Probabilistic analysis of structures using stochastic finite elements
Most of the published literature in the area of uncertainty quantification of structural systems via probabilistic methods, is concerned with the representation of uncertain quantities as random fields. These types of models allow a robust representation of the random nature of different kinds of st...
- Autores:
-
Uribe Castillo, Felipe
- Tipo de recurso:
- Fecha de publicación:
- 2015
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/55609
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/55609
http://bdigital.unal.edu.co/51037/
- Palabra clave:
- 51 Matemáticas / Mathematics
62 Ingeniería y operaciones afines / Engineering
Finite element method
Random fields
Karhunen-Loève expansion
Polynomial chaos
Stochastic finite elements
Monte Carlo simulation
Projection on the homogeneous chaos
Método de los elementos finitos
Campos aleatorios
Expansión de Karhunen Loève
Caos polinomial
Elementos finitos estocásticos
Simulación de Monte Carlo
Proyección sobre el caos polinomial homogéneo
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
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Universidad Nacional de Colombia |
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dc.title.spa.fl_str_mv |
Probabilistic analysis of structures using stochastic finite elements |
title |
Probabilistic analysis of structures using stochastic finite elements |
spellingShingle |
Probabilistic analysis of structures using stochastic finite elements 51 Matemáticas / Mathematics 62 Ingeniería y operaciones afines / Engineering Finite element method Random fields Karhunen-Loève expansion Polynomial chaos Stochastic finite elements Monte Carlo simulation Projection on the homogeneous chaos Método de los elementos finitos Campos aleatorios Expansión de Karhunen Loève Caos polinomial Elementos finitos estocásticos Simulación de Monte Carlo Proyección sobre el caos polinomial homogéneo |
title_short |
Probabilistic analysis of structures using stochastic finite elements |
title_full |
Probabilistic analysis of structures using stochastic finite elements |
title_fullStr |
Probabilistic analysis of structures using stochastic finite elements |
title_full_unstemmed |
Probabilistic analysis of structures using stochastic finite elements |
title_sort |
Probabilistic analysis of structures using stochastic finite elements |
dc.creator.fl_str_mv |
Uribe Castillo, Felipe |
dc.contributor.advisor.spa.fl_str_mv |
Alvarez Marín, Diego Andrés (Thesis advisor) Bedoya Ruiz, Daniel Alveiro (Thesis advisor) |
dc.contributor.author.spa.fl_str_mv |
Uribe Castillo, Felipe |
dc.subject.ddc.spa.fl_str_mv |
51 Matemáticas / Mathematics 62 Ingeniería y operaciones afines / Engineering |
topic |
51 Matemáticas / Mathematics 62 Ingeniería y operaciones afines / Engineering Finite element method Random fields Karhunen-Loève expansion Polynomial chaos Stochastic finite elements Monte Carlo simulation Projection on the homogeneous chaos Método de los elementos finitos Campos aleatorios Expansión de Karhunen Loève Caos polinomial Elementos finitos estocásticos Simulación de Monte Carlo Proyección sobre el caos polinomial homogéneo |
dc.subject.proposal.spa.fl_str_mv |
Finite element method Random fields Karhunen-Loève expansion Polynomial chaos Stochastic finite elements Monte Carlo simulation Projection on the homogeneous chaos Método de los elementos finitos Campos aleatorios Expansión de Karhunen Loève Caos polinomial Elementos finitos estocásticos Simulación de Monte Carlo Proyección sobre el caos polinomial homogéneo |
description |
Most of the published literature in the area of uncertainty quantification of structural systems via probabilistic methods, is concerned with the representation of uncertain quantities as random fields. These types of models allow a robust representation of the random nature of different kinds of structural parameters, provided there exists sufficient information about their random fluctuations. The inclusion of this probabilistic variation into the physical model affects directly the overall behavior of the structural system, which is generally simulated using the finite element method. Therefore, an instinctive way of proceeding is to extend the classical finite element approach for the solution of stochastic problems involving random structural properties, constituting the so-called stochastic finite element method. This technique has received a considerable attention over the last decade, due to its versatility in dealing with a broad range of stochastic problems. The fundamental idea of this thesis is to present a review of the stochastic finite element method, and to develop a collection of programs that allow a better understanding of this technique. Initially, a general overview of common methods used for the representation of random fields is carried out; special attention is made to the Karhunen-Loève and polynomial chaos expansions, since they are key concepts in the construction of the spectral stochastic finite element method. Secondly, the stochastic finite element is introduced by making a general description of its variants; where the spectral approach using the projection on the homogeneous chaos and the Monte Carlo simulation method are particularly revisited. Finally, the performance of the implemented methodologies is evaluated using several numerical experiments. |
publishDate |
2015 |
dc.date.issued.spa.fl_str_mv |
2015 |
dc.date.accessioned.spa.fl_str_mv |
2019-07-02T11:22:48Z |
dc.date.available.spa.fl_str_mv |
2019-07-02T11:22:48Z |
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 |
dc.type.redcol.spa.fl_str_mv |
http://purl.org/redcol/resource_type/TM |
status_str |
acceptedVersion |
dc.identifier.uri.none.fl_str_mv |
https://repositorio.unal.edu.co/handle/unal/55609 |
dc.identifier.eprints.spa.fl_str_mv |
http://bdigital.unal.edu.co/51037/ |
url |
https://repositorio.unal.edu.co/handle/unal/55609 http://bdigital.unal.edu.co/51037/ |
dc.language.iso.spa.fl_str_mv |
spa |
language |
spa |
dc.relation.spa.fl_str_mv |
http://www.mathworks.com/matlabcentral/profile/authors/2912338-felipe-uribe |
dc.relation.ispartof.spa.fl_str_mv |
Universidad Nacional de Colombia Sede Manizales Facultad de Ingeniería y Arquitectura Departamento de Ingeniería Eléctrica, Electrónica y Computación Departamento de Ingeniería Eléctrica, Electrónica y Computación |
dc.relation.references.spa.fl_str_mv |
Uribe Castillo, Felipe (2015) Probabilistic analysis of structures using stochastic finite elements. Maestría thesis, Universidad Nacional de Colombia - Sede Manizales. |
dc.rights.spa.fl_str_mv |
Derechos reservados - Universidad Nacional de Colombia |
dc.rights.coar.fl_str_mv |
http://purl.org/coar/access_right/c_abf2 |
dc.rights.license.spa.fl_str_mv |
Atribución-NoComercial 4.0 Internacional |
dc.rights.uri.spa.fl_str_mv |
http://creativecommons.org/licenses/by-nc/4.0/ |
dc.rights.accessrights.spa.fl_str_mv |
info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Atribución-NoComercial 4.0 Internacional Derechos reservados - Universidad Nacional de Colombia http://creativecommons.org/licenses/by-nc/4.0/ http://purl.org/coar/access_right/c_abf2 |
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openAccess |
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application/pdf |
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Universidad Nacional de Colombia |
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spelling |
Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Alvarez Marín, Diego Andrés (Thesis advisor)561685f8-a034-487b-826e-f9fe7ed3dcde-1Bedoya Ruiz, Daniel Alveiro (Thesis advisor)a6b672b1-d67b-4fe7-9524-4d2a1870485a-1Uribe Castillo, Felipe0987ef68-cec3-438b-919a-4c779092da363002019-07-02T11:22:48Z2019-07-02T11:22:48Z2015https://repositorio.unal.edu.co/handle/unal/55609http://bdigital.unal.edu.co/51037/Most of the published literature in the area of uncertainty quantification of structural systems via probabilistic methods, is concerned with the representation of uncertain quantities as random fields. These types of models allow a robust representation of the random nature of different kinds of structural parameters, provided there exists sufficient information about their random fluctuations. The inclusion of this probabilistic variation into the physical model affects directly the overall behavior of the structural system, which is generally simulated using the finite element method. Therefore, an instinctive way of proceeding is to extend the classical finite element approach for the solution of stochastic problems involving random structural properties, constituting the so-called stochastic finite element method. This technique has received a considerable attention over the last decade, due to its versatility in dealing with a broad range of stochastic problems. The fundamental idea of this thesis is to present a review of the stochastic finite element method, and to develop a collection of programs that allow a better understanding of this technique. Initially, a general overview of common methods used for the representation of random fields is carried out; special attention is made to the Karhunen-Loève and polynomial chaos expansions, since they are key concepts in the construction of the spectral stochastic finite element method. Secondly, the stochastic finite element is introduced by making a general description of its variants; where the spectral approach using the projection on the homogeneous chaos and the Monte Carlo simulation method are particularly revisited. Finally, the performance of the implemented methodologies is evaluated using several numerical experiments.Resumen : La mayoría de la literatura publicada en el área de cuantificación de la incertidumbre de sistemas estructurales usando métodos probabilísticos, está interesada en la representación de variables inciertas por medio de campos aleatorios. Este tipo de modelos permiten una representación robusta de la naturaleza aleatoria de diferentes tipos de parámetros estructurales, siempre y cuando se cuente con información suficiente sobre su variación probabilística. La inclusión de esta variación en el modelo físico afecta directamente el comportamiento general del sistema estructural, el cual es generalmente simulado usando el método de los elementos finitos. Por lo tanto, una forma instintiva de proceder consiste en extender el clásico enfoque de los elementos finitos para la solución de problemas estocásticos, constituyendo así el llamado método de los elementos finitos estocásticos. Esta técnica numérica ha recibido gran atención durante los últimos años, dada su versatilidad a la hora de resolver una amplia gama de problemas probabilísticos. La idea fundamental de esta tesis consiste en presentar una revisión del método de los elementos finitos estocásticos, y de igual forma desarrollar un conjunto de programas que permitan un mejor entendimiento de esta técnica. Inicialmente, se lleva a cabo un vistazo general de los métodos más comunes para la representación de campos aleatorios; se hace énfasis en las expansiones de Karhunen-Loève y de caos polinomial, dado que ellas representan conceptos primordiales en la construcción del método de los elementos finitos estocásticos espectrales. En segundo lugar, se hace una introducción al método de los elementos finitos estocásticos, haciendo una descripción general de sus diversas alternativas; donde se revisa particularmente el enfoque espectral basado en la proyección sobre el caos homogéneo y el método de simulación de Monte Carlo. Finalmente, el desempeño de las metodologías implementadas es evaluado por medio de varios experimentos numéricosMaestríaapplication/pdfspahttp://www.mathworks.com/matlabcentral/profile/authors/2912338-felipe-uribeUniversidad Nacional de Colombia Sede Manizales Facultad de Ingeniería y Arquitectura Departamento de Ingeniería Eléctrica, Electrónica y ComputaciónDepartamento de Ingeniería Eléctrica, Electrónica y ComputaciónUribe Castillo, Felipe (2015) Probabilistic analysis of structures using stochastic finite elements. Maestría thesis, Universidad Nacional de Colombia - Sede Manizales.51 Matemáticas / Mathematics62 Ingeniería y operaciones afines / EngineeringFinite element methodRandom fieldsKarhunen-Loève expansionPolynomial chaosStochastic finite elementsMonte Carlo simulationProjection on the homogeneous chaosMétodo de los elementos finitosCampos aleatoriosExpansión de Karhunen LoèveCaos polinomialElementos finitos estocásticosSimulación de Monte CarloProyección sobre el caos polinomial homogéneoProbabilistic analysis of structures using stochastic finite elementsTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMORIGINAL1053799081.2015.pdfapplication/pdf11015235https://repositorio.unal.edu.co/bitstream/unal/55609/1/1053799081.2015.pdf26a078b09a6c5f9d39dfa20ae064b6d4MD51THUMBNAIL1053799081.2015.pdf.jpg1053799081.2015.pdf.jpgGenerated Thumbnailimage/jpeg4273https://repositorio.unal.edu.co/bitstream/unal/55609/2/1053799081.2015.pdf.jpg6f12cee52207479e84e5838e3ac602e1MD52unal/55609oai:repositorio.unal.edu.co:unal/556092024-03-18 23:08:42.49Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co |