Level set-based topology optimization for 2D heat conduction problems using BEM with objective function defined on design-dependent boundary with heat transfer boundary condition

Guoxian Jing, Hiroshi Isakari, Toshiro Matsumoto, Takayuki Yamada, Toru Takahashi

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)

Abstract

This paper proposes an optimum design method for two-dimensional heat conduction problem with heat transfer boundary condition based on the boundary element method (BEM) and the topology optimization method. The level set method is used to represent the structural boundaries and the boundary mesh is generated based on iso-surface of the level set function. A major novel aspect of this paper is that the governing equation is solved without ersatz material approach and approximated heat convection boundary condition by using the mesh generation. Additionally, the objective functional is defined also on the design boundaries. First, the topology optimization method and the level set method are briefly discussed. Using the level set based boundary expression, the topology optimization problem for the heat transfer problem with heat transfer boundary condition is formulated. Next, the topological derivative of the objective functional is derived. Finally, several numerical examples are provided to confirm the validity of the derived topological derivative and the proposed optimum design method.

Original languageEnglish
Pages (from-to)61-70
Number of pages10
JournalEngineering Analysis with Boundary Elements
Volume61
DOIs
Publication statusPublished - 2015 Jul 20
Externally publishedYes

Keywords

  • Boundary element method
  • Heat transfer problem
  • Level set method
  • Topological derivative
  • Topology optimization

ASJC Scopus subject areas

  • Analysis
  • Engineering(all)
  • Computational Mathematics
  • Applied Mathematics

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