José París

Block aggregation of stress constraints in topology optimization of structures

Structural topology optimization problems have been traditionally stated and solved by means of maximum stiffness formulations. On the other hand, some effort has been devoted to stating and solving this kind of problems by means of minimum weight formulations with stress (and/or displacement) constraints. It seems clear that the latter approach is closer to the engineering point of view, but it also leads to more complicated optimization problems, since a large number of highly non-linear (local) constraints must be taken into account to limit the maximum stress (and/or displacement) at the element level. In this paper, we explore the feasibility of defining a so-called global constraint, which basic aim is to limit the maximum stress (and/or displacement) simultaneously within all the structure by means of one single inequality. Should this global constraint perform adequately, the complexity of the underlying mathematical programming problem would be drastically reduced. However, a certain weakening of the feasibility conditions is expected to occur when a large number of local constraints are lumped into one single inequality. With the aim of mitigating this undesirable collateral effect, we group the elements into blocks. Then, the local constraints corresponding to all the elements within each block can be combined to produce a single aggregated constraint per block. Finally, we compare the performance of these three approaches (local, global and block aggregated constraints) by solving several topology optimization problems.

Improvements in the treatment of stress constraints in structural topology optimization problems

Topology optimization of continuum structures is a relatively new branch of the structural optimization field. Since the basic principles were first proposed by Bendsoe and Kikuchi in 1988, most of the work has been dedicated to the so-called maximum stiffness (or minimum compliance) formulations. However, since a few years different approaches have been proposed in terms of minimum weight with stress (and/or displacement) constraints. These formulations give rise to more complex mathematical programming problems, since a large number of highly non-linear (local) constraints must be taken into account. In an attempt to reduce the computational requirements, in this paper, we propose different alternatives to consider stress constraints and some ideas about the numerical implementation of these algorithms. Finally, we present some application examples.

Improvement of the computer methods for grounding analysis in layered soils by using high-efficient convergence acceleration techniques

In the last years the authors have developed a numerical formulation based on the Boundary Element Method for the analysis of grounding systems embedded in uniform soils. This approach has been implemented in a CAD system that currently allows to analyze real grounding grids in real-time in personal computers. The extension of this approach for the grounding analysis in layered soils is straightforward by application of the method of images. However in some practical cases the resulting series have a poor rate of convergence; consequently, the analysis of real earthing grids in multilayer soils requires an out of range computational cost. In this paper we present a CAD system based on this BEM numerical formulation for grounding analysis in multilayer soils that include an efficient technique based on the Aitken acceleration in order to improve the rate of convergence of the involved series expansions. Finally, we show some examples by using the geometry of real grounding systems.

Topology optimization of aeronautical structures with stress constraints: general methodology and applications

Structural optimization is a well known and frequently used discipline in aerospace applications since most of the optimization problems were stated in order to solve aeronautic structures. Since first works about structural topology optimization were published, different formulations have been proposed to obtain the most adequate design. Topology optimization of structures is the most recent branch of structural optimization. The first works about this topic were proposed by Bendsoe and Kikuchi in 1988 (Bendsoe, M. P. and Kikuchi, N. Generating optimal topologies in structural design using a homogenization method. Comput. Methods Appl. Mech. Engng., 1988, 71, 197–224). In this field of structural optimum design, the aim is to obtain the optimal material distribution of a given amount of material in a predefined domain. The most usual formulation tries to maximize the stiffness of the structure by using a given amount of material. In this paper, we present a minimum weight formulation with stress constraints that allows to avoid most of the drawbacks associated to maximum stiffness approaches. The proposed formulation is applied to the optimization of aeronautical structures. Some examples have been studied in order to validate the formulation proposed.

Topology optimization of structures with stress constraints: Aeronautical applications

Topology optimization of structures is nowadays the most active and widely studied branch in structural optimization. This paper develops a minimum weight formulation for the topology optimization of continuum structures. This approach also includes stress constraints and addresses important topics like the efficient treatment of a large number of stress constraints, the approach of discrete solutions by using continuum design variables and the computational cost. The proposed formulation means an alternative to maximum stiffness formulations and offers additional advantages. The minimum weight formulation proposed is based on the minimization of the weight of the structure. In addition, stress constraints are included in order to guarantee the feasibility of the final solution obtained. The objective function proposed has been designed to force the convergence to a discrete solution in the final stages of the optimization process. Thus, near discrete solutions are obtained by using continuum design variables. The robustness and reliability of the proposed formulation are verified by solving application examples related to aeronautical industry.

Grounding Analysis in Heterogeneous Soil Models: Application to Underground Substations

Most of the research and development work done until now in earthing analysis is devoted to cases where the soil can be modelled in terms of an homogeneous and isotropic semi-infinite continuous medium, being the soil resistivity an order of magnitude higher than the resistivity of the electrode itself. Furthermore, all formulations of this classical (single-layer) type can be quite easily extended for solving more complex cases in which the soil is stratified in two or more layers of different resistivities. Assuming that the soil is regularized before installing the earthing grid and that the surface is leveled right after (prior to the equipment being assembled and brought into service) this approach is suitable for computing the equivalent resistance and the step and touch voltage in most large electrical over ground facilities. This important category includes all step up and step-down transmission substations, as well as a number of distribution substations indeed. Nevertheless, the current trend in electric power Engineering moves in another direction, due to the growing preference for smaller underground substations as a general rule. This pushes the need for developing new earthing analysis techniques that could be applied to facilities of this kind. In an attempt to do so, we present a mathematical model for earthing analysis in soils with enbedded finite regions of different resistivities. We also present the Boundary Element formulation that we propose for the numerical solution of the resulting equations, which implemention is being considered at present. Finally, we present some preliminary results of the earthing analysis of an underground substation. These results have been obtained by means of an approximated technique which details will be given in forthcoming publications.

Numerical Simulation of Multilayer Grounding Grids in a User-friendly Open-source CAD Interface

In this paper we present TOTBEM: a freeware application for the in-house computer aided design and analysis of grounding grids. The actual version of the software is available for testing purposes (and also use) at no cost and can be run on any basic personal computer (as of 2011) with no special requirements. The distribution kit consists in a single ISO bootable image file that can be freely downloaded from the Internet and copied into a DVD or a USB flash memory drive. The application runs on the Ubuntu 10.04 (Lucid Lynx) LTS release of Linux and can be easily started by just booting the system from the live DVD/USB that contains the downloaded file. This operation does not modify the native operative system nor installs any software in the computer, but the application is still fully operational while the live DVD/USB is taking control. The pre- and post-processing engines of the application have been built on top of the open source SALOME platform toolkit. On the other hand, the analysis part of the code is based on the Boundary Element Method (BEM). The implemented BEM formulation (that has been presented by the authors in previous publications) is suitable for computing the equivalent resistance and the step and touch voltage in most large electrical over ground substations with a grounding grid embedded in a single- or multi-layer stratified soil.

Efficiency of bio- and socio-inspired optimization algorithms for axial turbomachinery design

Abstract Turbomachinery design is a complex problem which requires a lot of experience. The procedure may be speed up by the development of new numerical tools and optimization techniques. The latter rely on the parameterization of the geometry, a model to assess the performance of a given geometry and the definition of an objective functions and constraints to compare solutions. In order to improve the reference machine performance, two formulations including the off-design have been developed. The first one is the maximization of the total nominal efficiency. The second one consists to maximize the operation area under the efficiency curve. In this paper five optimization methods have been assessed for axial pump design: Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Cuckoo Search (CS), Teaching Learning Based Optimization (TLBO) and Sequential Linear Programming (SLP). Four non-intrusive methods and the latter intrusive. Given an identical design point and set of constraints, each method proposed an optimized geometry. Their computing time, the optimized geometry and its performances (flow rate, head (H), efficiency (η), net pressure suction head (NPSH) and power) are compared. Although all methods would converge to similar results and geometry, it is not the case when increasing the range and number of constraints. The discrepancy in geometries and the variety of results are presented and discussed. The computational fluid dynamics (CFD) is used to validate the reference and optimized machines performances in two main formulations. The most adapted approach is compared with some existing approaches in literature.

Numerical Modeling of Grounding Systems for Aboveground and Underground Substations

In this paper, we present a numerical model based on the boundary element method that allows to analyze the grounding systems (GSs) of aboveground and underground substations under different locations and considerations. The proposed formulation allows to consider most of the specific properties and conditions of this kind of substations, i.e., complex geometry, different material properties, and different grounding grid configurations, and to study phenomena like transferred potentials by earthing electrodes. Finally, GSs of real substations have been analyzed as application examples.