Dynamique des structures. Vulnérabilité aux bâtiments. Construction parasismique

La leçon s'addresse à la comprehension du comportement des bâtiments soumis à l'accéleration séismique, et présente une introduction au comportement dynamique de oscillateurs (un ou plusieurs dégrés de liberté), du comportément hystérétique des structures (selon modes de dissipation) et aux paramètres séismiques relevants à la conception parasismique, notamment aux spectres de réponse et de démande, et sa relation avec la capacité de la structure (courbe de capacité) où on peut identifier les niveaux de dommage -ou les critères de performance- pour des intensités séismique prévues au projet. Elle considère aussi les méthodes de définition et détermination de la vulnérabilité, façe aux séismes, des différentes typologies constructives, avec l'inclusion finale des typologies pour les sistèmes de contreventement et recomandations visées à éviter aux mêmes la concentration de dommage d'origine séismique. Lecture's goal focuses in the understanding of the behaviour of buildings under seismic excitation. It presents an introduction of dynamics (single or multiple degrees of freedom oscillators) and the hysteretic behaviour of ductile structures, introducing the seismic parameters relevant to the structural design, mostly in the context of response and demand spectra and their relations with capacity curves of structures. On the capacity curve obtained in pushover analysis, points representing the design objectives in terms of performance levels can be identified and related with seismic demand. Lecture deals also with methods on vulnerability analysis for building construction typologies and the behaviour (and related recommendations) of seismic resistant structural typologies, having the distribution of dissipative energy and damage in mind.

Fatigue damage modelling of steel structures

In the present work a constitutive model is developed which permits the simulation of the low cycle fatigue behaviour in steel framed structures. In the elaboration of this model, the concepts of the mechanics of continuum medium are applied on lumped dissipative models. In this type of formulation an explicit coupling between the damage and the structural mechanical behaviour is employed, allowing the possibility of considering as a whole different coupled phenomena. A damage index is defined in order to model elastoplasticity coupled with damage and fatigue damage.

Energy-entropy-momentum time integration methods for coupled smooth dissipative problems

Esta tesis aborda la formulación, análisis e implementación de métodos numéricos de integración temporal para la solución de sistemas disipativos suaves de dimensión finita o infinita de manera que su estructura continua sea conservada. Se entiende por dichos sistemas aquellos que involucran acoplamiento termo-mecánico y/o efectos disipativos internos modelados por variables internas que siguen leyes continuas, de modo que su evolución es considerada suave. La dinámica de estos sistemas está gobernada por las leyes de la termodinámica y simetrías, las cuales constituyen la estructura que se pretende conservar de forma discreta. Para ello, los sistemas disipativos se describen geométricamente mediante estructuras metriplécticas que identifican claramente las partes reversible e irreversible de la evolución del sistema. Así, usando una de estas estructuras conocida por las siglas (en inglés) de GENERIC, la estructura disipativa de los sistemas es identificada del mismo modo que lo es la Hamiltoniana para sistemas conservativos. Con esto, métodos (EEM) con precisión de segundo orden que conservan la energía, producen entropía y conservan los impulsos lineal y angular son formulados mediante el uso del operador derivada discreta introducido para asegurar la conservación de la Hamiltoniana y las simetrías de sistemas conservativos. Siguiendo estas directrices, se formulan dos tipos de métodos EEM basados en el uso de la temperatura o de la entropía como variable de estado termodinámica, lo que presenta importantes implicaciones que se discuten a lo largo de esta tesis. Entre las cuales cabe destacar que las condiciones de contorno de Dirichlet son naturalmente impuestas con la formulación basada en la temperatura. Por último, se validan dichos métodos y se comprueban sus mejores prestaciones en términos de la estabilidad y robustez en comparación con métodos estándar. This dissertation is concerned with the formulation, analysis and implementation of structure-preserving time integration methods for the solution of the initial(-boundary) value problems describing the dynamics of smooth dissipative systems, either finite- or infinite-dimensional ones. Such systems are understood as those involving thermo-mechanical coupling and/or internal dissipative effects modeled by internal state variables considered to be smooth in the sense that their evolutions follow continuos laws. The dynamics of such systems are ruled by the laws of thermodynamics and symmetries which constitutes the structure meant to be preserved in the numerical setting. For that, dissipative systems are geometrically described by metriplectic structures which clearly identify the reversible and irreversible parts of their dynamical evolution. In particular, the framework known by the acronym GENERIC is used to reveal the systems' dissipative structure in the same way as the Hamiltonian is for conserving systems. Given that, energy-preserving, entropy-producing and momentum-preserving (EEM) second-order accurate methods are formulated using the discrete derivative operator that enabled the formulation of Energy-Momentum methods ensuring the preservation of the Hamiltonian and symmetries for conservative systems. Following these guidelines, two kind of EEM methods are formulated in terms of entropy and temperature as a thermodynamical state variable, involving important implications discussed throughout the dissertation. Remarkably, the formulation in temperature becomes central to accommodate Dirichlet boundary conditions. EEM methods are finally validated and proved to exhibit enhanced numerical stability and robustness properties compared to standard ones.