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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/199135
Ver los metadatos del registro completo
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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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13.070432 |