Study of a topology optimization tool associating a hybrid algorithm with a Voronoï-based formalism for the design of electromagnetic devices (original) (raw)
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Mathematics and Computers in Simulation, 2013
Topology optimization methods are aimed to produce optimal design. These tools implement optimization algorithms that modify the distribution of some materials within a predefined design space without a priori ideas regarding the topology or the geometry of the best solution. In this paper, we study a specific tool that combines a genetic algorithm, a material distribution formalism based on Voronoi cells and a commercial FEM evaluation tool. In particular, this paper shows, through a simple but representative case study, that it is possible to improve the performance of the topology optimization tool during the local search phase, i.e. the geometrical and dimensional optimization phase for which the topology optimization methods are originally not well-suited.
Topology Optimization for Electromagnetics: A Survey
IEEE Access
The development of technologies for the additive manufacturing, in particular of metallic materials, is offering the possibility of producing parts with complex geometries. This opens up to the possibility of using topological optimization methods for the design of electromagnetic devices. Hence, a wide variety of approaches, originally developed for solid mechanics, have recently become attractive also in the field of electromagnetics. The general distinction between gradient-based and gradient-free methods drives the structure of the paper, with the latter becoming particularly attractive in the last years due to the concepts of artificial neural networks. The aim of this paper is twofold. On one hand, the paper aims at summarizing and describing the state-of-art on topology optimization techniques while on the other it aims at showing how the latter methodologies developed in non-electromagnetic framework (e.g., solid mechanics field) can be applied for the optimization of electromagnetic devices. Discussions and comparisons are both supported by theoretical aspects and numerical results.
A survey of topology optimization in electromagnetics: considerations and current trends
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Shape and Topological Optimization for Electromagnetism Problems
2010
This paper presents a topological shape optimization problem technique for electromagnetic problems using the topological sensitivity analysis and topological derivative. The objective function that represents the design objective is expressed in terms of magnetic field. The adjoint method is used to optimize the distribution of magnetics fields. Some numerical results that demonstrated the validity of the proposed approach are presented.
Topology optimization of electromagnetic systems considering magnetization direction
IEEE Transactions on Magnetics, 2005
The topology optimization of electromagnetic (EM) systems considering the effect of the magnetization direction in the magnet is investigated using the finite element method. The density method is used for topology optimization and continuum design sensitivity analysis is used for the sensitivity of EM systems. Also ANSYS is used for analysis. The force of a magnet is divided into two components of and direction in the rectangular coordinates. And the topology optimization of a c-core and a brushless dc motor are obtained.
Recent Advances in Optimization and its Applications in Engineering, 2010
We consider an evolutionary method applied to a topology optimization problem. We compare two material distribution formalisms (static vs. Voronoibased dynamic), and two sets of reproduction mechanisms (standard vs. topologyadapted). We test those four variants on both theoretical and practical test cases, to show that the Voronoi-based formalism combined with adapted reproduction mechanisms performs better and is less sensitive to its parameters.
IEEE Transactions on Magnetics, 2000
Topology optimization methods suffer from a lack of convexity for the design of electromagnetic devices. Local minimizers indeed prevent deterministic methods from attaining the optimal solution. The optimization result may then vary according to the initial conditions. This paper proposes a convexity-oriented method focusing on the maximization of the forces exerted on ferromagnetic parts in electromagnetic actuators. The method is based on a simultaneous optimization of two topologies by a gradient-based algorithm, the forces being computed by combining their magnetic fields within the Maxwell stress tensor. During the optimization, the two topologies converge towards a unique design using constraints whose shape is progressively modified. The method benefits from a fast convergence and produces consistent and efficient results, which is highlighted on a test problem. The method is eventually applied to a realistic problem related to the design of a switched reluctance actuator.
Topology gradient optimization in 2-D and 3-D for the design of microwave components
Microwave and Optical Technology Letters, 2008
A numerical model defined by a finite element method coupled with a topology gradient method is used for optimizing the shape of microwave components with respect to electrical specifications. The approach, which consists in minimizing a cost function with respect to the physical property of individual topological elements, which define the shape of the component, is first described. Regarding the given electrical specifications, the technique is applied for optimizing, respectively, in 2D, the distribution of metal upon the surface of a planar component and, in 3D, the distribution of dielectric material within a waveguide component.
IEEE Transactions on Magnetics, 2000
In order to perform parameter or shape optimizations, an initial topology is required which affects the final solution. This constraint is released in topology optimization methods. They are based on a splitting of the design space into cells, in which they attempt to distribute optimally predefined materials. In topology optimization, a lack of convexity has already been observed by several authors. Final results are often affected by the initial material distribution. This paper aims at improving the convexity in static electromagnetic problems where both ferromagnetic materials and coils are distributed in the design domain. The paper focuses on the mapping function used to derive the permeability of a cell from its composition. In addition to convexity issues, sensitivity concerns arise when the relative permeability of iron is large. Several methods based on a sensitivity-oriented mapping are suggested in the literature, such as the solid isotropic material with penalization (SIMP) method or the homogenization theory method (HDM). This paper shows that a geometric mapping is effective in combination with the convexity-oriented mapping to tackle both problems. This paper suggests computing the cell permeabilities by two successive mapping functions and illustrates the effectiveness of this method on the design of a switched reluctant actuator.
International Journal of Computer Mathematics, 2009
In this paper, we present a new stochastic hybrid technique for constrained global optimization. It is a combination of the electromagnetism-like (EM) mechanism with a random local search, which is a derivative-free procedure with high ability of producing a descent direction. Since the original EM algorithm is specifically designed for solving bound constrained problems, the approach herein adopted for handling the inequality constraints of the problem relies on selective conditions that impose a sufficient reduction either in the constraints violation or in the objective function value, when comparing two points at a time. The hybrid EM method is tested on a set of benchmark engineering design problems and the numerical results demonstrate the effectiveness of the proposed approach. A comparison with results from other stochastic methods is also included.