A topology optimisation of composite elastic metamaterial slabs based on the manipulation of far-field behaviours

Kei Matsushima, Hiroshi Isakari, Toru Takahashi, Toshiro Matsumoto

Research output: Contribution to journalArticlepeer-review

Abstract

We propose a numerical method for a topology optimisation of composite elastic metamaterial slabs. We aim to realise some anomalous functionalities such as perfect absorption, wave-mode conversion, and negative refraction by designing the shape and topology of (visco-)elastic inclusions. Instead of manipulating effective material constants, we propose to utilise the far-field characteristics of scattered waves. This allows us to achieve novel functionalities for waves in not only low- but also high-frequency ranges. The design sensitivity corresponding to the far-field characteristics is rigorously derived using the adjoint variable method and incorporated into a level-set–based topology optimisation algorithm. The design sensitivity is computed by the boundary element method with periodic Green’s function instead of the standard finite element method to rigorously deal with the radiation of scattered waves without absorbing boundaries. We show some numerical examples to demonstrate the effectiveness of the proposed method.

Original languageEnglish
Pages (from-to)231-243
Number of pages13
JournalStructural and Multidisciplinary Optimization
Volume63
Issue number1
DOIs
Publication statusPublished - 2021 Jan
Externally publishedYes

Keywords

  • Boundary element method
  • Elastic metamaterial
  • Periodic scattering
  • Topological derivative
  • Topology optimisation

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Control and Optimization

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