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ABSTRACT: This paper deals with a new topology optimization method based on the level set method. In the proposed method, the discretized
signed distance function, a kind of level set function, is used as the design variables, and these are then updated using
their sensitivities. The signed distance characteristic of the design variables are maintained by performing a re-initialization
at every update during the iterated optimization procedure. In this paper, a minimum mean compliance problem and a compliant
mechanism design problem are formulated based on the level set method. In the formulations of these design problems, a perimeter
constraint is imposed to overcome the ill-posedness of the structural optimization problem. The sensitivity analysis for the
above structural optimization problems is conducted based on the adjoint variable method. The augmented Lagrangian method
is incorporated to deal with multiple constraints. Finally, several numerical examples that include multiple constraints are
provided to confirm the validity of the method, and it is shown that appropriate optimal structures are obtained.
KeywordsTopology optimization-Level set method-Signed distance function-Sensitivity analysis-Augmented Lagrangian method-Perimeter constraint
Structural and Multidisciplinary Optimization 04/2012; 41(5):685-698. · 1.49 Impact Factor
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ABSTRACT: In the last decade, metamaterials have been gaining attention and have been investigated because of their unique characteristics, which conventional materials do not have, such as negative refraction indexes. However, it is sometimes difficult to design metamaterials on the basis of experience and theoretical considerations because the relationship between their electromagnetic characteristics and structure is often vague. A mathematical structural design methodology targeting metamaterials may therefore be useful for expanding the engineering applications of metamaterials in industry. In this paper, a new level set-based topology optimization method is proposed for designing composite right- and left-handed transmission lines, each of which consists of a waveguide and periodically located dielectric resonators. Such transmission lines function as a fundamental metamaterial. In the proposed method, the shape and topology of the dielectric resonators are represented by the level set function, and topology optimization problems are formulated on the basis of the level set-based representation. Copyright © 2011 John Wiley & Sons, Ltd.
International Journal for Numerical Methods in Engineering 10/2011; 89(10):1272 - 1295. · 2.01 Impact Factor
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ABSTRACT: In this paper, we propose a level set-based topology optimization method targeting metallic waveguide design problems, where the skin effect must be taken into account since the metallic waveguides are generally used in the high-frequency range where this effect critically affects performance. One of the most reasonable approaches to represent the skin effect is to impose an electric field constraint condition on the surface of the metal. To implement this approach, we develop a boundary-tracking scheme for the arbitrary Lagrangian Eulerian (ALE) mesh pertaining to the zero iso-contour of the level set function that is given in an Eulerian mesh, and impose Dirichlet boundary conditions at the nodes on the zero iso-contour in the ALE mesh to compute the electric field. Since the ALE mesh accurately tracks the zero iso-contour at every optimization iteration, the electric field is always appropriately computed during optimization. For the sensitivity analysis, we compute the nodal coordinate sensitivities in the ALE mesh and smooth them by solving a Helmholtz-type partial differential equation. The obtained smoothed sensitivities are used to compute the normal velocity in the level set equation that is solved using the Eulerian mesh, and the level set function is updated based on the computed normal velocity. Finally, the utility of the proposed method is discussed through several numerical examples. Copyright © 2011 John Wiley & Sons, Ltd.
International Journal for Numerical Methods in Engineering 02/2011; 87(9):844 - 868. · 2.01 Impact Factor
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IEICE Transactions. 01/2006; 89-C:1337-1344.
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ABSTRACT: Electromagnetic structures that incorporate certain structural periodicities are known to display special behavior when subjected to electromagnetic waves, and can be designed to have specific functions such as inhibiting the intrusion of electromagnetic waves of certain frequencies into the periodic structure.This paper proposes a novel topology optimization method for periodic microstructures of electromagnetic materials using the concept of propagation behavior to implement designs that inhibit electromagnetic wave propagation. First, a way to apply topology optimization to the design of electromagnetic structures is briefly discussed. Next, the design specifications are clarified, and a new objective function is proposed to satisfy these specification. The optimization algorithm is developed using sequential linear programming (SLP) and the adjoint variable method (AVM). Several numerical examples are provided to confirm that the proposed method is capable of automatically generating physically reasonable periodic structures that have desired specified functions without relying on a predefined basic lattice.
Finite Elements in Analysis and Design.
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ABSTRACT: Electromagnetic waveguides effectively conduct electromagnetic microwaves using resonance phenomena in RF-ranges, and are widely used in high-frequency electronic devices and equipment. The waveguide guiding characteristics related to eigen-frequencies and eigen-modes are critical factors determining the design performances pertaining to the bandwidth of appropriate response frequencies, and high performance electromagnetic waveguides can be obtained by designing cross-sections of waveguides that appropriately control such guiding characteristics at the conceptual design phase. This paper proposes a new application of a topology optimization method for the design of inhomogeneous electromagnetic waveguide cross-sections composed of dielectric material and air, with the resulting configurations performing according to specified guiding characteristics. First, the concept of topology optimization and a way to apply it to electromagnetic wave problems are explained. Next, design requirements for the design of waveguide cross-sections are clarified and corresponding objective functions and the optimization problem are formulated. A new multi-objective function is formulated to reduce grayscales since using a penalization parameter for physical property interpolation is ineffective in electromagnetic problems. The optimization algorithm is constructed based on these formulations, Sequential Linear Programming and the finite element method, where hybrid edge/nodal elements are used. Finally, several design examples of waveguide cross-sections are presented to confirm the usefulness of the proposed method.
Finite Elements in Analysis and Design.
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ABSTRACT: We investigate the usefulness of the topology optimization with the finite element method in the optimization of an H-plane waveguide component. Design sensitivity is computed efficiently using the adjoint variable method. Employing the optimization procedure, optimized structures of an H-plane waveguide filter and T-junction are obtained from an initial homogeneous structure.
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ABSTRACT: We apply a design method based on topology optimization technique to optical waveguide devices. In our approach, after a refractive index profile in a design region is automatically generated using a topology optimization method, the obtained structure is redefined using primitive geometries with some design parameters and those parameters are optimized by a sequential linear programming. As numerical examples, we demonstrate how the method can be used for 90 bends and T-branching waveguides with arbitrary splitting ratio.
