Gradient-Based Truss Topology Optimization with Local Stress and Buckling Constraints Considering Chain Effects
Autor(a) principal: | |
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Data de Publicação: | 2021 |
Tipo de documento: | Dissertação |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10362/141299 |
Resumo: | In this dissertation, a gradient-based optimization, utilizing both MMA and GCMMA optimization algorithms, is applied to a truss topology optimization problem including local stress and buckling constraints. The problems with these constraints are prone to be affected by the singularity phenomenon where the global optimum is in a degenerated region of the design domain. This can prevent the elimination of bars when their areas tend to zero because the stress/buckling constraints are violated. Through a combination of relaxation techniques, namely ε-relaxation, a continuation approach and an adaptation of the constraint's formula- tion, the singularity phenomenon can be overcome. The known chain effect in truss topology optimization is addressed by implementing a reverse SIMP function that is used to smooth out the "jump" in the buckling length. This buckling length correction is thus performed in the continuum set of the problem design variables which allows the use of gradient-based algo- rithms. The developed methodology is firstly tested resorting to a set of problems with analyti- cal solutions. Then the proposed algorithm is applied to a new set of complementary examples increasing the number of bar elements. The results found by the MMA optimization algorithm represent reliable solutions that prove the efficiency of the proposed formulation to deal with buckling constraints. Finally, the GCMMA's results agreed with the MMA results in all but two examples, where it showed some difficulties in escaping from local minimum. |
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Gradient-Based Truss Topology Optimization with Local Stress and Buckling Constraints Considering Chain EffectsBucklingStressChain EffectTrussTopology OptimizationMMADomínio/Área Científica::Engenharia e Tecnologia::Engenharia MecânicaIn this dissertation, a gradient-based optimization, utilizing both MMA and GCMMA optimization algorithms, is applied to a truss topology optimization problem including local stress and buckling constraints. The problems with these constraints are prone to be affected by the singularity phenomenon where the global optimum is in a degenerated region of the design domain. This can prevent the elimination of bars when their areas tend to zero because the stress/buckling constraints are violated. Through a combination of relaxation techniques, namely ε-relaxation, a continuation approach and an adaptation of the constraint's formula- tion, the singularity phenomenon can be overcome. The known chain effect in truss topology optimization is addressed by implementing a reverse SIMP function that is used to smooth out the "jump" in the buckling length. This buckling length correction is thus performed in the continuum set of the problem design variables which allows the use of gradient-based algo- rithms. The developed methodology is firstly tested resorting to a set of problems with analyti- cal solutions. Then the proposed algorithm is applied to a new set of complementary examples increasing the number of bar elements. The results found by the MMA optimization algorithm represent reliable solutions that prove the efficiency of the proposed formulation to deal with buckling constraints. Finally, the GCMMA's results agreed with the MMA results in all but two examples, where it showed some difficulties in escaping from local minimum.Nesta dissertação, uma otimização baseada no gradiente, utilizando os algoritmos de otimização MMA e GCMMA, é aplicada a um problema de otimização de topologia de treliças incluindo constrangimentos de tensão e de encurvadura locais. Os problemas com estes cons- trangimentos são propenso a ser afectados pelo fenômeno da singularidade onde o ótimo glo- bal está localizado numa região degenerada do domínio de projeto. Isso pode evitar a elimi- nação de barras quando as suas áreas tendem para zero porque os constrangimentos de ten- são/encurvadura são violados. Através de uma combinação de técnicas de relaxamento, no- meadamente, − , uma continuation approach e uma adaptação da formulação do constrangimento, o fenômeno da singularidade pode ser ultrapassado. O conhecido efeito de cadeia na otimização da topologia de treliça é abordado pela implementação de uma função SIMP reversa que é usada para suavizar o "salto" no comprimento de encurvadura. Esta cor- reção do comprimento de encurvadura é então realizada no conjunto contínuo das variáveis de projeto do problema, o que permite o uso de algoritmos de otimização baseados no gradi- ente. A metodologia desenvolvida é primeiro testada recorrendo a um conjunto de problemas com soluções analíticas. Em seguida, o algoritmo proposto é aplicado a um novo conjunto de exemplos complementares aumentando o número de elementos da barra. Os resultados en- contrados pelo algoritmo de otimização MMA representam soluções confiáveis que compro- vam a eficiência da formulação proposta para lidar com os constrangimentos de encurvadura. Finalmente, os resultados do GCMMA concordaram com os resultados do MMA em todos os exemplos, exceto dois, onde se verificaram algumas dificuldades em escapar a mínimos locais.Coelho, PedroAlmeida, CláudiaRUNEugénio, Luís Pedro Abelha2022-07-04T14:58:58Z2021-122021-12-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisapplication/pdfhttp://hdl.handle.net/10362/141299enginfo: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:RCAAP2024-03-11T05:18:31Zoai:run.unl.pt:10362/141299Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:49:57.397854Repositório 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 |
Gradient-Based Truss Topology Optimization with Local Stress and Buckling Constraints Considering Chain Effects |
title |
Gradient-Based Truss Topology Optimization with Local Stress and Buckling Constraints Considering Chain Effects |
spellingShingle |
Gradient-Based Truss Topology Optimization with Local Stress and Buckling Constraints Considering Chain Effects Eugénio, Luís Pedro Abelha Buckling Stress Chain Effect Truss Topology Optimization MMA Domínio/Área Científica::Engenharia e Tecnologia::Engenharia Mecânica |
title_short |
Gradient-Based Truss Topology Optimization with Local Stress and Buckling Constraints Considering Chain Effects |
title_full |
Gradient-Based Truss Topology Optimization with Local Stress and Buckling Constraints Considering Chain Effects |
title_fullStr |
Gradient-Based Truss Topology Optimization with Local Stress and Buckling Constraints Considering Chain Effects |
title_full_unstemmed |
Gradient-Based Truss Topology Optimization with Local Stress and Buckling Constraints Considering Chain Effects |
title_sort |
Gradient-Based Truss Topology Optimization with Local Stress and Buckling Constraints Considering Chain Effects |
author |
Eugénio, Luís Pedro Abelha |
author_facet |
Eugénio, Luís Pedro Abelha |
author_role |
author |
dc.contributor.none.fl_str_mv |
Coelho, Pedro Almeida, Cláudia RUN |
dc.contributor.author.fl_str_mv |
Eugénio, Luís Pedro Abelha |
dc.subject.por.fl_str_mv |
Buckling Stress Chain Effect Truss Topology Optimization MMA Domínio/Área Científica::Engenharia e Tecnologia::Engenharia Mecânica |
topic |
Buckling Stress Chain Effect Truss Topology Optimization MMA Domínio/Área Científica::Engenharia e Tecnologia::Engenharia Mecânica |
description |
In this dissertation, a gradient-based optimization, utilizing both MMA and GCMMA optimization algorithms, is applied to a truss topology optimization problem including local stress and buckling constraints. The problems with these constraints are prone to be affected by the singularity phenomenon where the global optimum is in a degenerated region of the design domain. This can prevent the elimination of bars when their areas tend to zero because the stress/buckling constraints are violated. Through a combination of relaxation techniques, namely ε-relaxation, a continuation approach and an adaptation of the constraint's formula- tion, the singularity phenomenon can be overcome. The known chain effect in truss topology optimization is addressed by implementing a reverse SIMP function that is used to smooth out the "jump" in the buckling length. This buckling length correction is thus performed in the continuum set of the problem design variables which allows the use of gradient-based algo- rithms. The developed methodology is firstly tested resorting to a set of problems with analyti- cal solutions. Then the proposed algorithm is applied to a new set of complementary examples increasing the number of bar elements. The results found by the MMA optimization algorithm represent reliable solutions that prove the efficiency of the proposed formulation to deal with buckling constraints. Finally, the GCMMA's results agreed with the MMA results in all but two examples, where it showed some difficulties in escaping from local minimum. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021-12 2021-12-01T00:00:00Z 2022-07-04T14:58:58Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/masterThesis |
format |
masterThesis |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10362/141299 |
url |
http://hdl.handle.net/10362/141299 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
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 |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799138097102848000 |