A level-set-based topology optimisation of carpet cloaking devices with the boundary element method

Nakamoto, Kenta; Isakari, Hiroshi; Takahashi, Tōru; Matsumoto, Toshiro

doi:10.1299/mej.16-00268

Cited by 10 publications

(3 citation statements)

References 29 publications

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“…Topology optimization led to other designs of optical [530,531], acoustical [532] and water wave [533] cloaks with similar performances. Topology optimization has been also applied to carpet cloaks [534]. Alternatively, unidirectional cloaks, both in 2d and 3d, can be obtained for acoustics by putting two carpet cloaks back to back [535][536][537].…”

Section: Bulk Acoustic Pressure Wavesmentioning

confidence: 99%

Mechanical metamaterials

2023

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Mechanical metamaterials, also known as architected materials, are rationally designed composites, aiming at elastic behaviors and effective mechanical properties beyond (“meta”) those of their individual ingredients – qualitatively and/or quantitatively. Due to advances in computational science and manufacturing, this field has progressed considerably throughout the last decade. Here, we review its mathematical basis in the spirit of a tutorial, and summarize the conceptual as well as experimental state-of-the-art. This summary comprises disordered, periodic, quasi-periodic, and graded anisotropic functional architectures, in one, two, and three dimensions, covering length scales ranging from below one micrometer to tens of meters. Examples include extreme ordinary linear elastic behavior from artificial crystals, e.g., auxetics and pentamodes, “negative” effective properties, behavior beyond classical linear elasticity, e.g., arising from local resonances, chirality, beyond-nearest-neighbor interactions, quasi-crystalline mechanical metamaterials, topological band gaps, cloaking based on coordinate transformations and on scattering cancellation, seismic protection, nonlinear and programmable metamaterials, as well as space-time-periodic architectures.

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Section: Bulk Acoustic Pressure Wavesmentioning

confidence: 99%

Mechanical metamaterials

2023

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“…This can be achieved by expanding δu n ′ with respect to ε around the point x. According to [31], we have…”

Section: S(ω;mentioning

confidence: 99%

A topology optimization of open acoustic waveguides based on a scattering matrix method

Matsushima,

Isakari,

Takahashi

et al. 2022

Preprint

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This study presents a topology optimization scheme for realizing a bound state in the continuum along an open acoustic waveguide comprising a periodic array of elastic materials. First, we formulate the periodic problem as a system of linear algebraic equations using a scattering matrix associated with a single unit structure of the waveguide. The scattering matrix is numerically constructed using the boundary element method. Subsequently, we employ the Sakurai-Sugiura method to determine resonant frequencies and the Floquet wavenumbers by solving a nonlinear eigenvalue problem for the linear system. We design the shape and topology of the unit elastic material such that the periodic structure has a real resonant wavenumber at a given frequency by minimizing the imaginary part of the resonant wavenumber. The proposed topology optimization scheme is based on a level-set method with a novel topological derivative. We demonstrate a numerical example of the proposed topology optimization and show that it realizes a bound state in the continuum through some numerical experiments.

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“…The boundary element method (BEM) is useful for topology optimization problems for linear problems, especially wave propagation problems and those for open domains [1,2]. Level-set method [3][4][5][6][7], which uses level-set function for expressing and controlling material distribution, is one of the popular methods among topology optimization methods, and the BEM can be effectively used with it by extracting the boundary of the material from the distribution of the level-set function [8].…”

Section: Introductionmentioning

confidence: 99%

A new adjoint problem for two-dimensional helmholtz equation to calculate topological derivatives of the objective functional having tangential derivative quantities

et al. 2021

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A special topology optimization problem is considered whose objective functional consists of tangential derivative of the potential on the boundary for two-dimensional Helmholtz equation. In order to derive the adjoint problem, the functional of the conventional topology optimizations required a boundary integral of the potential and its flux. For the present objective functional having the tangential derivative, integration by parts is applied to the part having the tangential derivative of the variation of the potential to generate a tractable adjoint problem. The derived adjoint problem is used in the variation of the objective function, and the topological derivative is derived in the conventional expression.

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A level-set-based topology optimisation of carpet cloaking devices with the boundary element method

Cited by 10 publications

References 29 publications

Mechanical metamaterials

Mechanical metamaterials

A topology optimization of open acoustic waveguides based on a scattering matrix method

A new adjoint problem for two-dimensional helmholtz equation to calculate topological derivatives of the objective functional having tangential derivative quantities

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