On numerical solutions of topology optimization problems

ilustraciones, diagramas

Autores:
Ortegón Villacorte, Andrés Felipe
Tipo de recurso:
Fecha de publicación:
2023
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
eng
OAI Identifier:
oai:repositorio.unal.edu.co:unal/85030
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/85030
https://repositorio.unal.edu.co/
Palabra clave:
510 - Matemáticas::518 - Análisis numérico
Dinámica topológica
Sistemas dinámicos diferenciales
Análisis numérico
Topological Dynamic
Differentiable dynamical systems
Numerical analysis
Topology Optimization
Partial Diferential Equations
Finite Elements
Numerical Analysis
Regularization
Structural Optimization
Optimización Topológica
Ecuaciones Diferenciales Parciales
Elementos Finitos
Análisis Numérico
Regularización
Optimización Estructural
Rights
openAccess
License
Atribución-NoComercial 4.0 Internacional
id UNACIONAL2_78daab73232bd7526da62c44649416a2
oai_identifier_str oai:repositorio.unal.edu.co:unal/85030
network_acronym_str UNACIONAL2
network_name_str Universidad Nacional de Colombia
repository_id_str
dc.title.eng.fl_str_mv On numerical solutions of topology optimization problems
dc.title.translated.spa.fl_str_mv Sobre soluciones numéricas a problemas de optimización topológica
title On numerical solutions of topology optimization problems
spellingShingle On numerical solutions of topology optimization problems
510 - Matemáticas::518 - Análisis numérico
Dinámica topológica
Sistemas dinámicos diferenciales
Análisis numérico
Topological Dynamic
Differentiable dynamical systems
Numerical analysis
Topology Optimization
Partial Diferential Equations
Finite Elements
Numerical Analysis
Regularization
Structural Optimization
Optimización Topológica
Ecuaciones Diferenciales Parciales
Elementos Finitos
Análisis Numérico
Regularización
Optimización Estructural
title_short On numerical solutions of topology optimization problems
title_full On numerical solutions of topology optimization problems
title_fullStr On numerical solutions of topology optimization problems
title_full_unstemmed On numerical solutions of topology optimization problems
title_sort On numerical solutions of topology optimization problems
dc.creator.fl_str_mv Ortegón Villacorte, Andrés Felipe
dc.contributor.advisor.none.fl_str_mv Galvis Arrieta, Juan Carlos
Norato Escobar, Julian Andrés
dc.contributor.author.none.fl_str_mv Ortegón Villacorte, Andrés Felipe
dc.subject.ddc.spa.fl_str_mv 510 - Matemáticas::518 - Análisis numérico
topic 510 - Matemáticas::518 - Análisis numérico
Dinámica topológica
Sistemas dinámicos diferenciales
Análisis numérico
Topological Dynamic
Differentiable dynamical systems
Numerical analysis
Topology Optimization
Partial Diferential Equations
Finite Elements
Numerical Analysis
Regularization
Structural Optimization
Optimización Topológica
Ecuaciones Diferenciales Parciales
Elementos Finitos
Análisis Numérico
Regularización
Optimización Estructural
dc.subject.lemb.spa.fl_str_mv Dinámica topológica
Sistemas dinámicos diferenciales
Análisis numérico
dc.subject.lemb.eng.fl_str_mv Topological Dynamic
Differentiable dynamical systems
Numerical analysis
dc.subject.proposal.eng.fl_str_mv Topology Optimization
Partial Diferential Equations
Finite Elements
Numerical Analysis
Regularization
Structural Optimization
dc.subject.proposal.spa.fl_str_mv Optimización Topológica
Ecuaciones Diferenciales Parciales
Elementos Finitos
Análisis Numérico
Regularización
Optimización Estructural
description ilustraciones, diagramas
publishDate 2023
dc.date.accessioned.none.fl_str_mv 2023-11-30T19:08:55Z
dc.date.available.none.fl_str_mv 2023-11-30T19:08:55Z
dc.date.issued.none.fl_str_mv 2023-10-03
dc.type.spa.fl_str_mv Trabajo de grado - Maestría
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/masterThesis
dc.type.version.spa.fl_str_mv info:eu-repo/semantics/acceptedVersion
dc.type.content.spa.fl_str_mv Text
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status_str acceptedVersion
dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/85030
dc.identifier.instname.spa.fl_str_mv Universidad Nacional de Colombia
dc.identifier.reponame.spa.fl_str_mv Repositorio Institucional Universidad Nacional de Colombia
dc.identifier.repourl.spa.fl_str_mv https://repositorio.unal.edu.co/
url https://repositorio.unal.edu.co/handle/unal/85030
https://repositorio.unal.edu.co/
identifier_str_mv Universidad Nacional de Colombia
Repositorio Institucional Universidad Nacional de Colombia
dc.language.iso.spa.fl_str_mv eng
language eng
dc.relation.references.spa.fl_str_mv Andreassen, E., Clausen, A., Schevenels, M., Lazarov, B. S., and Sigmund, O. (2010). Efficient topology optimization in matlab using 88 lines of code. Structural and Multidisciplinary Optimization, 43:1–16.
Barrón-Romero, C. and Gómez, S. (1991). The exponential tunneling method. Reporte de Investigacion IIMAS, 1:1–23.
Beghini, L. L., Beghini, A., Katz, N., Baker, W. F., and Paulino, G. H. (2014). Connecting architecture and engineering through structural topology optimization. Engineering Structures, 59:716–726
Bell, B., Norato, J., and Tortorelli, D. (2012). A Geometry Projection Method for Continuum-Based Topology Optimization of Structures.
Bendsøe, M. and Sigmund, O. (1999). Material interpolation schemes in topology optimization. Archive of Applied Mechanics, 69:635–654.
Bendsøe, M. and Sigmund, O. (2004). Topology Optimization. Chapter 1, pages 1–68. Springer, first edition.
Cavazzuti, M., Baldini, A., Bertocchi, E., Costi, D., Torricelli, E., and Moruzzi, P. (2011). High performance automotive chassis design: A topology optimization based approach. Structural and Multidisciplinary Optimization, 44:45–56.
Deaton, J. D. and Grandhi, R. V. (2014). A survey of structural and multidisciplinary continuum topology optimization: post 2000. Structural and Multidisciplinary Optimization, 49:1615–1488.
Donofrio, M. (2016). Topology optimization and advanced manufacturing as a means for the design of sustainable building components. Procedia Engineering, 145:638–645.
Gelfand, I. and Fomin, S. (2012). Calculus of Variations. Dover Books on Mathematics. Dover Publications.
Gockenbach, M. (2006). Understanding and Implementing the Finite Element Method. Other Titles in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104).
Gómez, S. and Levy, A. (1970). The tunnelling method for solving the constrained global optimization problem with several non-connected feasible regions, volume 909, pages 34–47.
Johnson, C. (2012). Numerical Solution of Partial Differential Equations by the Finite Element Method. Dover Books on Mathematics Series. Dover Publications, Incorporated.
Kreyszig, E. (2007). Introductory Functional Analysis with Applications. Wiley classics library. Wiley India Pvt. Limited.
Marheineke, N. (2020). Lecture notes: Numerics for differential equations. Trier University.
Matsimbi, M., Nziu, P., Masu, L. M., and Maringa, M. (2021). Topology optimization of automotive body structures: A review.
Norato, J., Bell, B., and Tortorelli, D. (2015). A geometry projection method for continuum-based topology optimization with discrete elements. Computer Methods in Applied Mechanics and Engineering, 293:306–327.
Orme, M., Gschweitl, M., Ferrari, M., Madera, I., and Mouriaux, F. (2017). Designing for additive manufacturing: Lightweighting through topology optimization enables lunar spacecraft. Journal of Mechanical Design, 139.
Ortegón-Villacorte, A. (2021). Pygpto. Github repository.
Ortegón-Villacorte, A. (2023). Topopt experiments. Github repository.
Papadopoulos, I. P. A., Farrell, P. E., and Surowiec, T. M. (2021). Computing multiple solutions of topology optimization problems. SIAM Journal on Scientific Computing, 43(3):A1555–A1582.
Paulino, G. H. and Le, C. H. (2009). A modified q4/q4 element for topology optimization. Structural and Multidisciplinary Optimization, 37:255–264.
Rahmatalla, S. and Swan, C. (2004). A q4/q4 continuum structural optimization implementation. Structural and Multidisciplinary Optimization, 27:130–135.
Rozvany, G. (2009). Rozvany, g.i.n.: A critical review of established methods of structural topology optimization. structural and multidisciplinary optimization 37, 217-237. Structural and Multidisciplinary Optimization, 37:217–237.
Rozvany, G. I. N. (1998). Exact analytical solutions for some popular benchmark problems in topology optimization. Structural optimization, 15(1):42–48.
Sigmund, O. (2022). On benchmarking and good scientific practise in topology optimization. Structural and Multidisciplinary Optimization, 65.
Sigmund, O. and Maute, K. (2013). Topology optimization approaches. Structural and Multidisciplinary Optimization, 48:1031 –1055.
Sigmund, O. and Petersson, J. (1998). Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Structural Optimization, 16:68–75.
Smith, H. and Norato, J. (2020). A matlab code for topology optimization using the geometry projection method. Structural and Multidisciplinary Optimization, pages 1162 –1166.
Smith, H. and Norato, J. (2022). Topology optimization of structures made of fiber-reinforced plates. Structural and Multidisciplinary Optimization, 65:58.
Stolpe, M. and Svanberg, K. (2001). On the trajectories of penalization methods for topology optimization. Structural and Multidisciplinary Optimization, 21:128–139.
Svanberg, K. (1987). The method of moving asymptotes—a new method for structural optimization. International Journal for Numerical Methods in Engineering, 24(2):359–373.
Svanberg, K. (1998). The method of moving asymptotes - modelling aspects and solution scheme.
Tarek, M. and Huang, Y. (2022). Simplifying deflation for non-convex optimization with applications in bayesian inference and topology optimization.
van Dijk, N. P., Langelaar, M., and van Keulen, F. (2010). Critical study of design parameterization in topology optimization ; the influence of design parameterization on local minima.
Watada, R. and Oshaki, M. (2009). Continuation approach for investigation of the non-uniqueness of optimal topology for minimum compliance. 8th World Congress of Structural and Multidisciplinary Optimization.
Wein, F., Dunning, P. D., and Norato, J. A. (2020). A review on feature-mapping methods for structural optimization. Structural and Multidisciplinary Optimization, 62:1597–1638.
Wein, F. and Stingl, M. (2018). A combined parametric shape optimization and ersatz material approach. Structural and Multidisciplinary Optimization, 57.
Yan, S., Wang, F., and Sigmund, O. (2018). On the non-optimality of tree structures for heat conduction. International Journal of Heat and Mass Transfer, 122:660–680.
Zhang, S. and Norato, J. (2018). Finding better local optima in topology optimization via tunneling. page V02BT03A014.
Zhu, J.-H., Zhang, W.-H., and Xia, L. (2016). Topology optimization in aircraft and aerospace structures design. Archives of Computational Methods in Engineering, 23:595–622.
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dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
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dc.format.extent.spa.fl_str_mv xiii, 83 páginas
dc.format.mimetype.spa.fl_str_mv application/pdf
dc.publisher.spa.fl_str_mv Universidad Nacional de Colombia
dc.publisher.program.spa.fl_str_mv Bogotá - Ciencias - Maestría en Ciencias - Matemática Aplicada
dc.publisher.faculty.spa.fl_str_mv Facultad de Ciencias
dc.publisher.place.spa.fl_str_mv Bogotá, Colombia
dc.publisher.branch.spa.fl_str_mv Universidad Nacional de Colombia - Sede Bogotá
institution Universidad Nacional de Colombia
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spelling Atribución-NoComercial 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Galvis Arrieta, Juan Carlos083500f8dbd93663cffc3776002b7be1Norato Escobar, Julian Andrésb6dfde419362f92aa870e08b5a15ea3bOrtegón Villacorte, Andrés Felipe08b7cce421284b683969dcd5d79850512023-11-30T19:08:55Z2023-11-30T19:08:55Z2023-10-03https://repositorio.unal.edu.co/handle/unal/85030Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/ilustraciones, diagramasEste trabajo de investigación estudia las técnicas de optimización topológica aplicadas al problema clásico del calor y al problema de la elasticidad. El estudio destaca varios aspectos clave encontrados durante el proceso de búsqueda de soluciones para problemas específicos, incluida la influencia de las condiciones iniciales y los parámetros del optimizador. Además, el documento explora enfoques novedosos y variaciones de métodos fundamentales encaminados a lograr soluciones finales mejoradas para cada problema. Estas adaptaciones abarcan ajustes del funcional minimizado, la representación del espacio de densidad y la aplicación de métodos de regularización. (Texto tomado de la fuente)This work studies topological optimization techniques applied to the classical heat problem and the elasticity problem. The study highlights various key aspects encountered during the solution search process for specific problems, including the influence of initial conditions and optimizer parameters. Moreover, the paper explores novel approaches and variations of fundamental methods aimed at achieving improved final solutions for each problem. These adaptations encompass adjustments to the minimized functional, the representation of density space, and the application of regularization methods.MaestríaMagíster en Ciencias - Matemática AplicadaOptimización EstructuralAnálisis Numéricoxiii, 83 páginasapplication/pdfengUniversidad Nacional de ColombiaBogotá - Ciencias - Maestría en Ciencias - Matemática AplicadaFacultad de CienciasBogotá, ColombiaUniversidad Nacional de Colombia - Sede Bogotá510 - Matemáticas::518 - Análisis numéricoDinámica topológicaSistemas dinámicos diferencialesAnálisis numéricoTopological DynamicDifferentiable dynamical systemsNumerical analysisTopology OptimizationPartial Diferential EquationsFinite ElementsNumerical AnalysisRegularizationStructural OptimizationOptimización TopológicaEcuaciones Diferenciales ParcialesElementos FinitosAnálisis NuméricoRegularizaciónOptimización EstructuralOn numerical solutions of topology optimization problemsSobre soluciones numéricas a problemas de optimización topológicaTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMAndreassen, E., Clausen, A., Schevenels, M., Lazarov, B. S., and Sigmund, O. (2010). Efficient topology optimization in matlab using 88 lines of code. Structural and Multidisciplinary Optimization, 43:1–16.Barrón-Romero, C. and Gómez, S. (1991). The exponential tunneling method. Reporte de Investigacion IIMAS, 1:1–23.Beghini, L. L., Beghini, A., Katz, N., Baker, W. F., and Paulino, G. H. (2014). Connecting architecture and engineering through structural topology optimization. Engineering Structures, 59:716–726Bell, B., Norato, J., and Tortorelli, D. (2012). A Geometry Projection Method for Continuum-Based Topology Optimization of Structures.Bendsøe, M. and Sigmund, O. (1999). Material interpolation schemes in topology optimization. Archive of Applied Mechanics, 69:635–654.Bendsøe, M. and Sigmund, O. (2004). Topology Optimization. Chapter 1, pages 1–68. Springer, first edition.Cavazzuti, M., Baldini, A., Bertocchi, E., Costi, D., Torricelli, E., and Moruzzi, P. (2011). High performance automotive chassis design: A topology optimization based approach. Structural and Multidisciplinary Optimization, 44:45–56.Deaton, J. D. and Grandhi, R. V. (2014). A survey of structural and multidisciplinary continuum topology optimization: post 2000. Structural and Multidisciplinary Optimization, 49:1615–1488.Donofrio, M. (2016). Topology optimization and advanced manufacturing as a means for the design of sustainable building components. Procedia Engineering, 145:638–645.Gelfand, I. and Fomin, S. (2012). Calculus of Variations. Dover Books on Mathematics. Dover Publications.Gockenbach, M. (2006). Understanding and Implementing the Finite Element Method. Other Titles in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104).Gómez, S. and Levy, A. (1970). The tunnelling method for solving the constrained global optimization problem with several non-connected feasible regions, volume 909, pages 34–47.Johnson, C. (2012). Numerical Solution of Partial Differential Equations by the Finite Element Method. Dover Books on Mathematics Series. Dover Publications, Incorporated.Kreyszig, E. (2007). Introductory Functional Analysis with Applications. Wiley classics library. Wiley India Pvt. Limited.Marheineke, N. (2020). Lecture notes: Numerics for differential equations. Trier University.Matsimbi, M., Nziu, P., Masu, L. M., and Maringa, M. (2021). Topology optimization of automotive body structures: A review.Norato, J., Bell, B., and Tortorelli, D. (2015). A geometry projection method for continuum-based topology optimization with discrete elements. Computer Methods in Applied Mechanics and Engineering, 293:306–327.Orme, M., Gschweitl, M., Ferrari, M., Madera, I., and Mouriaux, F. (2017). Designing for additive manufacturing: Lightweighting through topology optimization enables lunar spacecraft. Journal of Mechanical Design, 139.Ortegón-Villacorte, A. (2021). Pygpto. Github repository.Ortegón-Villacorte, A. (2023). Topopt experiments. Github repository.Papadopoulos, I. P. A., Farrell, P. E., and Surowiec, T. M. (2021). Computing multiple solutions of topology optimization problems. SIAM Journal on Scientific Computing, 43(3):A1555–A1582.Paulino, G. H. and Le, C. H. (2009). A modified q4/q4 element for topology optimization. Structural and Multidisciplinary Optimization, 37:255–264.Rahmatalla, S. and Swan, C. (2004). A q4/q4 continuum structural optimization implementation. Structural and Multidisciplinary Optimization, 27:130–135.Rozvany, G. (2009). Rozvany, g.i.n.: A critical review of established methods of structural topology optimization. structural and multidisciplinary optimization 37, 217-237. Structural and Multidisciplinary Optimization, 37:217–237.Rozvany, G. I. N. (1998). Exact analytical solutions for some popular benchmark problems in topology optimization. Structural optimization, 15(1):42–48.Sigmund, O. (2022). On benchmarking and good scientific practise in topology optimization. Structural and Multidisciplinary Optimization, 65.Sigmund, O. and Maute, K. (2013). Topology optimization approaches. Structural and Multidisciplinary Optimization, 48:1031 –1055.Sigmund, O. and Petersson, J. (1998). Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Structural Optimization, 16:68–75.Smith, H. and Norato, J. (2020). A matlab code for topology optimization using the geometry projection method. Structural and Multidisciplinary Optimization, pages 1162 –1166.Smith, H. and Norato, J. (2022). Topology optimization of structures made of fiber-reinforced plates. Structural and Multidisciplinary Optimization, 65:58.Stolpe, M. and Svanberg, K. (2001). On the trajectories of penalization methods for topology optimization. Structural and Multidisciplinary Optimization, 21:128–139.Svanberg, K. (1987). The method of moving asymptotes—a new method for structural optimization. International Journal for Numerical Methods in Engineering, 24(2):359–373.Svanberg, K. (1998). The method of moving asymptotes - modelling aspects and solution scheme.Tarek, M. and Huang, Y. (2022). Simplifying deflation for non-convex optimization with applications in bayesian inference and topology optimization.van Dijk, N. P., Langelaar, M., and van Keulen, F. (2010). Critical study of design parameterization in topology optimization ; the influence of design parameterization on local minima.Watada, R. and Oshaki, M. (2009). Continuation approach for investigation of the non-uniqueness of optimal topology for minimum compliance. 8th World Congress of Structural and Multidisciplinary Optimization.Wein, F., Dunning, P. D., and Norato, J. A. (2020). A review on feature-mapping methods for structural optimization. Structural and Multidisciplinary Optimization, 62:1597–1638.Wein, F. and Stingl, M. (2018). A combined parametric shape optimization and ersatz material approach. Structural and Multidisciplinary Optimization, 57.Yan, S., Wang, F., and Sigmund, O. (2018). On the non-optimality of tree structures for heat conduction. International Journal of Heat and Mass Transfer, 122:660–680.Zhang, S. and Norato, J. (2018). Finding better local optima in topology optimization via tunneling. page V02BT03A014.Zhu, J.-H., Zhang, W.-H., and Xia, L. (2016). Topology optimization in aircraft and aerospace structures design. Archives of Computational Methods in Engineering, 23:595–622.InvestigadoresLICENSElicense.txtlicense.txttext/plain; charset=utf-85879https://repositorio.unal.edu.co/bitstream/unal/85030/1/license.txteb34b1cf90b7e1103fc9dfd26be24b4aMD51ORIGINAL1071331304.2023.pdf1071331304.2023.pdfTesis de Maestría en Ciencias - Matemática Aplicadaapplication/pdf5362676https://repositorio.unal.edu.co/bitstream/unal/85030/2/1071331304.2023.pdfbefc305c27d485490650c3cca93ffa5eMD52THUMBNAIL1071331304.2023.pdf.jpg1071331304.2023.pdf.jpgGenerated Thumbnailimage/jpeg4183https://repositorio.unal.edu.co/bitstream/unal/85030/3/1071331304.2023.pdf.jpg2b9b06110d111e649c5cf6ba831b22e5MD53unal/85030oai:repositorio.unal.edu.co:unal/850302023-12-01 23:03:42.872Repositorio Institucional Universidad Nacional de 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