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dc.rights.licenseAtribución-NoComercial-CompartirIgual 4.0 Internacional
dc.contributor.advisorMontealegre Rubio, Wilfredo
dc.contributor.authorRamírez Gil, Francisco Javier
dc.date.accessioned2021-10-13T20:06:46Z
dc.date.available2021-10-13T20:06:46Z
dc.date.issued2021
dc.identifier.urihttps://repositorio.unal.edu.co/handle/unal/80544
dc.descriptionIlustraciones
dc.description.abstractLos materiales funcionalmente graduados (MFGs) son un tipo de compuestos en los que la microestructura, la composición u otras características se modifican de forma continua a través de una o varias direcciones, lo que permite una variación suave de las propiedades a lo largo del volumen. Este concepto también es aplicable a las estructuras, lo que se conoce como estructuras funcionalmente graduadas (EFGs). En particular, la idea de la gradación está ampliamente explotada en la naturaleza, por ejemplo, en los huesos, los dientes, los cuernos, los picos de las aves y la madera, donde la mayoría de las cargas son de tipo dinámico. Además, muchas de estas estructuras biológicas no solo son gradadas sino también porosas, lo que ayuda a la naturaleza a utilizar eficazmente el material y a construir estructuras ligeras. Así, siguiendo estos conceptos bioinspirados, esta investigación explora el diseño mediante el método de optimización topológica (MOT) de estructuras bajo cargas de impacto con porosidad gradada. Los impactos son fenómenos dinámicos de corta duración e intensidad elevada que pueden producir daños importantes a las estructuras impactadas. Dependiendo de la energía del impacto, el problema se puede modelar como un fenómeno transitorio lineal o un complejo problema que involucra parte o todas las formas de no linealidad como plasticidad, contacto y grandes deformaciones, desplazamientos y rotaciones. En esta tesis se trata el impacto en dos regímenes de acuerdo a la típica clasificación basada en la velocidad: impacto a baja velocidad que se modela como un fenómeno lineal e impacto a velocidad media en donde se incluirán todos los tipos de no linealidad. Para ello, se plantean dos líneas de investigación. La primera considera el diseño de estructuras bajo impacto lineal con el MOT basado en gradientes, la estructura se analiza mediante el método de los elementos finitos (MEF) y la ecuación de movimiento semidiscreta se integra en el tiempo con un método de integración directa implícito (Newmark). En esta línea se diseñan EFGs porosas a nivel macroscópico con porosidad variable de forma predefinida buscando la máxima rigidez y el mínimo peso cuando se aplican cargas transitorias. Para alcanzar dicho objetivo, utilizamos una restricción local por elemento especificando límites superiores en el volumen de material localizado en la proximidad de cada elemento, la cual se trata como una norma $p$ para formar una restricción global equivalente para facilitar un proceso de optimización eficiente. Esta restricción se explora de varias maneras para producir diversos EFG porosas. Todo este proceso se implementa en MATLAB. El segundo enfoque considera el diseño de estructuras bajo impacto no lineal de media velocidad usando el MOT sin gradientes, el MEF considera todas las no linealidades y se utiliza un método de integración explícita (diferencia central). La porosidad aquí se logra mediante la restricción de la fracción de volumen de cada capa de una estructura multicapa. Este proceso se realiza en el software comercial LS-TaSC para la optimización y LS-Dyna para el análisis MEF. Las EFG porosas diseñadas en este trabajo pueden potencialmente satisfacer tanto las necesidades de ligereza como las de alta absorción de energía requeridas para aplicaciones sometidas a cargas de impacto, como en la industria automovilística, biomédica y quizás en otras más complejas como en la industria militar. (Texto tomado de la fuente)
dc.description.abstractFunctionally graded materials (FGMs) are a kind of composites in which the microstructure, composition, or other characteristic is changed continuously through one or more directions allowing a smooth variation of properties over the volume. This concept is also applicable to structures where they are known as functionally graded structures (FGSs). In particular, the graded idea is widely exploited in nature, for instance, in bones, teeth, horns, bird beaks and wood, where most loads are of dynamic type. Moreover, most of these biological structures are not only graded, but also porous, which helps nature to use the material efficiently and to build lightweight structures. Thus, following these bio-inspired concepts, this research explores the design by the topology optimization method (TOM) of graded porous structures under impact loads. Impacts are dynamic phenomena of short duration and high intensity that can cause significant damage to impacted structures. Depending on the impact energy, the problem can be modeled as a linear transient phenomenon or a complex problem involving part or all forms of nonlinearity such as plasticity, contact and large deformations, large displacements and large rotations. In this thesis the impact is treated in two regimes according to the typical velocity-based classification: low velocity impact that is modeled as a linear phenomenon and medium velocity impact where all types of non-linearities will be included. To this end, two approaches are proposed. The first one considers the design of structures under linear impact with gradient-based TOM, the structure is analyzed using the finite element method (FEM) and the semi-discrete equation of motion is integrated in time with an implicit direct integration method (Newmark). Herein, functionally graded porous structures (FGPSs) are designed at macroscopic level with varying porosity in a predefined way looking for the maximum stiffness and minimum weight when transient loads are applied. To achieve this objective, we use a local per-element constraints by specifying upper bounds on the localized material volume in the proximity of each element, which is treated as a $p$-norm to form an equivalent global constraint to facilitate an efficient optimization process. This constraint is explored in several ways to produce several porous FGS. % in 2D and 3D. This whole process is implemented in MATLAB. The second approach considers the design of structures under nonlinear medium velocity impact using the TOM without gradients, the FEM considers all nonlinearities and an explicit integration method (central difference) is used. Porosity here is achieved by constraining the volume fraction of each layer of a multilayer structure. This process is performed in the commercial software LS-TaSC for the optimization and LS-Dyna for the FEM analysis. The porous FGS designed in this work can potentially satisfy both the lightweight and high-energy-absorption properties required for applications under impact loads such as in automotive, biomedical industry and perhaps in more complex ones such as in the military industry.
dc.description.sponsorshipBeca Doctorado Nacional de Colciencias: convocatoria 567/2012 Locomotora de la innovación para el apoyo del desarrollo tecnológico (Colciencias): convocatoria 621/2013
dc.format.extentxxxiii, 226 páginas
dc.format.mimetypeapplication/pdf
dc.language.isospa
dc.publisherUniversidad Nacional de Colombia
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/4.0/
dc.subject.ddc620 - Ingeniería y operaciones afines
dc.subject.ddc620 - Ingeniería y operaciones afines::621 - Física aplicada
dc.titleDiseño de placas funcionalmente gradadas mediante el método de optimización topológica para aplicaciones de impacto a velocidad baja y media.
dc.typeTrabajo de grado - Doctorado
dc.type.driverinfo:eu-repo/semantics/doctoralThesis
dc.type.versioninfo:eu-repo/semantics/acceptedVersion
dc.publisher.programMedellín - Minas - Doctorado en Ingeniería - Ingeniería Mecánica y Mecatrónica
dc.contributor.researchgroupGrupo de Diseño y Optimización Aplicada (DOA)
dc.description.degreelevelDoctorado
dc.description.degreenameDoctor en Ingeniería
dc.description.degreenameDoctor en Antropología
dc.description.researchareaMecánica computacional
dc.identifier.instnameUniversidad Nacional de Colombia
dc.identifier.reponameRepositorio Institucional Universidad Nacional de Colombia
dc.identifier.repourlhttps://repositorio.unal.edu.co/
dc.publisher.departmentDepartamento de Ingeniería Mecánica
dc.publisher.facultyFacultad de Minas
dc.publisher.placeMedellín, Colombia
dc.publisher.branchUniversidad Nacional de Colombia - Sede Medellín
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dc.rights.accessrightsinfo:eu-repo/semantics/openAccess
dc.subject.lembDiseño de estructuras
dc.subject.lembStructural design
dc.subject.lembStructural optimization
dc.subject.lembOptimización estructural
dc.subject.lembDiseño de máquinas
dc.subject.proposalDiseño mecánico
dc.subject.proposalMecánica computacional
dc.subject.proposalOptimización estructural
dc.subject.proposalOptimización topológica
dc.subject.proposalImpacto de baja y media velocidad
dc.subject.proposalMétodo de los Elementos Finitos
dc.subject.proposalMechanical design
dc.subject.proposalComputational mechanics
dc.subject.proposalStructural optimization
dc.subject.proposalTopology optimization
dc.subject.proposalLow- and medium-velocity impact
dc.subject.proposalFinite element method
dc.title.translatedDesign of functionally graded plates using the topology optimization method for low and medium velocity impact applications.
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oaire.awardtitleBeca Doctorado Nacional de Colciencias: convocatoria 567/2012
oaire.awardtitleLocomotora de la innovación para el apoyo del desarrollo tecnológico: convocatoria 621/2013
oaire.fundernameColciencias
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