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Research Papers

# A Level Set-Based Topology Optimization Method for Maximizing Thermal Diffusivity in Problems Including Design-Dependent Effects

[+] Author and Article Information

Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University, Kyoto 606-8501, Japanyamada@nuem.nagoya-u.ac.jp

Kazuhiro Izui

Department of Mechanical Engineering and Science, Graduate School of Engineering, Kyoto University, Kyoto 606-8501, Japanizui@prec.kyoto-u.ac.jp

Shinji Nishiwaki

Department of Mechanical Engineering and Science, Graduate School of Engineering, Kyoto University, Kyoto 606-8501, Japanshinji@prec.kyoto-u.ac.jp

1

Corresponding author.

J. Mech. Des 133(3), 031011 (Mar 15, 2011) (9 pages) doi:10.1115/1.4003684 History: Received June 20, 2010; Revised February 03, 2011; Published March 15, 2011; Online March 15, 2011

## Abstract

This paper proposes an optimum design method, based on our level set-based topology optimization method, for maximizing thermal diffusivity in problems dealing with generic heat transfer boundaries that include design-dependent boundary conditions. First, a topology optimization method using a level set model incorporating a fictitious interface energy for regularizing the topology optimization is briefly discussed. Next, an optimization method for maximizing thermal diffusivity is formulated based on the concept of total potential energy. An optimization algorithm that uses the finite element method when solving the equilibrium equation and updating the level set function is then constructed. Finally, several numerical examples are provided to confirm the utility and validity of the proposed topology optimization method.

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## Figures

Figure 1

Fixed design domain D and level set function ϕ

Figure 2

Flowchart of the optimization procedure

Figure 3

Fixed design domain and boundary conditions of the heat conduction problem

Figure 11

Optimal configurations of the internal heat generation problem: (a) regularization parameter τ=1.0×10−6, (b) regularization parameter τ=5.0×10−6, (c) regularization parameter τ=1.0×10−5, and (d) regularization parameter τ=5.0×10−5

Figure 12

Fixed design domain and boundary conditions of the two-dimensional heat convection problem

Figure 13

Optimal configurations of two-dimensional heat convection problem considering shape dependencies with respect to regularization parameter τ: (a) τ=1.0×10−6, (b) τ=5.0×10−6, (c) τ=1.0×10−5, and (d) τ=5.0×10−5

Figure 14

Optimal configurations of two-dimensional heat convection problem considering shape dependencies with respect to heat convection coefficient h: (a) h=1.0×105, (b) h=2.0×104, (c) h=1.0×104, and (d) h=1.0×102

Figure 15

Fixed design domain and optimal configuration of three-dimensional heat convection problem

Figure 5

Configurations for the heat conduction problem: (a) initial configuration of four holes, (b) initial configuration of nine holes, and (c) asymmetric initial configuration of a number of apertures

Figure 6

Temperature history at point A during the optimization procedure

Figure 7

Optimal configurations for different parameters of the approximated Heaviside function 25

Figure 8

Optimal configurations for different values of parameter Δt

Figure 9

Optimal configurations for different finite element mesh sizes

Figure 10

Fixed design domain and boundary conditions of the internal heat generation problem

Figure 4

Configurations for the heat conduction problem with a filled initial configuration

## Errata

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