987 resultados para Dynamic problems
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The use of 3-D fundamental solution is some axisymmetric problems is straightforward. The resulting algorithms seem to work better than the usual ones (at least for static solutions) and for dynamic cases, than those presented in the previous paragraph. The robustness of the method allows the computations for very high and very low frequencies without any noticeable difficulty.
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In this work, we introduce a new class of numerical schemes for rarefied gas dynamic problems described by collisional kinetic equations. The idea consists in reformulating the problem using a micro-macro decomposition and successively in solving the microscopic part by using asymptotic preserving Monte Carlo methods. We consider two types of decompositions, the first leading to the Euler system of gas dynamics while the second to the Navier-Stokes equations for the macroscopic part. In addition, the particle method which solves the microscopic part is designed in such a way that the global scheme becomes computationally less expensive as the solution approaches the equilibrium state as opposite to standard methods for kinetic equations which computational cost increases with the number of interactions. At the same time, the statistical error due to the particle part of the solution decreases as the system approach the equilibrium state. This causes the method to degenerate to the sole solution of the macroscopic hydrodynamic equations (Euler or Navier-Stokes) in the limit of infinite number of collisions. In a last part, we will show the behaviors of this new approach in comparisons to standard Monte Carlo techniques for solving the kinetic equation by testing it on different problems which typically arise in rarefied gas dynamic simulations.
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Tailoring specified vibration modes is a requirement for designing piezoelectric devices aimed at dynamic-type applications. A technique for designing the shape of specified vibration modes is the topology optimization method (TOM) which finds an optimum material distribution inside a design domain to obtain a structure that vibrates according to specified eigenfrequencies and eigenmodes. Nevertheless, when the TOM is applied to dynamic problems, the well-known grayscale or intermediate material problem arises which can invalidate the post-processing of the optimal result. Thus, a more natural way for solving dynamic problems using TOM is to allow intermediate material values. This idea leads to the functionally graded material (FGM) concept. In fact, FGMs are materials whose properties and microstructure continuously change along a specific direction. Therefore, in this paper, an approach is presented for tailoring user-defined vibration modes, by applying the TOM and FGM concepts to design functionally graded piezoelectric transducers (FGPT) and non-piezoelectric structures (functionally graded structures-FGS) in order to achieve maximum and/or minimum vibration amplitudes at certain points of the structure, by simultaneously finding the topology and material gradation function. The optimization problem is solved by using sequential linear programming. Two-dimensional results are presented to illustrate the method.
Implementação de formulações do método dos elementos de contorno para associação de placas no espaço
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Tese (doutorado)—Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia Mecânica, 2016.
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Tämä diplomityö on tehty Patria Vehicles Oy:n toimeksiannosta. Patria Vehicles Oy:n tuotantoon kuuluvat vaativiin maasto-olosuhteisiin soveltuvat sotilasajoneuvot. Tutkimuksen tarkoituksena oli kehittää menetelmäohjeet, kuinka FEM-analyysillä voidaan tutkia tuotekehitysvaiheessa ajoneuvon korin teräsrakenteiden värähtelyominaisuuksia ja dynaamista käyttäytymistä. Tutkimuksessa on käytetty Ideas-FEM-ohjelmistoa. Dynaamisten ongelmien ratkaisemiseksi on ymmärrettävä rakenteiden dynaamista käyttäytymistä. Rakenteiden käyttäytymistä ja muodonmuutoksia on tutkittava kriittisillä ominaistaajuuksilla. Tutkimuksessa on selvitetty, kuinka ajoneuvon elementtimallilla voidaan tehdä ominaisvärähtely- ja vastelaskentaa. Ominaisvärähtelylaskennalla selvitetään rakenteen ominaismuodot ja -taajuudet. Vastelaskennalla tutkitaan erilaisten herätteiden vaikutuksia ajoneuvon dynaamiseen käyttäytymiseen ja määritetään herätteistä rakenteeseen aiheutuvat vasteet ja herätteiden siirtyvyys rakenteessa. Lisäksi tutkitaan herätteiden aiheuttamia todellisia jännityksiä ja siirtymiä, jotta saadaan selville rakenteen todelliset rasitukset. Analyyseillä voidaan tutkia, kuinka ajoneuvon korirakennetta on jäykistettävä ja vaimennettava, jotta siinä ei esiinny haitallista melua ja värähtelyä.
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Tämä diplomityö on tehty Patria Vehicles Oy:n toimeksiannosta. Patria Vehicles Oy:n tuotantoon kuuluvat vaativiin maasto-olosuhteisiin soveltuvat sotilasajoneuvot sekä teleskooppimastot. Tutkimuksen tarkoituksena oli mallintaa mastoperävaunusta joustava malli, johon vaikuttavat tuulikuormat. Mallin avulla voidaan tutkia maston siirtymiä, kallistumia sekä kiertymiä. Tutkimuksessa on käytetty ADAMS-simulointiohjelmistoa sekä I-DEAS- FEM ohjelmistoa. Dynaamisten ongelmien ratkaisemiseksi on ymmärrettävä rakenteiden käyttäytymistä. Tuulikuormien mallintamisen edellytyksenä on tuulikuormien syntymisen ymmärtäminen. Tämän työn peruslähtökohtana on mallintaa kaikki maston jäykkyyteen vaikuttavat komponentit joustavina FE-menetelmän avulla. Luodaan superelementit Craig-Bamptonin ominaismuotojen superponointimenetelmällä. Nämä superelementit liitetään toisiinsa ja asetetaan niille tuulikuormat. Luodaan kosketukset puomien, sekä maan ja maston välille. Pienennetään joustavien osien ominaismuotojen määrää, jotta saataisiin nopeammat analyysit. Parametrisoidaan malli, jolloin voidaan analysoida mallilla useampia tapauksia. Verifioidaan malli varmistaaksemme sen oikeellisuuden. Taulukoidaan tulokset.
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In the present work we describe a method which allows the incorporation of surface tension into the GENSMAC2D code. This is achieved on two scales. First on the scale of a cell, the surface tension effects are incorporated into the free surface boundary conditions through the computation of the capillary pressure. The required curvature is estimated by fitting a least square circle to the free surface using the tracking particles in the cell and in its close neighbors. On a sub-cell scale, short wavelength perturbations are filtered out using a local 4-point stencil which is mass conservative. An efficient implementation is obtained through a dual representation of the cell data, using both a matrix representation, for ease at identifying neighbouring cells, and also a tree data structure, which permits the representation of specific groups of cells with additional information pertaining to that group. The resulting code is shown to be robust, and to produce accurate results when compared with exact solutions of selected fluid dynamic problems involving surface tension.
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The current thesis manuscript studies the suitability of a recent data assimilation method, the Variational Ensemble Kalman Filter (VEnKF), to real-life fluid dynamic problems in hydrology. VEnKF combines a variational formulation of the data assimilation problem based on minimizing an energy functional with an Ensemble Kalman filter approximation to the Hessian matrix that also serves as an approximation to the inverse of the error covariance matrix. One of the significant features of VEnKF is the very frequent re-sampling of the ensemble: resampling is done at every observation step. This unusual feature is further exacerbated by observation interpolation that is seen beneficial for numerical stability. In this case the ensemble is resampled every time step of the numerical model. VEnKF is implemented in several configurations to data from a real laboratory-scale dam break problem modelled with the shallow water equations. It is also tried in a two-layer Quasi- Geostrophic atmospheric flow problem. In both cases VEnKF proves to be an efficient and accurate data assimilation method that renders the analysis more realistic than the numerical model alone. It also proves to be robust against filter instability by its adaptive nature.
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Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal
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Wind energy has emerged as a major sustainable source of energy.The efficiency of wind power generation by wind mills has improved a lot during the last three decades.There is still further scope for maximising the conversion of wind energy into mechanical energy.In this context,the wind turbine rotor dynamics has great significance.The present work aims at a comprehensive study of the Horizontal Axis Wind Turbine (HAWT) aerodynamics by numerically solving the fluid dynamic equations with the help of a finite-volume Navier-Stokes CFD solver.As a more general goal,the study aims at providing the capabilities of modern numerical techniques for the complex fluid dynamic problems of HAWT.The main purpose is hence to maximize the physics of power extraction by wind turbines.This research demonstrates the potential of an incompressible Navier-Stokes CFD method for the aerodynamic power performance analysis of horizontal axis wind turbine.The National Renewable Energy Laboratory USA-NREL (Technical Report NREL/Cp-500-28589) had carried out an experimental work aimed at the real time performance prediction of horizontal axis wind turbine.In addition to a comparison between the results reported by NREL made and CFD simulations,comparisons are made for the local flow angle at several stations ahead of the wind turbine blades.The comparison has shown that fairly good predictions can be made for pressure distribution and torque.Subsequently, the wind-field effects on the blade aerodynamics,as well as the blade/tower interaction,were investigated.The selected case corresponded to a 12.5 m/s up-wind HAWT at zero degree of yaw angle and a rotational speed of 25 rpm.The results obtained suggest that the present can cope well with the flows encountered around wind turbines.The areodynamic performance of the turbine and the flow details near and off the turbine blades and tower can be analysed using theses results.The aerodynamic performance of airfoils differs from one another.The performance mainly depends on co-efficient of performnace,co-efficient of lift,co-efficient of drag, velocity of fluid and angle of attack.This study shows that the velocity is not constant for all angles of attack of different airfoils.The performance parameters are calculated analytically and are compared with the standardized performance tests.For different angles of ,the velocity stall is determined for the better performance of a system with respect to velocity.The research addresses the effect of surface roughness factor on the blade surface at various sections.The numerical results were found to be in agreement with the experimental data.A relative advantage of the theoretical aerofoil design method is that it allows many different concepts to be explored economically.Such efforts are generally impractical in wind tunnels because of time and money constraints.Thus, the need for a theoretical aerofoil design method is threefold:first for the design of aerofoil that fall outside the range of applicability of existing calalogs:second,for the design of aerofoil that more exactly match the requirements of the intended application:and third,for the economic exploration of many aerofoil concepts.From the results obtained for the different aerofoils,the velocity is not constant for all angles of attack.The results obtained for the aerofoil mainly depend on angle of attack and velocity.The vortex generator technique was meticulously studies with the formulation of the specification for the right angle shaped vortex generators-VG.The results were validated in accordance with the primary analysis phase.The results were found to be in good agreement with the power curve.The introduction of correct size VGs at appropriate locations over the blades of the selected HAWT was found to increase the power generation by about 4%
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The friction phenomena is present in mechanical systems with two surfaces that are in contact, which can cause serious damage to structures. Your understanding in many dynamic problems became the target of research due to its nonlinear behavior. It is necessary to know and thoroughly study each existing friction model found in the literature and nonlinear methods to define what will be the most appropriate to the problem in question. One of the most famous friction model is the Coulomb Friction, which is considered in the studied problems in the French research center Laboratoire de Mécanique des Structures et des Systèmes Couplés (LMSSC), where this search began. Regarding the resolution methods, the Harmonic Balance Method is generally used. To expand the knowledge about the friction models and the nonlinear methods, a study was carried out to identify and study potential methodologies that can be applied in the existing research lines in LMSSC and then obtain better final results. The identified friction models are divided into static and dynamic. Static models can be Classical Models, Karnopp Model and Armstrong Model. The dynamic models are Dahl Model, Bliman and Sorine Model and LuGre Model. Concerning about nonlinear methods, we study the Temporal Methods and Approximate Methods. The friction models analyzed with the help of Matlab software are verified from studies in the literature demonstrating the effectiveness of the developed programming
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The research activity described in this thesis is focused mainly on the study of finite-element techniques applied to thermo-fluid dynamic problems of plant components and on the study of dynamic simulation techniques applied to integrated building design in order to enhance the energy performance of the building. The first part of this doctorate thesis is a broad dissertation on second law analysis of thermodynamic processes with the purpose of including the issue of the energy efficiency of buildings within a wider cultural context which is usually not considered by professionals in the energy sector. In particular, the first chapter includes, a rigorous scheme for the deduction of the expressions for molar exergy and molar flow exergy of pure chemical fuels. The study shows that molar exergy and molar flow exergy coincide when the temperature and pressure of the fuel are equal to those of the environment in which the combustion reaction takes place. A simple method to determine the Gibbs free energy for non-standard values of the temperature and pressure of the environment is then clarified. For hydrogen, carbon dioxide, and several hydrocarbons, the dependence of the molar exergy on the temperature and relative humidity of the environment is reported, together with an evaluation of molar exergy and molar flow exergy when the temperature and pressure of the fuel are different from those of the environment. As an application of second law analysis, a comparison of the thermodynamic efficiency of a condensing boiler and of a heat pump is also reported. The second chapter presents a study of borehole heat exchangers, that is, a polyethylene piping network buried in the soil which allows a ground-coupled heat pump to exchange heat with the ground. After a brief overview of low-enthalpy geothermal plants, an apparatus designed and assembled by the author to carry out thermal response tests is presented. Data obtained by means of in situ thermal response tests are reported and evaluated by means of a finite-element simulation method, implemented through the software package COMSOL Multyphysics. The simulation method allows the determination of the precise value of the effective thermal properties of the ground and of the grout, which are essential for the design of borehole heat exchangers. In addition to the study of a single plant component, namely the borehole heat exchanger, in the third chapter is presented a thorough process for the plant design of a zero carbon building complex. The plant is composed of: 1) a ground-coupled heat pump system for space heating and cooling, with electricity supplied by photovoltaic solar collectors; 2) air dehumidifiers; 3) thermal solar collectors to match 70% of domestic hot water energy use, and a wood pellet boiler for the remaining domestic hot water energy use and for exceptional winter peaks. This chapter includes the design methodology adopted: 1) dynamic simulation of the building complex with the software package TRNSYS for evaluating the energy requirements of the building complex; 2) ground-coupled heat pumps modelled by means of TRNSYS; and 3) evaluation of the total length of the borehole heat exchanger by an iterative method developed by the author. An economic feasibility and an exergy analysis of the proposed plant, compared with two other plants, are reported. The exergy analysis was performed by considering the embodied energy of the components of each plant and the exergy loss during the functioning of the plants.
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In this chapter some applications of boundary element techniques to dynamic problems are presented. First, the basic theory is briefly reviewed in order to provide the necessary background to interpret the numerical results (for a fuller account of elastodynamic theory we recommend a study of the specialized literature). The second part of the chapter is devoted to the numerical implementation of the BEM. The presentation is based on the steady-state solution because this is the area in which most experience exists. This is by no means a limitation of the BEM method, and the use of integral transformations to obtain transient solutions is a well established procedure. Finally, in the third part three examples are presented. The first example is the steady-state solution of a plate under cyclic forces with and without a crack. The second example relies on the determination of soil compliances necessary to study soil-structure interaction and the third example treats the problem of the influence of different incidence angles of incoming waves in foundations. The last two examples are relevant to earthquake engineering problems for which the BEM is very well suited.
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In this paper some aspects of the use of non-reflecting boundaries in dynamic problems, analyzed in time domain, are considered. Current trends for treating the above mentioned problems are summarized with a particular emphasis on the use of numerical techniques, such as Boundary Element Method (BEM) or mixed and hybrid formulations, Finite Element Method (FEM) plus BEM. As an alternative to these methods, an easy time domain boundary condition, obtained from the well known consistent transmitting boundary developed by Waas for frequency domain analysis, can be applied to represent the reactions of the unbounded soil on the interest zone. The behaviour of this proposed boundary condition is studied when waves of different frequency to the one used for its obtention are acting on the physical edge of the model. As an application example,an analysis is made of the soil-structure interaction of a rigid strip foundation on a horizontal non-linear elastic layer on bed rock. The results obtained suggest the need of time domain solutions for this type of problem
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La “Actuación en la Crisis”, objetivo principal de esta tesis, trata de establecer y concretar los procedimientos y apoyos desde tierra y a bordo de los buques, tanto técnicos como operacionales, a seguir por el Capitán y tripulación de un buque después de un accidente, en especial cuando el buque tiene un riesgo importante de hundimiento o necesidad de abandono. La aparición de este concepto es relativamente reciente, es decir desde el año 1995, después de los estudios y propuestas realizados, por el Panel de Expertos de IMO, como consecuencia del hundimiento del buque de pasaje y carga rodada, Estonia, en el que perdieron la vida más de 850 personas a finales de Septiembre de 1994. Entre las propuestas recomendadas y aceptadas por los gobiernos en la Conferencia Internacional SOLAS 1995, figuraba este concepto novedoso, que luego fue adoptado de una forma generalizada para todos los tipos de buques, que hasta entonces sólo disponían de documentos dispersos y a veces contradictorios para la actuación en estos momentos de peligro, que dio lugar a un profundo tratamiento de este problema, que iba a afectar a los buques, tanto en los conceptos y parámetros de proyecto, como a la propia operación del buque. La tesis desarrolla los fundamentos, estado del arte, implantación y consecuencias sobre la configuración y explotación del buque, que han dado lugar a una serie de documentos, que se han incluido en diversos Convenios Internacionales, Códigos y otros documentos de obligada aplicación en la industria naval generados en IMO (SOLAS, Retorno Seguro a Puerto, Plano y Libro de Control de Averías, ISM). La consecuencia más novedosa e interesante de este concepto ha sido la necesidad de disponer cada compañía explotadora del buque, de un servicio importante de “apoyo en la crisis”, que ha dado lugar a implantar un “servicio de emergencia especial”, disponible las 24 horas del día y 365 de año que ofrecen las Sociedades de Clasificación. El know-how de los accidentes que tratan estos servicios, hacen que se puedan establecer ciertas recomendaciones, que se centran, en que el buque tenga, por sus propios medios, una posibilidad de aumentar el KM después de una avería, la garantía de la resistencia estructural adecuada y el aumento del tiempo de hundimiento o el tiempo de mantenimiento a flote (otro tipo de averías vinculadas con la maquinaria, equipo o protección y lucha contra incendios, no son objeto de tesis). Las conclusiones obtenidas, son objeto de discusión especialmente en IACS e IMO, con el fin de establecer las aplicaciones pertinentes, que permitan dar al buque una mayor seguridad. Como objetivo principal de esta tesis es establecer estos puntos de mejora consecuencia de esta actuación en la crisis, con la aportación de varias soluciones que mejorarían los problemas mencionados para los tres tipos de buques que consideramos más importantes (pasaje, petroleros y bulkcarriers) La tesis recorre, desde el principio en 1995, la evolución de esta actuación en la crisis, hasta el momento actual., los puntos básicos que se establecen, que van muy de la mano de la llamada “cultura de seguridad”, objetivo nacido durante los años 90, con el fin de implantar una filosofía distinta para abordar el tratamiento de la seguridad del buque, a la que se venía aplicando hasta el momento, en donde se contemplaba tratar el tema de forma singular y específica para cada caso. La nueva filosofía, trataba de analizar el problema, desde un aspecto global y por tanto horizontal, realizando un estudio exhaustivo de las consecuencias que tendría la aplicación de una nueva medida correctora, en los restantes equipos y sistemas del buque., relativos al proyecto, configuración, operación y explotación del buque. Se describen de manera sucinta las profundas investigaciones a que dio lugar todo lo anterior, estando muchas de ellas, vinculadas a grandes proyectos europeos. La mayor parte de estos proyectos fueron subvencionados por la Comunidad Económica Europea durante la primera década del siglo actual. Dentro de estas investigaciones, donde hay que destacar la participación de todos los agentes del sector marítimo europeo, se hacen imprescindibles la utilización de dos herramientas novedosas para nuestro sector, como son el “Estudio de Riesgos” y la “Evaluación de la Seguridad”, más conocida técnicamente por su nombre ingles “Safety Assessment”, cuyos principios también son incluidos en la tesis. Además se especifican las bases sobre las que se establecen la estabilidad intacta y en averías, con nuevos conceptos, no tratados nunca hasta entonces, como la “altura crítica de agua en cubierta” para la cual el buque se hundiría sin remisión, “estado de la mar” en la que se puede encontrar el buque averiado, el cálculo del tiempo de hundimiento, u otros aspectos como el corrimiento de la carga, o bien el tratamiento de los problemas dinámicos en el nuevo “Código de Estabilidad Intacta”. Con respecto a la resistencia estructural, especialmente el estudio de la “resistencia estructural después de la avería”, que tiene en cuenta el estado de la mar en la que se encontraría el buque afectado. Se analizan los tipos de buques mencionados uno por uno y se sacan, como aportación fundamental de esta tesis, separadamente, las acciones y propuestas a aplicar a estos buques. En primer lugar, las relativas al proyecto y configuración del buque y en segundo lugar, las de operación, explotación y mantenimiento, con el fin de acometer, con garantías de éxito, la respuesta a la ayuda en emergencia y la solución a la difícil situación que pueden tener lugar en condiciones extremas. Para ver el efecto de algunas de las propuestas que se incluyen, se realizan y aplican concretamente, a un buque de pasaje de carga rodada, a un petrolero y a un bulkcarrier, para demostrar el mejor comportamiento de estos buques en situación de emergencia. Para ello se han elegido un buque ejemplo para cada tipo, efectuándose los cálculos de estabilidad y resistencia longitudinal y comparar la situación, en la que quedaría el buque averiado, antes y después de la avería. La tesis se completa con una estadística real de buques averiados de cada uno de estos tres tipos, distinguiendo el tipo de incidente y el número de los buques que lo han sufrido, considerándose como más importantes los incidentes relacionados con varadas, colisiones y fuego resumiéndose lo más relevante de esta aportación también importante de esta tesis. ABSTRACT The "Response in an emergency" is the main objective of this thesis, it seeks to establish and define procedures for technical and operational support onboard and shore, to be followed by the captain and crew on of a ship after an accident, especially when the ship has a significant risk of sinking or a need to abandon it. The emergence of this concept is relatively recent, in 1995, after studies and proposals made by the Panel of Experts IMO, following the sinking of the “Estonia” vessel, where more than 850 people died in late September 1994. In the International Convention SOLAS 1995, among the recommended proposals and accepted regulations, this new concept was included, which was later adopted for all types of ships which until then had only scattered some documents, sometimes including contradictory actions in emergency situations. This led to a profound treatment of this problem, which would affect the vessels in both the concepts and design parameters, as to the proper operation of the vessel. The thesis develops the foundations, state of the art, implementation and consequences on the design and operation of the vessel, this has led to a series of Circulars and Regulations included in several International Codes and Conventions issued by IMO which are required to be complied with (SOLAS Safe Return to Port, Damage Control Plan and Booklet, ISM). The most novel and interesting consequence of this concept has been the need for every company operating the ship to have a shore based support service in emergency situations which has led to implement special emergency services offered by Class Societies which are available 24 hours a day, 365 days per year. The know-how of these services dealing with all types of accidents can establish certain recommendations, which focus on the ship capability to increase the KM after damage. It can also be determined adequate structural strength and the increase of the capsizing time or time afloat (other types of damages associated with the machinery, equipment or firefighting, are not the subject of this thesis). The conclusions are discussed especially in IACS and IMO, in order to establish appropriate applications to improve the security of the vessels. The main objective of this thesis is to establish actions to improve emergency actions, resulting from different responses in the crisis, with the contribution of several solutions that improve the problems mentioned for three types of ships that we consider most important (passenger vessels, tankers and bulk carriers) The thesis runs from the beginning in 1995 to date, the evolution of the response on the crisis. The basics established during the 90s with the "safety culture" in order to implement a different philosophy to address the treatment of the safety of the ship, which was being previously implemented, as something singular and specific to each case. The new philosophy tried to analyse the problem from a global perspective, doing an exhaustive study of the consequences of the implementation of the new regulation in the ship systems and equipment related to the design, configuration and operation of the vessel. Extensive investigations which led to the above are described, many of them being linked to major European projects. Most of these projects were funded by the European Union during the first decade of this century. Within these investigations, which it must be highlighted the participation of all players in the European maritime sector, a necessity to use two new tools for our industry, such as the "Risk Assessment" and "Safety Assessment" whose principles are also included in the thesis. The intact and damage stability principles are established including new concepts, never treated before, as the "critical height of water on deck" for which the ship would sink without remission, "sea state" where the damaged vessel can be found, calculation of capsizing time, or other aspects such cargo shifting or treatment of dynamic problems in the new Intact Stability Code in development. Regarding the structural strength, it has to be especially considered the study of the "residual strength after damage", which takes into account the state of the sea where the vessel damaged can be found. Ship types mentioned are analysed one by one, as a fundamental contribution of this thesis, different actions and proposals are established to apply to these types of vessels. First, those ones relating to the design and configuration of the vessel and also the ones related to the operation and maintenance in order to support successfully responses to emergency situations which may occur in extreme situations. Some of the proposals are applied specifically to a RoRo passenger ship, an oil tanker and a bulkcarrier, to demonstrate the improved performance of these vessels damaged. An example for each type vessel has been chosen, carrying out stability and longitudinal strength calculations comparing the situation of the ship before and after damage. The thesis is completed with incidents statics for each of these three types, distinguishing the type of incident and the number of ships having it. The most important incidents considered are the ones related to groundings, collisions and fire being this other relevant contribution of this thesis.