Topology optimization design scheme for broadband non-resonant hyperbolic elastic metamaterials

Rong, Junjie; Ye, Wenjing

doi:10.1016/j.cma.2018.10.034

Cited by 32 publications

(12 citation statements)

References 35 publications

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“…Herein, the satisfaction of Equation (12) has been reflected in the derivation process. Finally, by taking into account the relationships (11), (18), and Ω 1 = 0, we take the volume integration of Equation (10) over a unit cell to have the following homogenized wave equation:…”

Section: F I G U R E 1 Concept Of Homogenization For Bidirectional Unmentioning

confidence: 99%

“…For example, Yamasaki et al proposed a level set–based topology optimization (LTO) for right‐ and left‐handed lineal metamaterials by duplicating eigenvalues at a certain eigenmode. Also, Rong and Ye controlled the dispersion diagram around a target eigenvalue to obtain a hyperbolic elastic metamaterial by changing relative gaps between it and other eigenvalues.…”

Section: Introductionmentioning

confidence: 99%

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Isogeometric topology optimization of anisotropic metamaterials for controlling high‐frequency electromagnetic wave

Nishi

Yamada

Izui

et al. 2019

Numerical Meth Engineering

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Summary This study presents a level set–based topology optimization with isogeometric analysis (IGA) for controlling high‐frequency electromagnetic wave propagation in a domain with periodic microstructures (unit cells). The high‐frequency homogenization method is applied to characterize the macroscopic high‐frequency waves in periodic heterogeneous media whose wavelength is comparative to or smaller than the representative length of a unit cell. B‐spline basis functions are employed for the IGA discretization procedure to improve the performance of electromagnetic wave analysis in a unit cell and topology optimization. Also, to keep the same order of continuity on the periodic boundaries as on other element edges in the domain, we propose the extended domain approach, while incorporating Floquet periodic boundary condition (FPBC). Two types of optimization problems are taken as examples to demonstrate the effectiveness of the proposed method in comparison with the standard finite element analysis (FEA). The optimization results provide optimized topologies of unit cells qualified as anisotropic metamaterials with hyperbolic and bidirectional dispersion properties at the macroscale.

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Section: F I G U R E 1 Concept Of Homogenization For Bidirectional Unmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Isogeometric topology optimization of anisotropic metamaterials for controlling high‐frequency electromagnetic wave

Nishi

Yamada

Izui

et al. 2019

Numerical Meth Engineering

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“…Topology optimization (TO), which is considered as a powerful design tool to generate creative designs, 20 has been introduced to the PnCs for nearly two decades. [21][22][23][24][25] Many different TO based design methods have been proposed for satisfying various acoustic properties or functional requirements, including ultra-wide bandgap, 26 directional bandgap, 27,28 evanescent wave characters, 29,30 negative reflection, [31][32][33][34] topological insulators [35][36][37] and so on. Herein, Rong and Ye 31 proposed a two-step TO method for obtaining nonresonant hyperbolic metamaterials by simultaneously manipulating the dispersion band structure and the equi-frequency contour (EFC).…”

Section: Introductionmentioning

confidence: 99%

Topology optimization for realizing tailored self‐collimation in phononic crystals

Jia

Luo

Takezawa

et al. 2022

Numerical Meth Engineering

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Self‐collimation is a phenomenon that the waves propagate through a narrow channel in phononic crystals (PnCs) without diffusion. Although different self‐collimation PnCs configurations have been proposed with heuristic methods, it is still challenging to achieve a frequency‐specified self‐collimation. We propose a systematic topology optimization method to find the material distribution in PnCs for realizing a frequency‐specified self‐collimation within a wider incident wave angle range. To achieve the self‐collimation effect, the weighted slope index of equi‐frequency contours (EFCs) that effectively measures whether the wave propagation has a self‐collimation effect is introduced as the objective function of the optimization model. The material‐field series expansion (MFSE) technique is used to describe the complicated topologies of the unit cell with a low number of design variables. Then, the Kriging‐based optimization algorithm with a self‐adaptive strategy is adopted for solving the optimization problem. Numerical examples show that the optimized unit cell designs have flat EFCs within larger incident wave angle ranges and also demonstrate that the expected nondiffraction propagation characteristics can be achieved through optimization.

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“…The advent in additive manufacturing technologies has further broadened the application scope of TO. Advanced materials such as phononic materials (Sigmund and Jensen 2003), various metamaterials (Diaz and Sigmund 2010, Matsumoto et al 2011, Rong and Ye 2019 and artificial bone scaffolds and orthopaedic implants (Wang, X. et al 2016), have been successfully designed using TO methods.…”

Section: Introductionmentioning

confidence: 99%

Accelerating gradient-based topology optimization design with dual-model artificial neural networks

Qian

2020

Struct Multidisc Optim

Self Cite

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Topology optimization (TO) is a common technique used in free-form designs. However, conventional TO-based design approaches suffer from high computational cost due to the need for repetitive forward calculations and/or sensitivity analysis, which are typically done using high-dimensional simulations such as Finite Element Analysis (FEA). In this work, neural networks are used as efficient surrogate models for forward and sensitivity calculations in order to greatly accelerate the design process of topology optimization. To improve the accuracy of sensitivity analyses, dual-model neural networks that are trained with both forward and sensitivity data are constructed and are integrated into the Solid Isotropic Material with Penalization (SIMP) method to replace FEA. The performance of the accelerated SIMP method is demonstrated on two benchmark design problems namely minimum compliance design and metamaterial design. The efficiency gained in the problem with size of 64x64 is 137 times in forward calculation and 74 times in sensitivity analysis. In addition, effective data generation methods suitable for TO designs are investigated and developed, which lead to a great saving in training time. In both benchmark design problems, a design accuracy of 95% can be achieved with only around 2000 training data.

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Topology optimization design scheme for broadband non-resonant hyperbolic elastic metamaterials

Cited by 32 publications

References 35 publications

Isogeometric topology optimization of anisotropic metamaterials for controlling high‐frequency electromagnetic wave

Isogeometric topology optimization of anisotropic metamaterials for controlling high‐frequency electromagnetic wave

Topology optimization for realizing tailored self‐collimation in phononic crystals

Accelerating gradient-based topology optimization design with dual-model artificial neural networks

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