This work presents an analysis methodology based on the use of the Finite Element Method (FEM) nowadays considered one of the main numerical tools for solving Boundary Value Problems (BVPs). The proposed methodology, so-called cg-FEM (Cartesian grid FEM), has been implemented for fast and accurate numerical analysis of 2D linear elasticity problems. The traditional FEM uses geometry-conforming meshes; however, in cg-FEM the analysis mesh is not conformal to the geometry. This allows for defining very efficient mesh generation techniques and using a robust integration procedure, to accurately integrate the domain’s geometry. The hierarchical data structure used in cg-FEM together with the Cartesian meshes allow for trivial data sharing between similar entities. The cg-FEM methodology uses advanced recovery techniques to obtain an improved solution of the displacement and stress fields (for which a discretization error estimator in energy norm is available) that will be the output of the analysis. All this results in a substantial increase in accuracy and computational efficiency with respect to the standard FEM. cg-FEM has been applied in structural shape optimization showing robustness and computational efficiency in comparison with FEM solutions obtained with a commercial code, despite the fact that cg-FEM has been fully implemented in MATLAB.

Simulation of the pantograph-catenary dynamic interaction has now become a useful tool for designing and optimizing the system. In order to perform accurate simulations, including system non-linearities, the Finite Element Method is commonly employed combined with a time integration scheme, even though the computational time required may be longer than with the use of other simpler approaches. In this paper we propose a two-stage methodology (Offline/Online) which notably reduces the computational cost without any loss in accuracy and makes it possible to successfully carry out very efficient optimizations or even Hardware in the Loop simulations with real-time requirements.

This is the pre-peer reviewed version of the following article: Tur, M., Albelda, J., Nadal, E. and Ródenas, J. J. (2014) AbstractThe use of Cartesian meshes independent of the geometry has some advantages over the traditional meshes used in the finite element method. The main advantage is that their use together with an appropriate hierarchical data structure reduces the computational cost of the Finite Element analysis. This improvement is based on the substitution of the traditional mesh generation process by an optimized procedure for intersecting the Cartesian mesh with the boundary of the domain and the use efficient solvers based on the hierarchical data structure. One major difficulty associated to the use of Cartesian grids is the fact that the mesh nodes do not, in general, lie over the boundary of the domain, increasing the difficulty to impose Dirichlet boundary conditions. In this paper, Dirichlet boundary conditions are imposed by means of the Lagrange multipliers technique. A new functional has been added to the initial formulation of the problem that has the effect of stabilizing the problem. The technique here presented allows for a simple definition of the Lagrange multipliers field, that even allow us to directly condense the degrees of freedom of the Lagrange multipliers at element level.

Goal-oriented error estimates (GOEE) have become popular tools to quantify and control the local error in quantities of interest (QoI), which are often more pertinent than local errors in energy for design purposes (e.g. the mean stress or mean displacement in a particular area, the stress intensity factor for fracture problems). These GOEE are one of the key unsolved problems of advanced engineering applications in, for example, the aerospace industry. This work presents a simple recovery-based error estimation technique for QoIs whose main characteristic is the use of an enhanced version of the Superconvergent Patch Recovery (SPR) technique previously used for error estimation in the energy norm. This enhanced SPR technique is used to recover both the primal and dual solutions. It provides a nearly statically admissible stress field that results in accurate estimations of the local contributions to the discretisation error in the QoI and, therefore, in an accurate estimation of this magnitude. This approach leads to a technique with a reasonable computational cost that could easily be implemented into already available finite element codes, or as an independent postprocessing tool.KEY WORDS: goal-oriented, error estimation, recovery, quantities of interest, error control, mesh adaptivity arXiv:1209.3102v3 [math.NA]

The quality of current collection becomes a limiting factor when the aim is to increase the speed of the present railway systems. In this work an attempt is made to improve current collection quality optimising catenary geometry by means of a Genetic Algorithm. As dropper lengths and dropper spacing are thought to be highly influential parameters they were chosen as the optimisation variables. The results obtained show that a Genetic Algorithm can be used to optimise catenary geometry to improve current collection quality measured in terms of the standard deviation of the contact force. Furthermore, it is highlighted that apart from the usual pre-sag, other geometric parameters should also be taken into account when designing railway catenaries.