APRÈN. Portal de la producció docent del professorat de la UPC

Optimal control problems are used in a wide range of fields, such us engineering or physics. To solve them, it is important to take into account their geometric properties, such as Hamilton's invariance or symplecticity, because they describe the behaviour of the problem. Symplectic operators have been typically used for Hamiltonian systems, but this thesis aims to explore and develop structure-preserving discretization methods for optimal control problems. The project presents different properties of continuous Hamiltonian and control systems, to later explore their preservation in the discretized form of the problems. Numerical simulations are performed using Matlab to validate the proposed methods. These simulations, tested on realworld examples, will help to validate the results obtained in the previous sections, and also to investigate and overcome some numerical-derived problems or study the convergence using different discretization schemes.

Understanding fracture behavior is crucial to optimizing the design of engineering structures and components, from civil infrastructure to aircraft components. The phase-field model has become popular among these models because it can explain fracture formation and propagation as a continuous and diffuse process. The goal of this thesis is to study the behavior of crack propagation in heterogeneous materials by performing numerical simulations and analyzing them. Heterogeneity is defined as the ratio of the fracture toughness between different parts of the material. An adaptive phase-field code for fracture in homogeneous materials has been extended to heterogeneous materials, and two dimensional experiments have been carried out to explore the mechanical response and capabilities of the adaptive phase-field modeling of fracture in heterogeneous materials. An assessment of the crack's behavior when interacting with heterogeneities is performed, and some behaviors are related to the force-displacement plot. It is determined that the peak force and the total displacement generally increase when the ratio of fracture toughness increases, but this relation may not necessarily be true infinitely. Increasing the ratio may result in a change in the mode of fracture (from penetration of the inclusion to the deflection of it) and decrease the peak force and/or the total displacement. It is important to carry out several tests to determine what ratio best suits the desired objective and to avoid any unexpected behaviors. The length of deflection and penetration have been related to the mode of fracture. The crack has been guided through less-resistant thin paths. We can state that for a more resistant, constant area in the material, in the case where the crack has no chance other than penetrating through all of it, splitting this area will result in an increase in the peak force and a decrease in the total displacement, and concentrating the area will result in the opposite.

The main objective of this report is to compute the energy balance for the modelling of fractures in 2D materials using Phase-fields models as a tool to verify the results. For a civil engineer, it is important to compute the resistance of materials as fractures are responsible of structures failures. The strategy is to use an adaptive refinement method for phase-fields models developed by A.Muixí and to study how the spatial and temporal characteristics of the model affects the balance. The energy balance is composed as the sum of the elastic and brittle fracture or crack energy, the total energy is calculated as the work of the external forces using Newton-Cotes methods to compute it. For the elastic energy and crack energy, the weak form and discretization methods were applied to solve PDEs and to compute volume integrals. The analysis of the results of the energy balance, shows that the balance can adapt to complex geometries with discontinuities or cyclic loading cases. The crack length and the balance error can be indeed used as a tool to verify if the precision of the model numeric parameters is enough. The parameters studied are the temporal and spatial discretization and the tolerance of the non-linear iterative solution of the damage. Although the results found are satisfactory, an error appears when the crack propagation speed is important product of the kinetic energy not taken into account in the balance. As the velocity of propagation is relatively slow at the loading phase, the kinetic energy can be ignored and the obtained balance is correct. For an analysis post-failure this thesis proposes a dynamic approach of the hybrid phase-field model taking into account the inertia

Running training plans have become a trend between professional and amateur runners to train for races. However, not all of them have a preliminary study to guarantee their effectivity. In this project, we analyse running sessions using the Principal Component Analysis method in order to find which are those parameters that a running training plan needs to focus on and how they are trained to help the runner to be faster. As an application, we analyse a particular training plan with the information obtained from the method and we find out how its indicator qualify every run, compared with the planned one.

A usual trick in various modelling approaches for computational fracture (i.e. damage models, phase-field approaches) is to include an artificial residual stiffness. This is done to avoid singularity of the tangent stiffness matrix. The goal of this MSc thesis is to assess how this numerically motivated parameter affects the mechanical response. Alternative ways to include the desired residual stiffness without an accompanying, undesired, residual load-carrying capacity will also be explored, and tested by means of one- and two-dimensional numerical examples.

The work is based on the research on two-phase flows in pressurized pipes with non-Newtonian fluids. Experiments are carried out in a pipe loop at the Water Engineering Laboratory (WEL) of the Czech Technical University (CTU). One of the features describing the flow behaviour is a distribution of solid particles in the flowing liquid. The measuring technique of Electrical Resistance Tomography (ERT) is used to obtain maps of distribution of solids in a pipe cross section. One of the challenges associated with ERT is processing of raw images and their interpretation.

Removing air from bagged bulk material is a major concern for the material handling industry. A common technique is the application of suction by means of a probe, right before sealing the bag. Recent industrial experience shows that, for some granular materials, the effectiveness of this de-aeration technique is limited, probably due to the reduction in permeability associated to the decrease in porosity. The goal of this project is to understand and to remedy this limited effectiveness. The hypothesis that has been handled in this work, is the creation of an over compressed bulb of granular material that prevents the complete suction of the excess air and limits the compaction of the material. The creation of the bulb is defined by the permeability of the material, since it has been decompressed, is very susceptible to the pressure. Therefore, the dependency of the permeability with the pressure is the main reason why the bulb is created. In order to solve the issues behind the de-aeration process, the bulb creation process is modelled using mathematical models, which describe the suction in a porous media under certain conditions. The first one is a steady model, which describes the final state of the suction. The other one is a transient model, consequently, it describes the entire suction process. Those models are solved using numerical methods, obtaining information about the suction behaviour in granular materials and the bulb generation. Finally, with the knowledge acquired, the same models are used to optimize the suction processes and propose a new method. The method, consist in a mobile probe that moves during the suction, reducing the over-compressed bulb behaviour.

Fracture modelling has always been a direction of research in engineering, more specifically in civil engineering. In this last quarter of century, the implementation of nonlocality in damage models has been a direction of study for materials fracture, more specifically for quasi-brittle materials such as concrete or rocks. This type of damage model allows a more accurately characterization of the behavior of this type of materials and it has been seen that it is not possible to accurately model the behavior of this materials without a nonlocal formulation, because it characterizes the behavior of the material as a whole, weighting the value of a variable of a point on its neighborhood. This dissertation aims for an investigation on new models able to characterize the damage effect on quasi-brittle materials. In this direction, this thesis focuses on models with a variable internal length which sees its value reduced due to the increase on damage. Furthermore, two models in this dissertation are presented on how to treat this internal length reduction. One model presents an unbounded internal length reduction allowing a vanish of its value for high damage values, whereas the other model do not allow a null value of the internal length, even for high damage values, imposing a minimum value –threshold– for the internal length. Finally, both models and an original model with a constant internal length –where these two models are based from– are tested on a uniaxial strain and stress problem and its results and parameters discussed.

Una de les parts més importants a l'hora de voler resoldre un sistema mecànic o vibroacústic recau en la subdivisió del domini d'estudi, afectant directament en el procés. Així doncs, en la present tesi es realitza un estudi detallat de la tècnica d'identificació de subsistemes, que en el cas del mètode SEA (Statistical Energy Analysis) es basa en la classificació del domini en funció de l'energia de transferència entre els subsistemes. Un subsistema és un conjunt de nodes amb un comportament similar, que ens permet subdividir un domini en diferents grups. Aquesta subdivisió s'aconsegueix realitzant una anàlisi clúster de les potències de la matriu de transferència. La matriu de transferència, obtinguda arran de les propietats mecàniques de la nostra estructura, ens permet descriure i quantificar la transmissió directa de senyal entre nodes. Aquesta identificació de subsistemes en geometries complexes o de grans dimensions, és de gran utilitat en l'aplicació del mètode SEA a problemes vibroacústics, però també ho és per a la reducció del cost operacional d'un problema d'elements finits, tal com hem realitzat en aquesta tesi, optimitzant el mètode de Newmark. Tots aquests conceptes són posats en pràctica a posteriori a l'anàlisi de problemes vibroacústics mitjançant diferents geometries representatives, amb el fi d'analitzar la precisió i aplicabilitat del mètode.

La selección de alternativas en el trazado de carreteras es un problema muy complejo debido al gran número de factores conflictivos que deben ser resueltos, la gran cantidad y variedad de información que debe ser recopilada y procesada, y las numerosas evaluaciones que se deben realizar. Por tanto, la motivación de la investigación de la Tesina de Máster ha sido la de automatizar el proceso de diseño para lograr mejores resultados en un periodo de tiempo menor y con un coste menor, para superar así las limitaciones actuales de los procesos tradicionales de evaluación y diseño de alternativas de trazado de carreteras. Con esta finalidad, la tesina presenta un modelo tridimensional de optimización de trazado de carreteras que desarrolla de forma simultanea la optimización del trazado horizontal y vertical a lo largo de un corredor. El modelo tiene integrado un algoritmo de optimización heurística de búsqueda vecinal desarrollado en dos etapas. A lo largo del documento se analiza cuales son los costes y restricciones más importantes asociados a la optimización del trazado de carreteras, se presentan los pasos principales del algoritmo de optimización de dos etapas y desarrolla una primera fase de un modelo de software de optimización con interfaz de Matlab que podría automatizar notablemente el proceso de diseño y elección de alternativas en el futuro. Por último, las capacidades y aplicabilidad del modelo se estudian mediante la aplicación del modelo de optimización en un caso de estudio real de un proyecto de construcción de una carretera. Gracias a la aplicación del modelo a un estudio de caso real, se ha demostrado que el modelo de optimización proporciona una alternativa efectiva de trazado de la carretera, que satisface las restricciones de diseño y también proporciona información práctica sobre el trazado optimizado. También se observa que el trazado optimizado por el modelo es muy similar al obtenido mediante métodos manuales convencionales, pero el modelo puede reducir en gran medida el tiempo requerido (13 horas) para la planificación y diseño de la carretera, así como producir una alternativa de menor coste. A pesar de la complejidad del terreno del área de estudio, el trazado óptimo se encuentra sin ninguna dificultad. El coste total del tramo de carretera estudiado con el trazado de proyecto (6 226 610 €) es similar al coste total del trazado de la carretera optimizado (6 136 872 €), pero sin duda contribuye a reducir el costo en 89 738 € (-1,4%). Como resumen de la investigación, el modelo de optimización propuesto puede contribuir en gran medida a la productividad de los ingenieros de trazado de carreteras, así como a la calidad de la infraestructura resultante. Se concluye que con el algoritmo heurístico implementado el modelo de optimización logra un trazado horizontal óptimo localmente (dentro del corredor) y un trazado vertical que es globalmente óptimo para todos los trazados analizados, cumpliendo además, las principales restricciones geométricas.

Cracking of quasi-brittle materials (such as concrete, rocks,) may be modelled by means of continuous, discontinuous or continuous-discontinuous models. The latter combine a continuous damage model for the initial stages of degradation with a discontinuous model later on. This switching from a smeared to an explicit representation of the crack is useful in many applications, to model the interaction between the cracked structure and a fluid inside the crack. The capabilities of a continuous-discontinuous model to simulate hydraulic fracture are explored in this work.

Understanding the material failure of quasi-brittle materials, such as concrete, is of vital importance in civil engineering. A continuous-discontinuous model using X-FEM enrichment can be useful when an explicit representation of cracks is required. Besides crack propagation, crack branching can also be modelled by the appropriate X-FEM enrichment. Multiple applications of crack branching simulation can be found, including fracking and dynamic crack propagation.

Elastomers are viscoelastic polymers with low Young's modulus and high failure strain that are used in many c ivil e ngineering applications, including bridge bearings, seismic isolators for buil dings and resilient rail wheels. Their constitutive behaviour i s characterized by a nonlinear stress - strain relation with an extensibility limit . This contrasts with materials that have instead a limit on the tensile stresses, such as mild steel. This MSc thesis is concerned with the numerical modeling of elastomers. T his involves dealing with a medium with two phases: a constrained region, wher e the particles have reached their maxi mum allowable deformation, and a free region, where the inextensibility constraint is still inactive. Moreover, one can think of an interf ace splitting the two phases of the medium. If the focus is put in obtaining methods to locate and evolve such interface, then a two phase medium with a moving interface is considered. From the mathematical point of view, this is a constrained minimization problem. One of the strategies to solve it is to turn the minimization problem into a shape equilibrium one. This approach has b een successfully employed for an interface location problem in small strains and serves as the starting point of this work. T hu s, t he main purpose of this thesis is to extend this formulation to a large strains interface locating and evolving scenario. A first analysis of the problem reveals two sources of nonlinearity : the inextensibility constraint and the kinematics in large st rains. A simple but thorough one - dimensional study of the problem is then developed to find methods to sort out both nonlinearities. Following this, explicit iterative schemes to locate and evolve one or multiple interfaces are straightforwardly obtained i n 1D linear elasticity. However, the same ideas applied to a simple St.Venant - Kirchhoff hyperelasticity model , evidences that even very simple 1D problems become rather complex and cannot be solved as directly and explicit as before. Numerical examples are provided throughout this analysis and they are also useful to conclude that both locating and evolving the interface can be essentially seen as the same problem, but with different driving effects. After that, an extension of the one - dimensional schemes t o two or more dimensions is explored . Although the same ideas can be applied, more sophisticated modeling tools are required, namely, the X - FEM and Level set methods, the shape sensitivity analysis and the Arbitrary Lagrangian - Eulerian methods . A complemen tary numerical implementation of the pr oposed strategy is to show its computational benefits. In particular, a combination of the three previous techniques shall make unnecessary a stepwise update of the Level set. T he work presented here may not be limite d to this particular case and be r elevant to other engineering problems involving moving interfaces and boundaries , such as plasticity analysis or the saturation of a porous medium.

Es pretén en aquesta tesina estudiar l'afectació en l'atenuació global de vibracions que suposa considerar o no l'efecte Payne d'una manta elastomèrica reforçada amb filler incorporada a un sistema de via, així com analitzar la incidència de l'efecte Payne en la funció de transferència inversa i l'energia dissipada per cicle.

To numerically simulate a failure process, damage models can be used. In order to avoid mesh dependency problems of local damage models, nonlocal models are employed. The use of nonlocal displacements is an efficient computational technique that allows to obtain physically realistic results. The goal of this research project is the numerical modelling of failure processes by means of this nonlocal technique. Special emphasis will be placed on numerical tests that deal with multiple cracks.  

The endocytosis is the process used by cells to uptake selected external particles such as viruses, drugs or microorganisms among others. The receptor mediated endocytosis is one of the most effective methods to capture nanoparticles no bigger than 100 nm in diameter. During this process, some proteins located on the cell surface bind to countermolecules decorating the particle surface, creating unions strong enough to wrap the lipid bilayer that conforms the cell membrane around the external particle. Recently, due to the nature of this union, some investigators have developed new drug delivery tools that can target meds to a specific type of cell. However, as the mechanics of the endocytic process are still unknown, the treatment evolves slowly. Therefore, it is fundamental to create a numerical model that helps us to understand the mechanics behind this method and accelerates the  development of the investigations.

Esta tesina final de carrera estudia la posibilidad de utilizar metaheurísticas en problemas de optimización en ingeniería. Las metaheurísticas son métodos computacionales basados en la naturaleza, con cierta aleatoriedad en su comportamiento, desarrollados en las últimas décadas que permiten encontrar aproximaciones aceptables a problemas de optimización muy complejos. En este estudio se implementan dos metaheurísticas, Algoritmo Genético y Recocido Simulado, y se ponen a prueba mediante problemas típicos de optimización relacionados con la ingeniería. A su vez, se compara los resultados obtenidos con los de métodos clásicos como son la búsqueda exhaustiva o el método de Newton.