A topology optimization method for design of negative permeability metamaterials

Diaz, Alfredo Peña; Sigmund, Ole

doi:10.1007/s00158-009-0416-y

Cited by 161 publications

(77 citation statements)

References 17 publications

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“…This type of method including homogenization method ( [3]), solid isotropic material with penalization (SIMP) method ( [4,8]), evolutionary structural optimization (ESO) method ( [6]), and its improved algorithm C bidirectional evolutionary structural optimization (BESO) method ( [9][10][11][12]) has tackled various problems, including uncertain design ( [13][14][15][16][17]), dynamic problems ( [18][19][20]), and designing metamaterials ( [21]). The aforementioned elementbased topology optimization methods have applications successfully in a number of fields.…”

Section: Introductionmentioning

confidence: 99%

An Efficient Topology Description Function Method Based on Modified Sigmoid Function

Yang

Liu

Yang

et al. 2018

Mathematical Problems in Engineering

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Optimal geometries extracted from traditional element-based topology optimization outcomes usually have zigzag boundaries, leading to being difficult to fabricate. In this study, a fairly accurate and efficient topology description function method (TDFM) for topology optimization of linear elastic structures is developed. By employing the modified sigmoid function, a simple yet efficient strategy is presented to tackle the computational difficulties because of the nonsmoothness of Heaviside function in topology optimization problem. The optimization problem is to minimize the structural compliance, with highest stiffness, while satisfying the volume constraint. The design problem is solved by a Sequential Linear Programming method. Convergent, crisp, and smooth final layouts are obtained, which can be fabricated without postprocessing, demonstrated by a series of numerical examples. Further, the proposed method has a rather higher accuracy and efficiency compared with traditional TDFM, when the classical topology optimization methods, such as bidirectional evolutionary structural optimization (BESO) and solid isotropic material with penalization (SIMP) method, are taken as benchmark.

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Section: Introductionmentioning

confidence: 99%

An Efficient Topology Description Function Method Based on Modified Sigmoid Function

Yang

Liu

Yang

et al. 2018

Mathematical Problems in Engineering

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“…During the last decade, topology optimization has started to be applied to the design of various electromagnetic components, such as antennas (Nomura et al 2007;Erentok and Sigmund 2011;Zhou et al 2010;Aage 2011;Hassan et al 2014b), metamaterials (Diaz and Sigmund 2010;Otomori et al 2012), and filters (Kiziltas et al 2004;Nomura et al 2013;Aage and Egede Johansen 2017). As opposed to classical topology optimization approaches applied to elastic material, the layout optimization of conducting materials suffers from an ohmic barrier issue.…”

Section: Introductionmentioning

confidence: 99%

Topology optimization of compact wideband coaxial-to-waveguide transitions with minimum-size control

Hassan

Wadbro

Hägg

et al. 2017

Struct Multidisc Optim

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This paper presents a density-based topology optimization approach to design compact wideband coaxialto-waveguide transitions. The underlying optimization problem shows a strong self penalization towards binary solutions, which entails mesh-dependent designs that generally exhibit poor performance. To address the self penalization issue, we develop a filtering approach that consists of two phases. The first phase aims to relax the self penalization by using a sequence of linear filters. The second phase relies on nonlinear filters and aims to obtain binary solutions and to impose minimum-size control on the final design. We present results for optimizing compact transitions between a 50-Ohm coaxial cable and a standard WR90 waveguide operating in the X-band (8-12 GHz).

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“…For this complexity, physical intuitionbased electromagnetic structure design has its limitations. To overcome these bounds, several inverse design tests have been implemented based on structural optimization methods [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34], in which the method employed most is the topology optimization method. Topology optimization is currently regarded to be the most robust methodology for the inverse determination of material distribution in structures that meet given structural performance criteria.…”

Section: Introductionmentioning

confidence: 99%

Topology optimization for three-dimensional electromagnetic waves using an edge element-based finite-element method

Deng

Korvink

2016

Proc. R. Soc. A.

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A topology optimization method for design of negative permeability metamaterials

Cited by 161 publications

References 17 publications

An Efficient Topology Description Function Method Based on Modified Sigmoid Function

An Efficient Topology Description Function Method Based on Modified Sigmoid Function

Topology optimization of compact wideband coaxial-to-waveguide transitions with minimum-size control

Topology optimization for three-dimensional electromagnetic waves using an edge element-based finite-element method

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