropic and Heterogeneous Heat Diffusion Problem; Pergamon-Elsevier Science Ltd; Mechanics Research Communications; 46; 12-2012; 26-33
0093-6413
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0093641312001401
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.mechrescom.2012.08.005
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Pergamon-Elsevier Science Ltd
publisher.none.fl_str_mv Pergamon-Elsevier Science Ltd
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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