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[EN] A novel algorithm called the Proper Generalized Decomposition (PGD) is widely used by the engineering community to compute the solution of high dimensional problems. However, it is well-known that the bottleneck of its practical implementation focuses on the computation of the so-called best rank-one approximation. Motivated by this fact, we are going to discuss some of the geometrical aspects of the best rank-one approximation procedure. More precisely, our main result is to construct explicitly a vector field over a low-dimensional vector space and to prove that we can identify its stationary points with the critical points of the best rank-one optimization problem. To obtain this result, we endow the set of tensors with fixed rank-one with an explicit geometric structure

[EN] A necessity in the design of a path planning algorithm is to account for the environment. If the movement of the mobile robot is through a dynamic environment, the algorithm needs to include the main constraint: real-time collision avoidance. This kind of problem has been studied by different researchers suggesting different techniques to solve the problem of how to design a trajectory of a mobile robot avoiding collisions with dynamic obstacles. One of these algorithms is the artificial potential field (APF), proposed by O. Khatib in 1986, where a set of an artificial potential field is generated to attract the mobile robot to the goal and to repel the obstacles. This is one of the best options to obtain the trajectory of a mobile robot in real-time (RT). However, the main disadvantage is the presence of deadlocks. The mobile robot can be trapped in one of the local minima. In 1988, J.F. Canny suggested an alternative solution using harmonic functions satisfying the Laplace partial differential equation. When this article appeared, it was nearly impossible to apply this algorithm to RT applications. Years later a novel technique called proper generalized decomposition (PGD) appeared to solve partial differential equations, including parameters, the main appeal being that the solution is obtained once in life, including all the possible parameters. Our previous work, published in 2018, was the first approach to study the possibility of applying the PGD to designing a path planning alternative to the algorithms that nowadays exist. The target of this work is to improve our first approach while including dynamic obstacles as extra parameters.

[EN] Rolling noise emitted by railway wheels is a problem that affects human health and limits the expansion of the railway network. It is caused by the wheel vibration due to the wheelrail contact force, and it is important in almost all the vehicle velocity range. The minimization of noise radiation associated with changes on the wheel web is discussed in this work, focusing on potential shape modifications in existing wheels in the form of a perforation distribution over the web. Such a post-manufacturing technique is a cost-effective solution that can be performed in a relatively short term. The implemented objective function is directly related to the overall radiated sound power, which is minimized using a genetic algorithmbased optimizer. In the acoustic model, radiation efficiencies are approximated to unity, the accuracy of this assumption being also studied in the work. The results reflect that an optimized distribution of perforations on the web of a railway wheel can reduce the total sound power level, by about 5 dB(A) and 2 dB(A) for curved and straight web, respectively. The mitigation of the radiated sound power is due to the fact that certain wheel vibration modes are modified and shifted to other frequencies where they are less excited. Finally, the relevance of the cross-sectional curvature of the web is explored by studying two different web geometries, suggesting that it can strongly influence the noise mitigation effects of the perforation pattern.

"This is the peer reviewed version of the following article: Navarro-Jiménez, José Manuel, Enrique Nadal, Manuel Tur, José Martínez-Casas, and Juan José Ródenas. 2020. "On the Use of Stabilization Techniques in the Cartesian Grid Finite Element Method Framework for Iterative Solvers." International Journal for Numerical Methods in Engineering 121 (13). Wiley: 3004-20. doi:10.1002/nme.6344, which has been published in final form at https://doi.org/10.1002/nme.6344. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.", [EN] Fictitious domain methods, like the Cartesian grid finite element method (cgFEM), are based on the use of unfitted meshes that must be intersected. This may yield to ill-conditioned systems of equations since the stiffness associated with a node could be small, thus poorly contributing to the energy of the problem. This issue complicates the use of iterative solvers for large problems. In this work, we present a new stabilization technique that, in the case of cgFEM, preserves the Cartesian structure of the mesh. The formulation consists in penalizing the free movement of those nodes by a smooth extension of the solution from the interior of the domain, through a postprocess of the solution via a displacement recovery technique. The numerical results show an improvement of the condition number and a decrease in the number of iterations of the iterative solver while preserving the problem accuracy.

[EN] Background and objectives: A constant voltage (DC voltage) is usually used in radiofrequency ablation (RFA) computer models to mimic the radiofrequency voltage. However, in some cases a low frequency sine wave voltage (AC voltage) may be used instead. Our objective was to assess the thermal impact of replacing DC voltage by low-frequency AC voltage in RFA computer modeling. Methods: A 2D model was used consisting of an ablation electrode placed perpendicular to the tissue fragment. The Finite Element method was used to solve a coupled electric-thermal problem. Quasi-static electrical approximation was implemented in two ways (both with equivalent electrical power): (1) by a constant voltage of 25 V in the ablation electrode (DC voltage), and (2) applying a sine waveform with peak amplitude of 25 root 2 V (AC voltage). The frequency of the sine signal (f(AC)) varied from 0.5 Hz to 50 Hz. Results: Sine wave thermal oscillations (at twice the f(AC) frequency) were observed in the case of AC voltage, in addition to the temperature obtained by DC voltage. The amplitude of the oscillations: (1) increased with temperature, remaining more or less constant after 30 s; (2) was of up to +/- 3 degrees C for very low f(AC) values (0.5 Hz); and (3) was reduced at higher f(AC) values and with distance from the electrode (almost negligible for distances > 5 mm). The evolution of maximum lesion depth and width were almost identical with both DC and AC. Conclusions: Although reducing f(AC) reduces the computation time, thermal oscillations appear at points near the electrode, which suggests that a minimum value of f(AC) should be used. Replacing DC voltage by low-frequency AC voltage does not appear to have an impact on the lesion depth. (C) 2020 Elsevier B.V. All rights reserved.

[EN] In the framework of the European Higher Education area, university teaching has focused in recent years on adapting Master's and Bachelor's degrees to the demands of the professional sector. To do this, the training and development of the generic and specific skills recommended for the incorporation of students into the job market have been priority objectives in the approach to study plans. However, there is no consensus on the methodologies for evaluating these skills, especially regarding how to separate the acquisition and / or improvement of the skills from the specific knowledge and skills of the subjects. Due to the lack of time, teaching staff seek methodologies that do not involve additional tests for the evaluation of competences, which would increase the number of tests to a non-realistic number with the corresponding assessment duties for the professors. In order to make a contribution in this regard, this work presents an approach for evaluating the ability to handle specific software applied to problems in the area of mechanical engineering. This work proposes a methodology for acquiring the required skills and an evaluation system to grade the degree of expertise in the manipulation of the software. In our University, this skill is called the Specific Instrumental Skill, which measures the ability of the students for using the tools in engineering, like, in this case, the use of software to run structural numerical simulations as ANSYS®. The methodology proposed is based on an a priori training. This training is based on 2 hours weekly sessions where the students should solve, in groups of 2 or 3 students, a set of labs with the help of the professor. The students do not need to deliver any report to the professor since the objective of the sessions is the training of the students. Therefore, the pressure over the student is low and the professor avoid to mark a high number of student¿s reports, allowing him to focus only on the learning process

[EN] This article presents a Topology Optimization (TO) method developed for maximizing the acoustic attenuation of a perforated dissipative muffler in the targeted frequency range by optimally distributing the absorbent material within the chamber. The Finite Element Method (FEM) is applied to the wave equation formulated in terms of acoustic pressure (chamber) and velocity potential (central duct, due to the existence of thermal gradients and mean flow) in order to evaluate the acoustic performance of the noise control device in terms of Transmission Loss (TL). Sound propagation through the chamber fibrous material is modelled considering complex equivalent acoustic properties, which vary spatially not only as a function of temperature, but also as a function of the lling density, since non-homogeneous density distributions are considered. The acoustic coupling at the perforated duct is performed by introducing a coordinate-dependent equivalent impedance. The objective function to maximize is expressed as the mean TL in the targeted frequency range. The sensitivities of this function with respect to the filling density of each element in the chamber are evaluated following the standard adjoint method. The Method of Moving Asymptotes (MMA) is used to update the design variables at each iteration of the TO process, keeping the weight of absorbent material equal or lower than a given value, while maximizing attenuation. Additionally, several particular designs inferred from the topology optimization results are analyzed. For example, the sizing optimization of a number of rings is carried out simultaneously with the aforementioned TO process (density layout). A reactive chamber is added in order to evaluate the TL of a hybrid muffler and its shape optimization is also carried out simultaneously with the aforementioned TO. Results show an increase in the muffler's mean TL at target frequencies, for all cases under study, while the amount of absorbent material used is

[EN] This article presents a study of the backward bending mode of a simply supported rotating Rayleigh beam with internal damping. The study analyses the natural frequency behaviour of the backward mode according to the internal viscous damping ratio, the slenderness of the beam and its spin speed. To date, the behaviour of the natural frequency of the backward mode is known to be a monotonically decreasing function with spin speed due to gyroscopic effects. In this article, however, it is shown that this behaviour of the natural frequency may not hold for certain damping and slenderness conditions, and reaches a minimum value (concave function) from which it begins to increase. Accordingly, the analytical expression of the spin speed for which the natural frequency of the backward mode attains the minimum value has been obtained. In addition, the internal damping ratio and slenderness intervals associated with such behaviour have been also provided.

"This is the peer reviewed version of the following article: Huerta, Antonio, Enrique Nadal, and Francisco Chinesta. 2018. Proper Generalized Decomposition Solutions within a Domain Decomposition Strategy. International Journal for Numerical Methods in Engineering 113 (13). Wiley: 1972 94. doi:10.1002/nme.5729, which has been published in final form at https://doi.org/10.1002/nme.5729. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.", [EN] Domain decomposition strategies and proper generalized decomposition are efficiently combined to obtain a fast evaluation of the solution approximation in parameterized elliptic problems with complex geometries. The classical difficulties associated to the combination of layered domains with arbitrarily oriented midsurfaces, which may require in-plane-out-of-plane techniques, are now dismissed. More generally, solutions on large domains can now be confronted within a domain decomposition approach. This is done with a reduced cost in the offline phase because the proper generalized decomposition gives an explicit description of the solution in each subdomain in terms of the solution at the interface. Thus, the evaluation of the approximation in each subdomain is a simple function evaluation given the interface values (and the other problem parameters). The interface solution can be characterized by any a priori user-defined approximation. Here, for illustration purposes, hierarchical polynomials are used. The repetitiveness of the subdomains is exploited to reduce drastically the offline computational effort. The online phase requires solving a nonlinear problem to determine all the interface solutions. However, this problem only has degrees of freedom on the interfaces and the Jacobian matrix is explicitly determined. Obviously, other parameters characterizing the solution (material constants, external loads, and geometry) can also be incorporated in the explicit description of the solution.

[EN] In this paper, a method to in vivo estimate the relative stifness between a hepatic lesion and the liver parenchyma is presented. Tis method is based on the fnite element simulation of the deformation that the liver undergoes during the breathing process. Boundary conditions are obtained through a registration algorithm known as Coherent Point Drif (CPD), which compares the liver form in two phases of the breathing process. Finally, the relative stifness of the tumour with respect to the liver parenchyma is calculated by means of a Genetic Algorithm, which does a blind search of this parameter. Te relative stifness together with the clinical information of the patient can be used to establish the type of hepatic lesion. Te developed methodology was frst applied to a test case, i.e., to a control case where the parameters were known, in order to verify its validity. Afer that, the method was applied to two real cases and low errors were obtained.

[EN] Even if the diffusion equation has been widely used in physics and engineering, and its physical content is well understood, some variants of it escape fully physical understanding. In particular, anormal diffusion appears in the so-called fractional diffusion equation, whose main particularity is its non-local behavior, whose physical interpretation represents the main part of the present work.

The use of resistant, rigid, low-weight materials with good both acoustic and thermal properties is very interesting in today’s industry. Among these materials, one can find aluminium foams, whose mechanical behaviour is necessary for their application. In order to obtain the geometry of an aluminium foam, several techniques can be applied, and all of them are based in the fact that information is initially obtained by a Computed Axial Tomography (CAT). One of these techniques, known as segmentation, involves a CAD being generated from an image in order to build the Finite Element (FE) model. Another option is to use techniques such as CutFEM or cgFEM, in which a certain amount of pixels, which define the properties of the material, are embedded in each element. Among the existing methods for evaluating the material properties matrix, this study proposes the use of homogenization techniques, sped up by the use of machine learning techniques. This method has been applied to real problems obtaining a high speed up, conserving precision., En la industria actual, el uso de materiales resistentes, rígidos, de bajo peso y con buenas propiedades tanto acústicas como térmicas es de gran interés. Entre estos materiales encontramos las espumas de aluminio. Para su uso, es necesario conocer su comportamiento estructural. Para la obtención de la geometría de una espuma de aluminio se pueden plantear diversas técnicas, todas ellas basadas en que la información inicial proviene de una imagen obtenida mediante una Tomografía Axial Computarizada (TAC). Una posible metodología, conocida comúnmente como segmentación, consiste en generar un CAD a partir de la imagen y de ahí el modelo de Elementos Finitos (EF). Otra opción es usar técnicas como el CellFEM o el cgFEM, donde cierta cantidad de píxeles, que definen las propiedades del material, son embebidos en cada elemento. De entre los diversos métodos que existen para evaluar la matriz de propiedades del material, en este trabajo se propone el uso de técnicas de homogeneización aceleradas mediante técnicas de machine learning. Dicha técnica se ha aplicado a problemas reales obteniendo un elevado speed up sin sacrificar la precisión.

[EN] The acoustic modelling of automotive exhaust devices, such as catalytic converters (CC) and diesel particulate filters (DPF), usually requires the use of multidimensional analytical and numerical techniques. The presence of higher order modes and three-dimensional waves in the expansion and contraction subdomains, as well as sound propagation within the monolith capillary ducts, can be considered through the finite element method (FEM), although this approach is traditionally thought to be very time consuming. With a view to overcome this limitation and to reduce the computational effort of the FEM, alternative modelling techniques are presented in the current work to speed up transmission loss calculations in exhaust devices incorporating monoliths. These approaches are based on the point collocation technique and the mode matching method. As shown in earlier studies, the sound attenuation of an exhaust device incorporating a monolith can be properly predicted if the latter is replaced by a plane wave four-pole transfer matrix providing a relationship between the acoustic fields at both sides of the monolithic region. Therefore, this work combines the presence of multidimensional higher order modes in the expansion and contraction regions with one-dimensional wave propagation within the capillary ducts of the central monolith. The point collocation technique and the mode matching method are applied to the compatibility conditions of the acoustic fields at all the subdomain interfaces to couple the solutions of the wave equation in the corresponding exhaust device subcomponents. For the particular case of rigid circular ducts, Bessel functions are considered as transversal pressure modes. The computational efficiency and accuracy of the results associated with the two analytical modelling techniques presented here are assessed, including the effect of the number of modes and collocation points, as well as their location. All the analytical approaches proposed i

[EN] The use of resistant, rigid, low-weight materials with good both acoustic and thermal properties is very interesting intoday¿s industry. Among these materials, one can find aluminium foams, whose mechanical behaviour is necessaryfor their application. In order to obtain the geometry of an aluminium foam, several techniques can be applied, and allof them are based in the fact that information is initially obtained by a Computed Axial Tomography (CAT). One ofthese techniques, known as segmentation, involves a CAD being generated from an image in order to build the FiniteElement (FE) model. Another option is to use techniques such as CutFEM or cgFEM, in which a certain amount ofpixels, which define the properties of the material, are embedded in each element. Among the existing methods forevaluating the material properties matrix, this study proposes the use of homogenization techniques, sped up by the useof machine learning techniques. This method has been applied to real problems obtaining a high speed up, conservingprecision., [ES] En la industria actual, el uso de materiales resistentes, rígidos, de bajo peso y con buenas propiedades tanto acústicas como térmicas es de gran interés. Entre estos materiales encontramos las espumas de aluminio. Para su uso, es necesario conocer su comportamiento estructural. Para la obtención de la geometría de una espuma de aluminio se pueden plantear diversas técnicas, todas ellas basadas en que la información inicial proviene de una imagen obtenida mediante una Tomografía Axial Computarizada (TAC). Una posible metodología, conocida comúnmente como segmentación, consiste en generar un CAD a partir de la imagen y de ahí el modelo de Elementos Finitos (EF). Otra opción es usar técnicas como el CellFEM o el cgFEM, donde cierta cantidad de píxeles, que definen las propiedades del material, son embebidos en cada elemento. De entre los diversos métodos que existen para evaluar la matriz de propiedades del material, en este trabajo se propone el uso de técnicas de homogeneización aceleradas mediante técnicas de machine learning. Dicha técnica se ha aplicado a problemas reales obteniendo un elevado speed up sin sacrificar la precisión.