Abstract

The objective of this monograph is to apply the computation methods for critical points to more complex mechanical problems involving inequality constraints. Prior to this extension to a new class of problems appropriate methods among the existing ones for the critical point detection are chosen. Therefore the CDM and the extended system as the most primising techniques will be compared and evaluated. A one step prediction of the critical load based on the extended system will be developed that enables a better evaluation. The possibilities of a combination of both methods will be examined. A conceivable combination is to use the prediction of a CDM computation as starting value for the extended system and enhance the convergence of the latter. In a second step critical point detection methods are extended to problems that involve inequality constraints. In this context constitutive damage models and contact problems are studied.

Abstract

En este documento se presentan la metodología seguida y los resultados obtenidos en el contexto de un exhaustivo estudio experimental encaminado a la caracterización del comportamiento de los hormigones reforzados con fibras de acero, utilizando distintos procedimientos de ensayo contemplados en las normativas internacionales vigentes. Esta campaña experimental se ha desarrollado sobre tres hormigones base (C-20, C-30 y C-70), a los cuales se han incorporado fibras metálicas de distinto tipo y en diferentes cantidades.

Abstract

El presente trabajo tiene por objeto hacer una revisión introductoria sobre el estado actual delos pulvimateriales y en particular sobre los nuevos cer´amicos ingenieriles. Sería interminable escribir una relación profunda sobre las distintas tipologías de cerámicos que existen en la actualidad; sin embargo es posible presentar conceptos que puedan delinear en forma general una respuesta a la pregunta: ¿qué son los nuevos cerámicos en ingeniería? Responder a esta pregunta es precisamente parte del trabajo que se presenta.  Al final, en el capítulo 4, se desarrolla una idea para tratar en forma global el comportamiento mecánico térmico de los pulvimateriales. Es decir, desde su fabricación a la puesta en servicio. Es conveniente resaltar, que esta primera presentación del tema solamente pretende introducir al lector en el conocimiento sobre el comportamiento mecánico de los pulvimateriales. Por lo tanto, es mi esperanza que sirva de utilidad para aclarar las dudas básicas y permita iniciar estudios más profundos.

Abstract

La principal dificultad que se encuentra en el momento de diseñar estructuras con materiales compuestos es la falta de modelos constitutivos que permitan si- mular su comportamiento.  Las técnicas analíticas convencionales utilizadas para el estudio de materiales simples isótropos no resultan adecuadas para el análisis de materiales compuestos. Tampoco ha resultado satisfactoria la representación de un compuesto mediante un único material ortótropo con propiedades del conjunto. Puede observarse en distintas referencias los intentos que ha habido para modelar el comportamiento de materiales compuestos, utilizando la técnica de elementos fi- nitos para el análisis y diseño de estructuras, donde la correlación entre los análisis y los resultados experimentales no resulta satisfactoria (Ali, 1996) (Klintworth y Macmillian, 1992). El proceso de diseño de componentes en materiales compuestos se ha basado, principalmente, en métodos empíricos, observándose en la literatura la ausencia de análisis o simulaciones del comportamiento de materiales compuestos sometidos a niveles de esfuerzos que sobrepasan el límite elástico.  

Abstract

En este trabajo se desarrollan diferentes métodos evolutivos para la optimización topológica de estructuras resistentes: Algoritmo Genético, Estrategias Evolutivas, Método de Escalada, Método de Baluja, Métodos de Segag y Schoenauer, Recocido Simulado

Abstract

This work is about the development of a general algorithm for the numerical solution of flow equations: the Navier-Stokes set. This set of differential equations models the time dependent behavior of fluids. It is formed by continuity, linear momentum and an energy transport equations. The algorithm here described is a general one since it can handle equally a great variety of problems, ranging from incompressible to compressible flows, viscous to inviscid, stationary and transient, all of them phisically modeled by the same set of differential equations. In the present work, a quest for a general algorithm is described, following one of many possible ways to tackle the problem. In general, this is done extending methods either from compressible to incompressible flows or from incompressible to compressible ones.

Abstract

The  main objective of the research presented in this work is the formulation, analysis and implementation of efficient numerical algorithms for dissipate dynamical systems in solids mechanics. The dissipate structure exhibited by the systems considered is described in detail for the coupled thermoviscoplastic problem including phase change phenomena and extended to the frictional thermomechanical contact problem.

Abstract

En el presente trabajo se desarrolla un nuevo modelo constitutivo, basado en la mecánica de medios continuos, que permite modelar el comportamiento a fatiga isotérmica bajo cargas periódicas. Este modelo permite tratar en forma conjunta fenómenos acoplados, tales como la combinación de fatiga con daño, plasticidad, fenómenos viscosos y temperatura. Se presenta una formulación basada en la teoría de la plasticidad y daño y se establecen las modificaciones necesarias a realizar en estas teorías, para garantizar la inclusión del fenómeno de fatiga. El estudio de la fatiga ha sido tema de continuos trabajos de investigación en los últimos setenta años. Esto ha echado luz sobre esta disciplina, generando una cantidad de publicaciones y teorías de distinta importancia. A pesar del gran volumen de trabajo que ha realizado la ingeniería sobre este tema, se encuentran aun grandes lagunas en cuanto a la simulación numérica del mismo y a la predicción de vida útil en las piezas. Sobre este último tema pocas teorías han acertado y por lo tanto no hay caminos claros para garantizar aciertos en este tema. Basado en el estado actual del tema, se ha querido en este trabajo avanzar en la dirección de la predicción de vida útil y utilizar las herramientas de la mecánica de medios continuos para garantizar la concreción de las ideas. Otra motivación del desarrollo de este trabajo se asienta en la peligrosidad que involucra la falta de conocimientos para la realización de la predicción de vida útil de las piezas. Las roturas por fatiga son especialmente peligrosas por que no suelen presentar indicios de fallo inminente, sino que este se produce de modo repentino y sin observar deformaciones plásticas de conjunto. Se trata pues de roturas frágiles que se caracterizan por presentar zonas bien diferenciadas, una de textura lisa con muestra de rotura dúctil y otra de textura gruesa rugosa más brillante que es donde se localiza la rotura final al rebasar la resistencia máxima disminuida por el fenómeno de fatiga. Hay que recordar que normalmente la fatiga no sobreviene sola y que siempre está acompañada de otros efectos mecánicos que en un principio pueden parecer secundarios, pero al final se tornan determinantes en la vida de las piezas. En la esperanza de abrir un camino para el tratamiento de este fenómeno desde la mecánica de medios continuos, es que se desarrolla el presente trabajo.

Abstract

La mampostería es uno de los materiales de construcción con mayor abanico de usos, ya sea en el pasado como en el presente, así es como hoy en día también se puede encontrar en la construcción de edificaciones modernas. Los materiales utilizados a lo largo de la historia como elementos componentes de la mampostería han sido muchos y muy variados: desde la simple roca unida con mortero de cal (sillería), pasando por los enormes bloques de mármol usados en la construcción de los grandes monumentos del apogeo de la arquitectura del Renacimiento, hasta llegar a elementos cerámicos refractarios como los que se utilizan para la construcción de hornos, centrales nucleares e incluso como aislante térmico de naves espaciales. Los métodos de cálculo  avanzado  (modelos constitutivos de la mecánica del medio continuo) deben ser el pilar sobre el que desarrollar elementos más objetivos de análisis estructural de la mampostería. Los elementos finitos son una herramienta potente en la que apoyar el cálculo de la obra de fábrica pero, debido a que ésta tiene un tamaño pequeño respecto a las dimensiones globales de la estructura, se hacen inviables desde el punto de vista computacional. La necesidad de encontrar un método que equilibre sencillez, objetividad y rapidez de cálculo es la que motiva el desarrollo de formulaciones con tratamiento al nivel de macromodelo de la mampostería. La inquietud por conseguir este equilibrio hace a Jacob Lubliner  y  Sergio  Oller   sentar  las  bases  que  permitirán  el  desarrollo  del  modelo constitutivo homogeneizado que se presenta en este trabajo.

Abstract

The objective of the work is to develop a numerical tool to describe how the concentration of one or more substances distributed in a fluid environment changes under the effect of three transport processes: advection, diffusion and absorption. For that purpose, it is essential to know the interaction of the transported substance with the fluid medium. The work aims to develop stabilized numerical methods for solving the transport and fluid flow equations in a coupled manner for greater accuracy, efficiency and speed when predicting the motion of the transported substances in the fluid. Emphasis is put in the transport of substances in fluids at high P\'eclet numbers. The practical motivation of the work is predicting the transport of a pollutant in air in urban environments. The work document summarizes the research published in three papers published in JCR journals of high impact. The author of the work is also the first author in the three papers. The papers are attached to the document in the corresponding chapters. The description of the work developments has been organized as follows. First, we present the research carried out in the work for the development of a generalized stabilized Finite Increment Calculus-Finite Element Method (FIC--FEM) formulation for solving the multidimensional transient advection-diffusion-absorption equation. The starting point of the developments are the governing equations for the multidimensional steady advection-diffusion-absorption and the unidimensional transient advection-diffusion-absorption problems obtained via the FIC procedure. The good behaviour of the new FIC--FEM formulation is shown in several examples of application. This work was published in the first of the three papers mentioned. In the following chapter we present an innovative numerical method for solving transport problems with high values of advection and / or absorption. A Lagrangian approach based on the updated version of the classical Particle Finite Element Method (PFEM) has been developed to calculate the advection of substances in fluids, while a Eulerian strategy based on the stabilized FIC--FEM formulation is adopted to compute diffusion and absorption effects. The new semi-Lagrangian approach has been validated in its application of a series of academic examples of transport of substances for different values of the P\'eclet and Damk\"ohler numbers. Finally, we derive a procedure for coupling the fluid and transport equations to model the distribution of a pollutant in a street canyon. In our case, we have considered black carbon (BC) as the pollutant. The evolution of the fluid flow is calculated with a standard stabilized finite element method using the Quasi-Static Variational Multiscale (QS-VMS) technique. For the temperature and pollutant transport we use the semi-Lagrangian procedure developed in the work. Several examples of application have been solved to illustrate the accuracy and practicability of the proposed numerical tool for predicting the transport of a pollutant in air in urban environments. One of the examples are presented in the third paper, while another academic one is presented in the appendix of this document.

Abstract

It is well known that in civil engineering structures are designed so that they remain, whenever possible, in an elastic regime and with their mechanical properties intact. The truth is that in reality there are uncertainties either in the execution of the work (geometric errors or material quality) or during its subsequent use (loads not contemplated or its value has been estimated incorrectly) that can lead to the collapse of the structure. This is why the study of the failure of structures is inherently interesting and, once is known, its design can be improved to be the less catastrophic as possible or to dissipate the maximum energy before collapsing. Another area of application of fracture mechanics is that of processes of which interest lies in the breakage or cracking of a medium. Within the mining engineering we can enumerate several processes of this nature, namely: hydraulic fracture processes or fracking, blasting for tunnels, explosion of slopes in open pit mines, among others. Equally relevant is the analysis of structural failures due to natural disasters, such as large avenues or even tsunamis impacting protection structures such as walls or dikes. In this work numerous implementations and studies have been made in relation to the mentioned processes. That said, the objective of this work is to develop an advanced numerical method capable of simulating multi-fracture processes in materials and structures. The general approach of the proposed method can be seen in various publications made by the author and directors of this work. This methodology is meant to cover the maximum spectrum of engineering applications possible. For this purpose, a coupled formulation of the Finite Element Method (FEM) and the Discrete Element Method (DEM) is used, which employs an isotropic damage constitutive model to simulate the initial degradation of the material and, once the strength of the material has been completely exhausted, those Finite Element (FE) are removed from the FEM mesh and a set of Discrete Element (DE) are generated at its nodes. In addition to ensure the conservation of the mass of the system, these DE prevent the indentation between the fissure planes thanks to the frictional repulsive forces calculated by the DEM, if any. Additionally, in this work it has been studied how the proposed coupled method named FEM-DEM together with the smoothing of stresses based on the super-convergent patch is able to obtain reasonably meshindependent results but, as one can imagine, the crack width is directly related to the size of the elements that have been removed. This favours the inclusion of an adaptive remeshing technique that will refine the mesh where it is required (according to the Hessian of a nodal indicator of interest) thus improving the discretization quality of the crack obtained and thereby optimizing the simulation cost. In this sense, the procedures for mapping nodal and internal variables as well as the calculation of the nodal variable of interest will be discussed. As far as the studies of natural disasters are concerned, especially those related to free-surface water flows such as tsunamis, one more level of coupling between the aforementioned method FEM-DEM and one Computational Fluid Dynamics (CFD) formulation commonly referred to as Particle Finite Element Method (PFEM) has been implemented. With this strong coupled formulation, many cases of wave impacts and fluid flows have been simulated against solid structures such as walls and dikes, among others.

Abstract

The notion of metamaterials as artificially engineered structures designed to obtain specific material properties, typically unachievable in naturally occurring materials, has captured the attention of the scientific and industrial communities. Among the broad range of applications for such kind of materials, in the field of acoustics, the possibility of creating materials capable of efficiently attenuating noise in target frequency ranges is of utmost importance for a lot of industrial areas. In this context, the so-called locally resonant acoustic metamaterials (LRAMs) can play an important role, as their internal topology can be designed to exhibit huge levels of attenuation in specific frequency regions by taking advantage of internal resonance modes. With a proper, optimized topological design, LRAMs can be used, for instance, to build lightweight and thin noise insulation panels that operate in a low-frequency regime, where standard solutions for effectively attenuating the noise sources require dense and thick materials. Given the importance of the topological structure in obtaining the desired properties in acoustic metamaterials, the use of novel numerical techniques can be exploited to create a set of computational tools aimed at the analysis and design of optimized solutions. These are based on three fundamental pillars: (1) the multiscale homogenization of complex material structures in the microscale to get a set of effective properties capable of describing the material behavior in the macroscale, (2) the model-order reduction techniques, which are used to decrease the computational cost of heavy computations while still maintaining a sufficient degree of accuracy, and (3) the topology optimization methods that can be employed to obtain optimal configurations with a given set of constraints and a target material behavior. This set of computational tools can be applied to design acoustic metamaterials that are both efficient and practical, i.e. they behave according to their design specifications and can be produced easily, for instance, making use of novel additive manufacturing techniques.

Abstract

This document contains the result resulting from the work in the doctoral thesis Innovative mathematical and numerical models for studying the deformation of shells during industrial forming processes with the Finite Element Method. The objective of this thesis is to contribute to the development of finite element methods for the analysis of the stamping processes, an area of problems with a very clear industrial application. Indeed these kinds of problems involve multiple disciplines and require the understanding of different mechanical problems, being the most relevant disciplines the continuous mechanics, the plasticity, contact problems, among others, depending of the problematic of study.

Abstract

This monograph develops a numerical tool (the Virtual Wind Tunnel, VWT) for the reso-lution of problems involving fluid flow around structures. Due to the limitations that traditional methods may have in this context, the VWT is based on the use of fixed mesh technologies (CutFEM-type) combined with an implicit representation of the embedded bodies. One of the main contributions of the monograph is the use of such fixed mesh methods to solve lightweight thin-walled structures problems. Hence, two embedded formulations capable of representing the flow around bodies with and without internal volume are proposed. The first one results in a simpler implementation and lower computational effort but can only represent a slip behavior of the wall. The second one gets rid of such limitation by including a Nitsche imposition of the Navier-slip condition, thus allowing modelling any wall behavior as a wall law would do. The applicability range of the VWT includes the fluid–structure i nteraction problem (FSI). To that purpose an improvement for the boundary condition imposition of the FM-ALE algorithm mesh motion problem is also proposed. Moreover, the implementation, which has been conceived to be easily extended to any other coupled problem, is also treated. The validation of the technologies within the VWT includes multiple theoretical test cases as well as feasible industrial applications. Among these, the FSI analysis of a 4-point tent during a strong wind episode deserves to be highlighted as it showcases the achievement of the initial objective of the monograph.

Abstract

Through the interconnection of electrical elements such as a resistor, inductor and capacitor, has been developed a reduced-order model of the arterial system capable of describing the behaviour of blood flow. In this modelling, the different differential equations that describe the behaviour of this system are represented implicitly. This allows us to obtain quickly and regulate the performance of the joint model, both in normal physiological conditions and in pathological situations, which makes it a useful tool for teaching or research in cardiovascular physiology. It was implemented two different arterial models, an elastic model and a viscoelastic model, with the aim of analysing the flow and blood pressure that could occur under different physiological conditions. In order to analyse both models, it was contrasted using different orders of elasticity, the pathology of aortic dissection was studied and the results were compared qualitatively with similar solutions observed in the literature. In order to perform these simulations, it was implemented in Matlab a code for solving ordinary differential equations (DAE).

Abstract

Bulk handling, transport and processing of granular materials and powders are fundamental operations in a wide range of industrial processes and geophysical phenomena. Particulate materials, which can be found in nature, are usually characterized by a grain size which can range across several scales: from nanometre to the order of metre. Depending on the volume fraction and on the shear strain conditions, granular materials can have different behaviours and often can be expressed as a new state of matter with properties of solids, liquids and gases. For the above reasons, both the experimental and the numerical analysis of granular media is still a difficult task and the prediction of their dynamic behaviour still represents, nowadays, an important challenge. The main goal of the current monograph is the development of a numerical strategy with the objective of studying the macroscopic behaviour of dry granular flows in quasi-static and dense flow regime. The problem is defined in a continuum mechanics framework and the balance laws, which govern the behaviour of a solid body, are solved by using a Lagrangian formalism. The Material Point Method (MPM), a particle-based method, is chosen due to its features which make it very suitable for the solution of large deformation problems involving complex history-dependent constitutive laws. An irreducible formulation using a Mohr-Coulomb constitutive law, which takes into account geometric non-linearities, is implemented within the MPM framework. The numerical strategy is verified and validated against several benchmark tests and experimental results, available in the literature. Further, a mixed formulation is implemented for the solution of granular flows that undergo undrained conditions. Finally, the developed MPM strategy is used and tested against the experimental study performed for the characterization of the flowability of several types of sucrose. The capabilities and limitations of this numerical strategy are observed and discussed and the bases for future research are outlined.

Abstract

The physics lying behind rotordynamics is complex tomodel, so that in many cases numerical processing is the only feasible approach. Being rotordynamics a field of great interest in the aerospace industry, the efforts devoted to its understanding are increasing day by day. Following this tendency, the aim of the present study is to develop a simplified elastodynamic model for the case of rotating structures such that can be addressed through numerical tools, built using the finite element method. For the purpose of analysing the vibration phenomena, modal decomposition and numerical integration have been taken advantage from. In this context, it has been found that the singular value decomposition could be applied in structural analysis to extract dominant displacement fluctuations, allowing the unfolding of global properties of the dynamic response. In the present report, the singular value decomposition has been applied to cantilever beams undergoing a single rotation, giving rise to reasonably satisfactory results.

Abstract

The world of computing simulation has experienced great progresses in recent years and requires more exigent multidisciplinary challenges to satisfy the new upcoming demands. Increasing the importance of solving multi-disciplinary problems makes developers put more attention to these problems and deal with difficulties involved in developing software in this area. Conventional finite element codes have several difficulties in dealing with multi-disciplinary problems. Many of these codes are designed and implemented for solving a certain type of problems, generally involving a single field. Extending these codes to deal with another field of analysis usually consists of several problems and large amounts of modifications and implementations. Some typical difficulties are: predefined set of degrees of freedom per node, data structure with fixed set of defined variables, global list of variables for all entities, domain based interfaces, IO restriction in reading new data and writing new results and algorithm definition inside the code. A common approach is to connect different solvers via a master program which implements the interaction algorithms and also transfers data from one solver to another. This approach has been used successfully in practice but results duplicated implementation and redundant overhead of data storing and transferring which may be significant depending to the solvers data structure. The objective of this work is to design and implement a framework for building multi-disciplinary finite element programs. Generality, reusability, extendibility, good performance and memory efficiency are considered to be the main points in design and implementation of this framework. Preparing the structure for team development is another objective because usually a team of experts in different fields are involved in the development of multi-disciplinary code. Kratos, the framework created in this work, provides several tools for easy implementation of finite element applications and also provides a common platform for natural interaction of its applications in different ways. This is done not only by a number of innovations but also by collecting and reusing several existing works. In this work an innovative variable base interface is designed and implemented which is used at different levels of abstraction and showed to be very clear and extendible. Another innovation is a very efficient and flexible data structure which can be used to store any type of data in a type-safe manner. An extendible IO is also created to overcome another bottleneck in dealing with multi-disciplinary problems. Collecting different concepts of existing works and adapting them to coupled problems is considered to be another innovation in this work. Examples are using an interpreter, different data organizations and variable number of dofs per node. The kernel and application approach is used to reduce the possible conflicts arising between developers of different fields and layers are designed to reflect the working space of different developers also considering their programming knowledge. Finally several technical details are applied in order to increase the performance and efficiency of Kratos which makes it practically usable. This work is completed by demonstrating the framework’s functionality in practice. First some classical single field applications like thermal, fluid and structural applications are implemented and used as benchmark to prove its performance. These applications are used to solve coupled problems in order to demonstrate the natural interaction facility provided by the framework. Finally some less classical coupled finite element algorithms are implemented to show its high flexibility and extendibility.

Abstract

The extended use of simulation programs has leaned on the advances in user-friendly interfaces and in the capability to generate meshes for any generic complex geometry. More than ten years of development have made Gid grow to become one of the more popular pre ans postprocessing systems at international level. The constant dialogue between the GiD development team and the users has guided the development of giD to cover the pre-post needs of many disciplines in science and engineering. Following gthis philosophy, the biannual GiD Conference has become an important forum for discussion and interchange of experiences among the GiD community. This monograph includes the contributions of the participants to the fourth edition of the GiD Conference held in the island of Ibiza from 8-9 May 2008.