A topology optimisation for three-dimensional acoustics with the level set method and the fast multipole boundary element method

Isakari, Hiroshi; Kuriyama, Kohei; Harada, Shinya; Yamada, Takayuki; Takahashi, Tōru; Matsumoto, Toshiro

doi:10.1299/mej.2014cm0039

Cited by 49 publications

(33 citation statements)

References 19 publications

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“…In those research studies the topological sensitivities are formulated through the BEM framework accelerated with the Fast Multipole method. In the research work of Isakari et al [45] a topology optimisation method was presented through the integration of LSM, Fast Multipole boundary element method and topological sensitivity analysis. The proposed method was applied to three-dimensional wave scattering problems.…”

Section: Introductionmentioning

confidence: 99%

A boundary element and level set based topology optimisation using sensitivity analysis

Ullah

Trevelyan

2016

Engineering Analysis with Boundary Elements

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Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractThe structural topology optimisation method presented in this paper is based on the boundary element method, level set method and shape sensitivity analysis for two-dimensional linear elastic problems. The proposed method automatically nucleates holes within the design domain during the optimisation process using a topological derivative based hole insertion criterion. The level set method is used to provide an implicit description of the structural geometry, which is capable of automatically handling topological changes, i.e. holes merging with each other or with the boundary. During the optimisation process non-uniform rational b-splines are fitted through the zero level set contours, which links an implicit geometry representation to its structural model. In addition, this provides an optimal design in standard CAD format, and without intermediate material densities, which can be directly used in other design processes. The proposed optimisation method is tested against different benchmark examples and the optimal geometries generated are in close agreement those available in the literature of topology optimisation.

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Section: Introductionmentioning

confidence: 99%

A boundary element and level set based topology optimisation using sensitivity analysis

Ullah

Trevelyan

2016

Engineering Analysis with Boundary Elements

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“…A similar procedure toû i andp in Ω ε together with Eqs. (15), (16), (19) and (24) gives the following identity:…”

Section: 2mentioning

confidence: 99%

“…In order to realise a topology optimisation for three-dimensional realistic design problems of wave devices, we have been investigating level-set-based topology optimisations with the BEM accelerated by the FMM. In our methodology, a candidate for optimal configuration is expressed with a level set function which is iteratively updated with the help of the topological derivative [19,8,35,9] to find an optimal distribution of sound scatterers. In [19], we have investigated a topology optimisation for rigid materials to minimise sound pressure on some observation points.…”

Section: Introductionmentioning

confidence: 99%

A level-set-based topology optimisation for acoustic–elastic coupled problems with a fast BEM–FEM solver

Isakari

Kondo

Takahashi

et al. 2017

Computer Methods in Applied Mechanics and Engineering

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This paper presents a structural optimisation method in three-dimensional acoustic-elastic coupled problems. The proposed optimisation method finds an optimal allocation of elastic materials which reduces the sound level on some fixed observation points. In the process of the optimisation, configuration of the elastic materials is expressed with a level set function, and the distribution of the level set function is iteratively updated with the help of the topological derivative. The topological derivative is associated with state and adjoint variables which are the solutions of the acoustic-elastic coupled problems. In this paper, the acoustic-elastic coupled problems are solved by a BEM-FEM coupled solver, in which the fast multipole method (FMM) and a multi-frontal solver for sparse matrices are efficiently combined. Along with the detailed formulations for the topological derivative and the BEM-FEM coupled solver, we present some numerical examples of optimal designs of elastic sound scatterer to manipulate sound waves, from which we confirm the effectiveness of the present method.

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“…Level set-based shape 24 and topology 25 optimization methods enable clear structural boundaries to be obtained because they are defined by the iso-surface of the level set function. Yamada et al 25 proposed a level set-based topology optimization method using a design variable on the basis of a reaction-diffusion equation, ensuring the smoothness of structural boundaries in the optimized configurations, and their method has been applied to different kinds of physics problems, especially wave propagation problems, such as for elastic waves, 26 electromagnetic waves, 27 acoustic waves, 28 and an acoustic-elastic coupled system. 29 A topological derivative is adopted as a sensitivity of the objective functional so that topological changes are allowed during optimization.…”

Section: Introductionmentioning

confidence: 99%

Optimum design of an acoustic metamaterial with negative bulk modulus in an acoustic‐elastic coupled system using a level set–based topology optimization method

Noguchi

Yamada

Izui

et al. 2017

Numerical Meth Engineering

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This paper presents a level set-based topology optimization method for the design of an acoustic metamaterial with negative bulk modulus in an acoustic-elastic coupled system. To represent the coupled system, we propose a two-phase material model in which the solid and acoustic phases are mixed. This model allows the coupled system to be represented uniformly and avoids the need to impose the coupling conditions typically required in analyses of acoustic-elastic coupled systems. The effective bulk modulus of the acoustic metamaterial is represented using an S-parameter-based method and the optimization problem is formulated as a level set-based topology optimization. The topological derivatives for the two-phase material model are obtained using the relationship between the topological and shape derivatives. Numerical examples demonstrate the validity of the proposed two-phase material model and topological derivatives, and an optimal unit cell design for an acoustic metamaterial with negative bulk modulus is obtained at a targeted frequency. KEYWORDSacoustic metamaterial, level set-based topology optimization method, negative bulk modulus, topological derivative, two-phase material model Recently, acoustic metamaterials have been investigated on the basis of certain analogous properties of acoustic and electromagnetic waves. After Liu et al 6 first described a sonic crystal composed of lead, silicone rubber, and epoxy that exhibits acoustic bandgaps, a variety of acoustic metamaterials were proposed, such as those with a negative bulk modulus 7 or a negative refractive index, 8,9 and it is expected that acoustic metamaterials can be used to make functional acoustic devices such as acoustic cloaks 10 and acoustic superlenses. 11

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A topology optimisation for three-dimensional acoustics with the level set method and the fast multipole boundary element method

Cited by 49 publications

References 19 publications

A boundary element and level set based topology optimisation using sensitivity analysis

A boundary element and level set based topology optimisation using sensitivity analysis

A level-set-based topology optimisation for acoustic–elastic coupled problems with a fast BEM–FEM solver

Optimum design of an acoustic metamaterial with negative bulk modulus in an acoustic‐elastic coupled system using a level set–based topology optimization method

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