Sensitivity Analysis of a Nonlinear Obstacle Plate Problem
Autor(a) principal: | |
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Data de Publicação: | 2002 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10316/14410 https://doi.org/10.1051/cocv:2002006 |
Resumo: | We analyse the sensitivity of the solution of a nonlinear obstacle plate problem, with respect to small perturbations of the middle plane of the plate. This analysis, which generalizes the results of Rao and Sokolowski 1987, Rockafeller 1989 for the linear case, is done by application of an abstract variational result Levy 1999, where the sensitivity of parameterized variational inequalities in Banach spaces, without uniqueness of solution, is quantified in terms of a generalized derivative, that is the proto-derivative. We prove that the hypotheses required by this abstract sensitivity result are verified for the nonlinear obstacle plate problem. Namely, the constraint set defined by the obstacle is polyhedric and the mapping involved in the definition of the plate problem, considered as a function of the middle plane of the plate, is semi-differentiable. The verification of these two conditions enable to conclude that the sensitivity is characterized by the proto-derivative of the solution mapping associated with the nonlinear obstacle plate problem, in terms of the solution of a variational inequality. |
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Sensitivity Analysis of a Nonlinear Obstacle Plate ProblemPlate problemVariational inequalitySensitivity analysisWe analyse the sensitivity of the solution of a nonlinear obstacle plate problem, with respect to small perturbations of the middle plane of the plate. This analysis, which generalizes the results of Rao and Sokolowski 1987, Rockafeller 1989 for the linear case, is done by application of an abstract variational result Levy 1999, where the sensitivity of parameterized variational inequalities in Banach spaces, without uniqueness of solution, is quantified in terms of a generalized derivative, that is the proto-derivative. We prove that the hypotheses required by this abstract sensitivity result are verified for the nonlinear obstacle plate problem. Namely, the constraint set defined by the obstacle is polyhedric and the mapping involved in the definition of the plate problem, considered as a function of the middle plane of the plate, is semi-differentiable. The verification of these two conditions enable to conclude that the sensitivity is characterized by the proto-derivative of the solution mapping associated with the nonlinear obstacle plate problem, in terms of the solution of a variational inequality.PRAXIS/PCEX/C/MAT/38/96 \Variational Models and Optimization", and Sapiens Proj99, No. 34471 \Nonlinear Partial Di erential Equations and Interfaces Problems" of the Ministry of Science and Technology of PortugalEDP Sciences2002-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/14410http://hdl.handle.net/10316/14410https://doi.org/10.1051/cocv:2002006engFIGUEIREDO, Isabel N.; LEAL, Carlos F. - Sensitivity Analysis of a Nonlinear Obstacle Plate Problem. "ESAIM: COCV". ISSN 1262-3377. Vol. 7 (2002) 135-1551262-3377http://www.esaim-cocv.orgFigueiredo, Isabel N.Leal, Carlos F.info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2021-09-16T10:09:43Zoai:estudogeral.uc.pt:10316/14410Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T21:00:47.935953Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Sensitivity Analysis of a Nonlinear Obstacle Plate Problem |
title |
Sensitivity Analysis of a Nonlinear Obstacle Plate Problem |
spellingShingle |
Sensitivity Analysis of a Nonlinear Obstacle Plate Problem Figueiredo, Isabel N. Plate problem Variational inequality Sensitivity analysis |
title_short |
Sensitivity Analysis of a Nonlinear Obstacle Plate Problem |
title_full |
Sensitivity Analysis of a Nonlinear Obstacle Plate Problem |
title_fullStr |
Sensitivity Analysis of a Nonlinear Obstacle Plate Problem |
title_full_unstemmed |
Sensitivity Analysis of a Nonlinear Obstacle Plate Problem |
title_sort |
Sensitivity Analysis of a Nonlinear Obstacle Plate Problem |
author |
Figueiredo, Isabel N. |
author_facet |
Figueiredo, Isabel N. Leal, Carlos F. |
author_role |
author |
author2 |
Leal, Carlos F. |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Figueiredo, Isabel N. Leal, Carlos F. |
dc.subject.por.fl_str_mv |
Plate problem Variational inequality Sensitivity analysis |
topic |
Plate problem Variational inequality Sensitivity analysis |
description |
We analyse the sensitivity of the solution of a nonlinear obstacle plate problem, with respect to small perturbations of the middle plane of the plate. This analysis, which generalizes the results of Rao and Sokolowski 1987, Rockafeller 1989 for the linear case, is done by application of an abstract variational result Levy 1999, where the sensitivity of parameterized variational inequalities in Banach spaces, without uniqueness of solution, is quantified in terms of a generalized derivative, that is the proto-derivative. We prove that the hypotheses required by this abstract sensitivity result are verified for the nonlinear obstacle plate problem. Namely, the constraint set defined by the obstacle is polyhedric and the mapping involved in the definition of the plate problem, considered as a function of the middle plane of the plate, is semi-differentiable. The verification of these two conditions enable to conclude that the sensitivity is characterized by the proto-derivative of the solution mapping associated with the nonlinear obstacle plate problem, in terms of the solution of a variational inequality. |
publishDate |
2002 |
dc.date.none.fl_str_mv |
2002-01 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10316/14410 http://hdl.handle.net/10316/14410 https://doi.org/10.1051/cocv:2002006 |
url |
http://hdl.handle.net/10316/14410 https://doi.org/10.1051/cocv:2002006 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
FIGUEIREDO, Isabel N.; LEAL, Carlos F. - Sensitivity Analysis of a Nonlinear Obstacle Plate Problem. "ESAIM: COCV". ISSN 1262-3377. Vol. 7 (2002) 135-155 1262-3377 http://www.esaim-cocv.org |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
EDP Sciences |
publisher.none.fl_str_mv |
EDP Sciences |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799133898416848896 |