A consistent grayscale-free topology optimization method using the level-set method and zero-level boundary tracking mesh

Shintaro Yamasaki*, Atsushi Kawamoto, Tsuyoshi Nomura, Kikuo Fujita

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)

Abstract

This paper proposes a level-set based topology optimization method incorporating a boundary tracking mesh generating method and nonlinear programming. Because the boundary tracking mesh is always conformed to the structural boundary, good approximation to the boundary is maintained during optimization; therefore, structural design problems are solved completely without grayscale material. Previously, we introduced the boundary tracking mesh generating method into level-set based topology optimization and updated the design variables by solving the level-set equation. In order to adapt our previous method to general structural optimization frameworks, the incorporation of the method with nonlinear programming is investigated in this paper. To successfully incorporate nonlinear programming, the optimization problem is regularized using a double-well potential. Furthermore, the sensitivities with respect to the design variables are strictly derived to maintain consistency in mathematical programming. We expect the investigation to open up a new class of grayscale-free topology optimization. The usefulness of the proposed method is demonstrated using several numerical examples targeting two-dimensional compliant mechanism and metallic waveguide design problems.

Original languageEnglish
Pages (from-to)744-773
Number of pages30
JournalInternational Journal for Numerical Methods in Engineering
Volume101
Issue number10
DOIs
Publication statusPublished - 2015 Mar 9
Externally publishedYes

Keywords

  • Boundary tracking mesh
  • Double-well potential
  • Level-set method
  • Nonlinear programming
  • Topology optimization

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics

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