Aprèn - Joan Baiges Aznar

The aim of this project is designing and programming a seismic analysis module in the CME2.01 application, which is able to calculate frame structures of two or three dimensions. This application has been developed in Matlab® in order to become a learning tool in structural analysis for future students of the School of Civil Engineering in Barcelona. The module, until now, included a sort of modules which enable a user to analyse and solve frame structures in the static, dynamic, plastic and instability cases. Incorporating this new module, the whole application will be able to analyse structures submitted to seismic accelerations from many different sources. Once the development and programming of the previous modules have been analysed, it have been taken advantage of all the possible resources that may be shared with the new module (as loads and data gathering, graphical interface, coordination functions, animated results…) in order to optimise, as much as possible, the performance of the software. The module consists on a dynamic environment such as a GUI (Graphical User Interface), which allows the user, in an interactive way, to design frame structures and its properties, application of loads and boundary conditions and visualisation of results. For the process of solving the seismic problem, the modal superposition method has been chosen, whose deeper explanation will be carried out in the following chapters. As a summary, this method calculates the natural vibrating modes of the structure and, thanks to the uncoupling of the partial differential equations of motion, obtains the final solution as a linear combination of these modes. Once the solution of the displacements in time has been found, the application shows an animation of the movement in time of the structure, as well as the possibility of showing graphically the spatial-temporal evolution of a selected node. It also allows us to use an optimisation tool which optimises the calculating process for high complexity structures. At the same time, some interesting results for the user or some results due to the user interaction will appear in the Command Window2 of the program. After programming the module, it has been validated through comparison of results among classical structural cases found in the existent literature. Moreover, an analysis of a real structure has been carried out in order to proof the utility of the module even in very complex scenarios. Finally, in the last part of this work, a set of critical conclusions about the program and its design have been presented. This conclusions will corroborate the utility of the module as a learning tool and as a way of developing structural competencies in students.

La realización de este trabajo tiene como fin el diseño y programación de un módulo de cálculo sísmico de estructuras de barras en dos y tres dimensiones incorporado en el programa CME2.03. Dicho programa ha sido desarrollado en Matlab®, con el objetivo de servir como herramienta de aprendizaje en las materias de estructuras para futuros estudiantes de la escuela. El programa, hasta la fecha, incluía diversos módulos que permitían el análisis y resolución de estructuras de barras en los casos estáticos, dinámicos, plásticos y de inestabilidad. Con la incorporación de este nuevo último módulo, el programa será también capaz de analizar estructuras bajo el efecto de aceleraciones sísmicas de diversa índole. Una vez estudiada la programación y desarrollo de los módulos anteriores, se han aprovechado al máximo todos los recursos que puedan ser compartidos con el nuevo módulo (carga y obtención de datos, interfaz gráfica, funciones de coordinación, muestra gráfica de resultados, etc.) con el fin de optimizar, en la medida de lo posible, el funcionamiento del software. El módulo consiste en un entorno dinámico a modo de IGU (Interfaz gráfica de usuario) que permite al usuario, de forma interactiva, el diseño de estructuras de barras y sus propiedades, aplicación de cargas y condiciones de contorno y visualización de resultados. Para el proceso de resolución del problema sísmico se ha escogido el método de superposición modal, cuya explicación en detalle se abordará en capítulos posteriores en este trabajo. De manera sintética, este método calcula los modos de vibración naturales de la estructura y, desacoplando las ecuaciones diferenciales del movimiento de la estructura, permite obtener la solución final como una combinación lineal de ellos. Una vez obtenida la solución en movimientos de la estructura en el tiempo, el programa ofrece una animación del movimiento temporal de la misma, así como la posibilidad de representar gráficamente la evolución espacio-temporal de un nodo concreto. También se permitirá utilizar una herramienta de optimización de cálculo para aquellas estructuras de mayor complejidad. Simultáneamente, se presentarán en la Command Window4 del programa algunos resultados de interés para el usuario o fruto de su interacción con el programa. Una vez terminada la fase de programación del módulo, la validación del mismo ha sido llevada a cabo mediante la comparación de los resultados obtenidos para casos clásicos de estructuras sísmicas que se han encontrado en la literatura existente. Además, se ha desarrollado un análisis de una estructura real, con el fin de comprobar la utilidad del módulo incluso en casos complejos. Finalmente, en la última parte de este trabajo se han expuesto una serie de conclusiones críticas acerca del programa y su diseño, en las que se corroborará la utilidad del programa como herramienta docente y de desarrollo de competencias en estructuras.

Approximate Dirichlet boundary conditions in time-evolving physical domains

Projecte Final de Màster Oficial

Arregui Bravo, Guillermo

Tutor/a - Director/a: Codina, Ramon; Baiges Aznar, Joan

Fecha de publicación: 2016

Escuela Técnica Superior de Ingeniería de Caminos, Canales y Puertos de Barcelona (ETSECCPB)

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In many coupled fluid-structure problems of practical interest the domain of at least one of the problems evolves in time. The most often applied approach to deal with such motion in numerical methods is the use of the Arbitrary Eulerian-Lagrangian (ALE) framework. However, the use of a pure fixed-mesh could allow us to get rid of choosing the arbitrary mesh velocity and is often more adapted for fluid motion. Nevertheless, several other problems arise from such a strategy when applied to the finite element method (FEM), especially regarding the application of Dirichlet boundary conditions (BCs). The usual strategy to prescribe Dirichlet BCs in FEM is to define the boundary of the domain by placing nodes and facets on it, which allows us to strongly impose the condition by defining the unknown as such in the given nodes. However, it is quite straightforward to see that if a fixed-mesh strategy is to be used on, for example, a solid moving domain inside a fluid, non-matching or non-conforming grids will appear at every time step of calculation. In this cases, the boundary geometry intersects the boundary cells in an arbitrary way. To solve such a problem several techniques have been developed, such as the immersed boundary method, the penalty method, Nitsche's method, the use of Lagrange multipliers and other techniques that combine several of these strategies. These methods impose the BCs in an approximate way once the discretization has been carried out, either by modifying the differential operators near the interface (in finite differences) or by modifying the unknowns near the interface. In this work we describe such numerical techniques for approximating Dirichlet BCs for the transient incompressible Navier-Stokes (N-S) equations. Some of these techniques have been programmed on FEMUSS (Finite Element Method Using Subscale Stabilitzation), one of the multiphysics Fortran code used at the International Centre for Numerical Methods in Engineering (CIMNE) and we applied them to study the flow of fluids around time-evolving prescribed solids.