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In this paper, a 2D isogeometric formulation of the material distribution for structural topology optimization considering minimum weight and local stress constraints using the overweight approach is proposed. The aim of this isogeometric formulation is to provide solutions with high spatial definition using a lower number of design variables in comparison with the formulations previously developed to define the material layout. Despite of this, an important number of local stress constraints has to be considered in the solution of the problem. For this purpose, an Overweight Constraint is used to consider all of them. The structural analysis is performed by means of the Isogeometric Analysis (IGA) and the distribution of material is modeled by means of quadratic B-splines. Moreover, the optimization is addressed by means of the Sequential Linear Programming algorithm (SLP) that is driven by the information provided by a full first-order sensitivity analysis extension of the IGA formulation. Finally, the proposed formulation is tested by means of some benchmark problems, and the results show that the isogeometric formulation provides solutions with high spatial definition. A comparison with a Finite Element Method (FEM) topology optimization formulation is included.

Topology structural optimization problems have been usually stated in terms of a maximum stiffness (minimum compliance) approach. The objective of this type of approach is to distribute a given amount of material in a certain domain, so that the stiffness of the resulting structure is maximized (that is, the compliance, or energy of deformation, is minimized) for a given load case. Thus, the material mass is restricted to a predefined percentage of the maximum possible mass, while no stress or displacement constraints are taken into account. This paper presents a different strategy to deal with topology optimization: a minimum weight with stress constraints Finite Element formulation for the topology optimization of continuum structures. We propose two different approaches in order to take into account stress constraints in the optimization formulation. The local approach of the stress constraints imposes stress constraints at predefined points of the domain ( i.e. at the central point of each element). On the contrary, the global approach only imposes one global constraint that gathers the effect of all the local constraints by means of a certain so-called aggregation function. Finally, some application examples are solved with both formulations in order to compare the obtained solutions.

This paper presents a computer software for the optimization of power transmission structures. The software employs a modified version of the Simulated Annealing algorithm that has been proven effective in large engineering problems. The target structures are three-dimensional steel trusses to be used as supporting towers of electrical lines. A mixed formulation merging continuous and discrete design variables is proposed for optimizing the size and shape of the trusses, including a first-order sensitivity analysis that reduces the computational cost. The implementation can be adapted to any kind of transmission tower and allows to quickly create a model to be analyzed and optimized in a few sequential steps. Despite its simplicity of use, the tools provided by the proposed framework allow to perform a full analysis of the design and provide an entire comprehension of its structural behavior. The software also includes a post-process and visualization tool set in a user-friendly graphical interface.

The design of safe grounding systems in electrical installations is essential to assure the protection of the equipment, the power supply continuity and the security of the persons. In order to achieve these goals, it is necessary to compute the equivalent electrical resistance of the system and the potential distribution on the earth surface when a fault condition occurs. In the last years the authors have developed a numerical formulation based on the BEM for the analysis of grounding systems embedded in uniform and layered soils. As it is known, in practical cases the underlying series have a poor rate of convergence and the use of multilayer soils requires an out of range computational cost. In this paper we present an efficient technique based on the Aitken δ2-process in order to improve the rate of convergence of the involved series expansions.

Structural optimization has been usually applied to singular projects (e.g. a dam) and/or to common designs largely repeated (e.g. automotive components), and high voltage transmission towers can be included in both groups since they are expensive and a large number of them is required. In this paper, the authors propose a general formulation for obtaining the structural optimum design of latticed high voltage towers. The formulation is devoted to obtaining the most common objective in engineering (minimum cost) considering the limitations imposed in actual norms for this kind of structure. According to this idea, real applications are studied and modeled under real conditions (e.g. loads, constraints, building process). Constructive aspects like the specific geometry, the structural elements or the building process are specifically considered. The optimization model proposed also deals with continuum design variables (global geometry variables) and discrete design variables (area, inertia and/or cross section dimensions, for example) both together. The use of both types of design variables is crucial for defining a realistic model that can be used in practical applications in engineering. The optimum design formulation proposed is general and can be easily applied to other different types of 3D latticed structures. Finally, a real application example of a high voltage tower under real conditions and requirements is analyzed.

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.

In this paper we present a numerical study of the hyperbolic model for convection-diffusion transport problems that has been recently proposed by the authors [16]. This model avoids the infinite speed paradox, inherent to the standard parabolic model and introduces a new parameter τ called relaxation time. This parameter plays the role of an “inertia” for the movement of the pollutant. The analysis presented herein is twofold: first, we perform an accurate study of the 1D steady-state equations and its numerical solution. We compare the solution of the hyperbolic model with that of the parabolic model and we analyze the influence of the relaxation time on the solution. On the other hand, we explore the possibilities of the proposed model for real-world applications. With this aim we solve an example concerning the evolution of a pollutant being spilled in the harbor of A Coruña (northwest of Spain, EU).

On a regular basis, engineering analysis requires stating and solving systems of partial differential equations (PDEs). The most powerful and widely extended techniques for solving PDEs are the so-called Weighted Residuals Methods. To this group belong, among others, the Finite ElementMethod (FEM), the Boundary Element Method (BEM), the Finite Volume Method (FVM) and the Mesh-Free Method (MFM), as well as the many different formulations included in each of these categories. The new IsogeometricAnalysis (IGA) methodswere proposed by Hughes et al. in 2005, and it is our belief that they really deserve special attention. The key idea of IGA is to use a previously generated CAD model for discretizing both the geometry and the solution to the problem being analyzed. In return for some minor drawbacks, IGA offers a number of major advantages that make the technique specially attractive and promising in comparison with standard FEM, BEM, FVM and MFM formulations. In this presentation we will state a general formulation for the sensitivity analysis of Weighted Residual Methods, both for linear and non-linear problems with constant or varying geometry. The effects due to variation of geometry are addressed by defining a generic procedure for integration in manifolds on the basis of the metric tensor concept. The proposed approach leads to compact and relatively simple expressions to obtain directional derivatives of arbitrarily high order. The resulting scheme can be easily applied to IGA formulations, its implementation being quite a straightforward task. Finally, one application example is presented.

Topology optimization of continuum structures is a recent field in structural optimization. However, an increasing research activity in this area has been developed since the statement of the very first formulations. These formulations try to obtain the most adequate material distribution that satisfies the imposed structural limitations. The existence or absence of material in each part of the domain is usually defined by using a continuum variable (the relative density) in order to avoid dealing with a discrete optimization problem. This continuum approach of the material properties present important advantages since conventional optimization algorithms can be used. However, numerical models must be considered in order to develop the structural analysis for intermediate values of the relative densities. In this paper, we present some improvements in a minimum weight approach of the structural topology optimization problem. The main goal of this paper is to present an improved formulation that tries to reach binary 0-1 material distributions by using a continuum approach of the design variables. Furthermore, a perimeter penalization is included in the objective function to simplify the solutions obtained. In addition, some computational aspects are considered in order to reduce the computational effort. Finally, we compare the solutions obtained by using these formulations in two application examples.

Topology optimization of continuum structures is a relatively new branch of the structural optimization field. Since the basic principles were first proposed by Bendsøe and Kikuchi in 1988, most of the work has been devoted to the so-called maximum stiffness (or minimum compliance) formulations. However, for the past few years a growing effort is being invested in the possibility of stating and solving these kinds of problems in terms of minimum weight with stress (and/or displacement) constraints formulations because some major drawbacks of the maximum stiffness statements can be avoided. Unfortunately, this also gives rise to more complex mathematical programming problems, since a large number of highly non-linear (local) constraints at the element level must be taken into account. In an attempt to reduce the computational requirements of these problems, the use of a single so-called global constraint has been proposed. In this paper,we create a suitable class of global type constraints by grouping the elements into blocks. Then, the local constraints corresponding to all the elements within each block are combined to produce a single aggregated constraint that limits the maximum stress within all the elements in the block. Thus, the number of constraints can be drastically reduced. Finally, we compare the results obtained by our block aggregation technique with the usual global constraint formulation in several application examples. 1 Introduction Topology optimization problems have been usually stated as maximum stiffness (minimum compliance) continuum formulations. However, different approaches