Modelos sin malla en simulación numérica de estructuras aeroespaciales

La presente Tesis Doctoral aborda la introducción de la Partición de Unidad de Bernstein en la forma débil de Galerkin para la resolución de problemas de condiciones de contorno en el ámbito del análisis estructural. La familia de funciones base de Bernstein conforma un sistema generador del espacio de funciones polinómicas que permite construir aproximaciones numéricas para las que no se requiere la existencia de malla: las funciones de forma, de soporte global, dependen únicamente del orden de aproximación elegido y de la parametrización o mapping del dominio, estando las posiciones nodales implícitamente definidas. El desarrollo de la formulación está precedido por una revisión bibliográfica que, con su punto de partida en el Método de Elementos Finitos, recorre las principales técnicas de resolución sin malla de Ecuaciones Diferenciales en Derivadas Parciales, incluyendo los conocidos como Métodos Meshless y los métodos espectrales. En este contexto, en la Tesis se somete la aproximación Bernstein-Galerkin a validación en tests uni y bidimensionales clásicos de la Mecánica Estructural. Se estudian aspectos de la implementación tales como la consistencia, la capacidad de reproducción, la naturaleza no interpolante en la frontera, el planteamiento con refinamiento h-p o el acoplamiento con otras aproximaciones numéricas. Un bloque importante de la investigación se dedica al análisis de estrategias de optimización computacional, especialmente en lo referente a la reducción del tiempo de máquina asociado a la generación y operación con matrices llenas. Finalmente, se realiza aplicación a dos casos de referencia de estructuras aeronáuticas, el análisis de esfuerzos en un angular de material anisotrópico y la evaluación de factores de intensidad de esfuerzos de la Mecánica de Fractura mediante un modelo con Partición de Unidad de Bernstein acoplada a una malla de elementos finitos. ABSTRACT This Doctoral Thesis deals with the introduction of Bernstein Partition of Unity into Galerkin weak form to solve boundary value problems in the field of structural analysis. The family of Bernstein basis functions constitutes a spanning set of the space of polynomial functions that allows the construction of numerical approximations that do not require the presence of a mesh: the shape functions, which are globally-supported, are determined only by the selected approximation order and the parametrization or mapping of the domain, being the nodal positions implicitly defined. The exposition of the formulation is preceded by a revision of bibliography which begins with the review of the Finite Element Method and covers the main techniques to solve Partial Differential Equations without the use of mesh, including the so-called Meshless Methods and the spectral methods. In this context, in the Thesis the Bernstein-Galerkin approximation is subjected to validation in one- and two-dimensional classic benchmarks of Structural Mechanics. Implementation aspects such as consistency, reproduction capability, non-interpolating nature at boundaries, h-p refinement strategy or coupling with other numerical approximations are studied. An important part of the investigation focuses on the analysis and optimization of computational efficiency, mainly regarding the reduction of the CPU cost associated with the generation and handling of full matrices. Finally, application to two reference cases of aeronautic structures is performed: the stress analysis in an anisotropic angle part and the evaluation of stress intensity factors of Fracture Mechanics by means of a coupled Bernstein Partition of Unity - finite element mesh model.

Geometría de presas bóveda

Se presenta en este artículo un programa para cálculo mediante ordenador, de utilización frecuente en el Departamento de Estudios Experimentales de Presas del Labo¬ratorio Central. Este programa se refiere a presas bóvedas asimétricas de tres centros y determina: a) el replanteo geométrico de las mismas para su construcción en modelo reducido. b) la posición -punto de aplicación y dirección- de las cargas puntuales equivalentes a las acciones de peso propio y presión hidrostática, que se introducen en el modelo median¬te gatos hidráulicos. c) la directriz de la presa, dato necesario para un posible cálculo estático posterior. This paper presents a computer program currently used in the Department of Experimental Studies of Dams in the Laboratorio Central. This program concerns asymmetric arch dams of three centers and it determines: a) The geometrical definition of the arch dams for the scaled model construction. b) The position, acting point and direction of the punctual loads equivalent to the actions of self-weight and water pressure, which are applied to the model by means of hydraulic jacks. c) The middle surface of the dam, which later would be introduced for a stress analy¬sis of the dam itself

Analysis of the stress state of a halved and tabled traditional timber scarf joint with the Finite Element Method

The purpose of this study is to determine the stress distribution in the carpentry joint of halved and tabled scarf joint with the finite element method (FEM) and its comparison with the values obtained using the theory of Strength of Materials. The stress concentration areas where analyzed and the influence of mesh refinement was studied on the results in order to determine the mesh size that provides the stress values more consistent with the theory. In areas where stress concentration is lower, different mesh sizes show similar stress values. In areas where stress concentration occurs, the same values increase considerably with the refinement of the mesh. The results show a central symmetry of the isobar lines distribution where the centre of symmetry corresponds to the geometric centre of the joint. Comparison of normal stress levels obtained by the FEM and the classical theory shows small differences, except at points of stress concentration.

Analysis of thermo-mechanical stress effects on CPV receiver under high intensity light cycles

After construction of the LYSS (Light cYcling Stressing Source) in early 2014, several CPV receivers, with and without secondary optical element (SOE) have been aged under fast transient illumination cycling,. The test plan for Madrid consisted of 50000 cycles. Receivers with poor heat spreaders showed low reliability but those with thicker metal layers passed the test well. The operation of LYSS along 8 months, after more than 250000 cycles, did not show any significant failure, except lamp reposition every 120 hours, in average. The equipment seems valid for unveiling weak receiver designs with respect to intensive illumination, in steady and transient modes.