Método numérico para la evaluación holística del riesgo sísmico utilizando la teoría de conjuntos difusos

The fuzzy set theory offers a bridge between the symbolic and numerical processing, allowing managing qualitative concepts useful in the decision-making process related to the seismic risk management and, in general, to the disaster risk management. Its use in the seismic risk evaluation is necessary in the cases where the data required to apply a conventional method of assessing risk are not available or are insufficient. One possible solution, considered in this article, is to replace the missing information by expert opinions and to process the resulting qualitative variables and linguistic qualifications instead of numerical values. This process is based on the fuzzy set theory. In order to achieve an effective management, the risk must be defined as the potential physical, economic, social and environmental consequences which occur due to hazards in a given period of time. From this holistic perspective and using the fuzzy set theory, the proposed numerical method calculates a level of the physical risk and level of the aggravating conditions related to social fragility and to the lack of resilience, to determine a total risk level. In the article are included two examples of application of the proposed method and the obtained results are compared with those corresponding to a conventional method of holistic evaluation.     

Evaluación probabilista de la capacidad,fragilidad y daño sísmico de edificios de hormigón armado

Currently, many structures existing in seismic areas are highly vulnerable because they have been built without the use of seismic design codes or by using outdated codes. Often, methods for assessing the vulnerability of the structures do not take into account that their seismic behavior is dynamic and highly nonlinear and, moreover, that the structural characteristics and action have large uncertainties. This article aims to assess the vulnerability of structures taking into account that the mechanical properties of materials and the seismic action are random variables, by using advanced techniques based on the Monte Carlo method and on the nonlinear stochastic dynamics. The results obtained with these techniques are compared with those corresponding to a standard vulnerability assessment, based on deterministic models, in order to highlight the differences between both approaches. The main conclusion of this work is the need to address the vulnerability assessment problem from a probabilistic perspective which, combined with advanced nonlinear static and dynamic structural analysis techniques, provides a powerful tool giving information impossible to be captured by means of deterministic models. Finally, detailed results obtained for a building with waffle slabs, which is a structural typology widely used in Spain, are included and discussed.     

Evaluación sísmica de los edificios de mampostería típicos de Barcelona aplicando la metodología Risk-UE

In this work, a study about the vulnerability and seismic damage of unreinforced masonry buildings is carried out. Three models of buildings representatives of the Eixample district of Barcelona have been chosen. The seismic vulnerability is evaluated by means of the Risk-UE methodology. The seismic demand is described by elastic project spectrum, in this case, defined by the Eurocode 8. Fragility curves are obtained from a nonlinear analysis, considering the capacity spectra. Expected seismic damage is gotten with the damage probability matrices, which indicate the occurrence probability of a damage state for a seismic demand given. The analysis of the buildings has been performed by TreMuri program by means of a macroelements model, which represents of a whole masonry panel. The buildings, here, analyzed are real and detailed structural drawings and reports have been used to model them. The results shown a considerable vulnerability in this type of buildings, therefore, in spite of the seismic hazard the expected seismic risk is significant.     

Un modelo numérico para la simulación de disolución de precipitados en aleaciones de aluminio con endurecimiento utilizando redes neuronales

The motivation of this work is the modeling of the hardening precipitate and hardness evolutions of fully hardened heat treatable aluminium alloys during friction stir welding (FSW) and/or heat treatment processes. The model used is based on the kinetics of dissolution of precipitates model for hardened aluminium alloys given by Myhr and Grong (1991). This model contains a single independent variable, the time, and a single state variable, the volume fraction of hardening precipitates. A key point of this model is the identification of the effective activation energy for precipitates dissolution and the master curve defining the model, which was given by a look-up table. The goal of this work is to find an estimation of the effective activation energy and to model the dissolution rate of hardening precipitate in aluminium alloys using neural networks, avoiding the use of look-up tables. For this purpose a new and more convenient parametrization of the master curve is defined, a neural networks class is proposed, an objective functional is defined and a variational problem including independent parameters is solved. The novel methodology has been applied to different aluminium alloys, including the AA 6005A T6, AA 7449 T79 and AA 2198 T8. Experimental tests have been carried out for those aluminium alloys in order to get the HV1 hardness after isothermal heat treatments at different temperatures and for different treatment time durations. The effective activation energy for hardening precipitates dissolution and the master curve of the model have been obtained, using different network architectures, for the aluminium alloys considered in this work.     

Caracterización de la delaminación en materiales compuestos mediante la teoría de mezclas serie/paralelo

This paper presents a new procedure to deal with the delamination problem found in laminated composites, based in a continuum mechanics formulation. The procedure proposed obtains the composite constitutive performance with the Serial/Parallel mixing theory, developed by F. Rastellini. This theory characterizes composite materials by coupling the constitutive behaviour of the composite components, imposing an iso–strain relation among the components in the fibre (or parallel) direction and an iso-stress relation in the remaining directions (serial directions). The proposed procedure uses a damage formulation to characterize the constitutive behaviour of matrix component in order to obtain the stress-strain performance of this material.With these two formulations, the delamination phenomenon is characterized naturally by the numerical simulation, being unnecessary the definition of special elements or computationally expensive techniques like the definition of contact elements or mesh separation. Matrix failure, as a result of the stress state found in it, leads to a reduction of the stiffness and strength capacity of the composite in its serial directions, among them, the shear component. This stiffness reduction provides a composite performance equivalent to what is found in a delaminated material.To prove the ability of the formulation proposed to solve delamination problems, the End Notch Failure test is numerically simulated and the results obtained are compared with experimental ones. The agreement found in the results with both simulations, numerical and experimental, validate the proposed methodology to solve the delamination problem.     

Formulación de elementos finitos para vigas de sección abierta formadas por laminados compuestos incluyendo las deformaciones tangenciales por cortante y torsión

In this paper we derive the field of displacements and strains for thin-walled open composite beams with composite laminated material including in their kinematics flexural and torsional shear deformations effects. The equilibrium equations are defined through the variational formulation and show that is possible to formulate C_o finite elements taking into account the torsional shear deformation. Stress-strain relationships for the cross-section of thin-walled composite beams are obtained by extending first-order laminate (FSDT: first-order shear deformation) theory and using a «free stress resultant condition at the boundary». Three different one-dimensional finite elements with C_o continuity are formulated for the study of thin-walled open composite beams and they are labelled as BSW (beam with shear and warping). The influence of the integration strategy in the BSW elements is evaluated via the shear-locking phenomenon and the rate of convergence for displacements and rotations. The stiffness matrix integration is compared using exact and reduced integration methods. Examples of pure torsion and flexo-torsion in a cantilever composite beam are performed. Numerical results are compared to those reported by other authors.     

Modelo de un proceso de cristalización continua de un sorbete por medio de la metodología de momentos

Freezing is an important step in the manufacturing process of ice-cream and sorbet, since the operating conditions have a strong influence on the micro-structure, and consequently on the sensorial attributes of the final product. This steep of freezing is carried out by a scraped surface heat exchanger (SSHE) where the product quality is conditioned by process conditions as the evaporation temperature of a refrigerant fluid, the mix flow rate, the dasher speed and the cylinder pressure due to the air introduction. In order to study the relevance of a control system based on the influence of process variables on product quality, this paper presents a model for a continuous crystallization of a sorbet using the method of moments, which is validated by experimental data.The model created by this methodology has been able to represent the influence of the process conditions during the crystallization of the sorbet on the final product characteristics such as crystal size and the draw temperature in the outlet of the SSHE in absence of air. The model based in moments is studied as a reduced model of the population balance equation and includes the phenomena of heterogeneous nucleation and growth. This model developed represents minimal computational requirements and is highly adapted for optimization and/or process control tasks.     

Estudio de la estabilidad y dispersión del problema de propagación de ondas sísmicas en 2-D utilizando el método de diferencias finitas generalizadas

This paper shows the solution to the problem of seismic wave propagation in 2-D using generalized finite difference (GFD) explicit schemes. Regular and irregular meshes can be used with this method.As we are using an explicit method, it is necessary to obtain the stability condition by using the von Neumann analysis. We also obtained the star dispersion formulas for the phase velocities for the P and S waves, as well as the ones for the group velocities.As the control over the irregularity in the mesh is very important in the application of this method, we have defined an index of irregularity for the star (IIS) and another for the cloud (IIC), analyzing its relationship with the dispersion and time step used in the calculations.     

Propuesta y validación de un algoritmo Simulated annealing modificado para la solución de problemas de optimización

Over the last decades, heuristic optimization methods based on imitating natural, biological, social or cultural processes on a computational level have aroused the interest of the scientific community due to their ability to effectively explore multimodal and multidimensional solution spaces. Despite all the papers published in the international literature, most heuristic algorithms still have low precision and accuracy. In this context, a modified Simulated annealing algorithm (MSAA) is proposed and validated for solving optimization problems. Performance evaluation was performed on test functions (benchmark functions) with and without restrictions reported in the international literature and practical design problems in civil engineering. In all cases analyzed MSAA obtained equal or better results than those reported by other authors, illustrating the applicability of the proposed algorithm.     

Resolución numérica de las ecuaciones del movimiento de edificios de varias plantas con no linealidades severas

This paper presents a new algorithm for solving the equations of motion of multi-storey buildings that incorporate frictional energy dissipators as seismic protection. The behavior of the dissipators is represented by Coulomb dry friction models; they introduce severe nonlinearities in the dynamic behavior of the structure every time that the contact conditions (stick or slip) change in the dissipators. These nonlinearities complicate the resolution of the equations of motion as it usually is described by lumped masses models whose degrees of freedom are the displacements of the floors and, as the stick or slip conditions change, the degrees of freedom must be modified: for blocking conditions they are only the displacements of the storeys while under sliding conditions the displacements of the dissipators have to be also considered. In previous articles the accuracy of the proposed algorithm has been verified by comparison with experimental results; as well, the computational efficiency of the algorithm has been confirmed by comparing the required resources (in terms of computation time and of memory allocation) with those of other algorithms. The objectives of this paper are to describe in detail the numerical solution of the equations of motion and present representative examples confirming the ability of the algorithm to reproduce the dynamic behavior of buildings with friction dissipators and reporting preliminarily about the usefulness of such devices to reduce the oscillations of the structure to be protected.     

Integración temporal explícita con grandes pasos de tiempo de la ecuación de transmisión del calor

We present a novel fully explicit time integration method that remains stable for large time steps, requires neither matrix inversions nor solving a system of equations and therefore allows for nearly effort-less parallelization. In this first paper the proposed approach is applied to solve conduction heat transfer problems, showing that it is stable for any time step as is the case with implicit methods but with a much lower computation time.     

Evaluación numérica del efecto del espesor de la placa de contacto en la acción de palanca en conexión de acero tipo «T»

This paper presents a numerical study of «T-Stub» steel connections using FEM analyses. In such connections prying action phenomenon may take place. Prying action effect on the bolts has been studied before but the location of the prying action forces has always been simplified. The effect of the thickness of «T-Stub» flanges on contact areas between flanges and support base is investigated in this paper. A 3D finite element model is used and interface elements are employed for the investigation. Nonlinear FE analyses are undertaken on connection with different flange thickness and bolt preload with two bolts. Nonlinear gap elements are used as interfaces. Discussion and conclusions on contact areas and stresses, prying action distributions and resultant of loads on bolts in the «T-Stub» connections are presented.     

Aplicación de métodos computacionales en la evaluación de la respuesta aeroelástica de puentes soportados por cables

The possibilities of computational methods for assessing the response of cable supported bridges under wind action are considered in this work. The main objective is to study the possibilities of substituting wind tunnel campaigns by computer based analyses, particularly at the early design stage. The preliminary proposed design for a continuous cable-stayed bridge with two main spans of 650 m and a single box girder deck has been considered as a case study. The force coefficients of the deck cross-section have been computed and the unsteady response associated to vortex-shedding has been simulated using CFD commercial software. Furthermore, an in-house piece of software has been employed to obtain the response for flutter and buffeting phenomena adopting the hybrid approach; with that purpose the experimental flutter functions of a similar box girder deck were adopted. The computational results have been validated by comparison with similar experimental results published by other researchers. It has been verified that the set of adopted methods offers reliable results with moderate costs; therefore, the proposed approach is very suitable at the early design stage of long span bridges or at conceptual design works.     

Solución de la cinemática directa de la plataforma Gough-Stewart general usando un algoritmo híbrido de optimización

The direct kinematics problem for parallel robots can be stated as follows: given values of the joint variables, the corresponding Cartesian variable values, the pose of the end-effector, must be found. Most of the times the direct kinematics problem involves the solution of a system of non-linear equations. The most efficient methods to solve such kind of equations assume convexity in a cost function which minimum is the solution of the non-linear system. In consequence, the capacity of such methods depends on the knowledge about an starting point which neighboring region is convex, hence the method can find the global minimum. This article propose a method based on probabilistic learning about an adequate starting point for the Dogleg method which assumes local convexity of the function. The proposed method efficiently avoids the local minima, without need of human intervention or apriori knowledge, thus it shows a more robust performance than the simple Dogleg method or other gradient based methods. To demonstrate the performance of the proposed hybrid method, numerical experiments and the respective discussion are presented. The proposal can be extended to other structures of closed-kinematics chains, to the general solution of systems of non-linear equations, and to the minimization of non-linear functions.     

Optimización mixta de estructuras de transporte de energía: aplicación del algoritmo de recocido simulado

A general methodology to optimize the weight of power transmission structures is presented in this article. This methodology is based on the simulated annealing algorithm defined by Kirkpatrick in the early ‘80s. This algorithm consists of a stochastic approach that allows to explore and analyze solutions that do not improve the objective function in order to develop a better exploration of the design region and to obtain the global optimum. The proposed algorithm allows to consider the discrete behavior of the sectional variables for each element and the continuous behavior of the general geometry variables. Thus, an optimization methodology that can deal with a mixed optimization problem and includes both continuum and discrete design variables is developed. In addition, it does not require to study all the possible design combinations defined by discrete design variables. The algorithm proposed usually requires to develop a large number of simulations (structural analysis in this case) in practical applications. Thus, the authors have developed first order Taylor expansions and the first order sensitivity analysis involved in order to reduce the CPU time required. Exterior penalty functions have been also included to deal with the design constraints. Thus, the general methodology proposed allows to optimize real power transmission structures in acceptable CPU time.     

Determinación de la presión sonora radiada por pistones circulares y anillos no planos usando un método numérico simplificado

Although the study of the sound pressure radiation from membranes and plates is not new, current and future applications have produced a large body of recent research in the field. Several works have been published on the radiation from general plane surfaces and some particular geometries such as rectangular, circular, elliptic and annular. However, the case of sound radiation from non-planar axisymmetric rings that could be applied to the design of coaxial loudspeakers has not received much attention. In this article, a simplified numerical approach for determining the sound pressure radiated from symmetric non-planar pistons and rings is presented. The method can also include those cases having a radially-symmetric velocity distribution.     

Cálculo eficiente de las energías de formación de escalones dobles en materiales BCC

Motion of screw dislocations in BCC materials at low temperature is believed to be related to the formation of mobile kinks on the dislocation line. Therefore, the accurate prediction of kink nucleation energies is required to fully describe mobility of screw dislocations in these materials. Studies of fundamental dislocation processes at atomic length scale are numerically and computationally intensive problems. This work studies the calculation of zero-stress formation energies of kink-pair configurations for BCC crystals. Our model for stored energy associated to a dislocation line configuration is based on the theory of discrete dislocations of Ariza and Ortiz. Its value is computed efficiently using an algorithm developed on the NVIDIA Compute Unified Device Architecture (CUDA). Results confirm those obtained using atomistic potentials and first principles calculations, and those based on the continuum theory of dislocations.