Topology optimization using a reaction-diffusion equation

Jae Seok Choi, Takayuki Yamada, Kazuhiro Izui, Shinji Nishiwaki, Jeonghoon Yoo

Research output: Contribution to journalArticle

43 Citations (Scopus)

Abstract

This paper presents a structural topology optimization method based on a reaction-diffusion equation. In our approach, the design sensitivity for the topology optimization is directly employed as the reaction term of the reaction-diffusion equation. The distribution of material properties in the design domain is interpolated as the density field which is the solution of the reaction-diffusion equation, so free generation of new holes is allowed without the use of the topological gradient method. Our proposed method is intuitive and its implementation is simple compared with optimization methods using the level set method or phase field model. The evolution of the density field is based on the implicit finite element method. As numerical examples, compliance minimization problems of cantilever beams and force maximization problems of magnetic actuators are presented to demonstrate the method's effectiveness and utility.

Original languageEnglish
Pages (from-to)2407-2420
Number of pages14
JournalComputer Methods in Applied Mechanics and Engineering
Volume200
Issue number29-32
DOIs
Publication statusPublished - 2011 Jul 1

Fingerprint

reaction-diffusion equations
Shape optimization
topology
optimization
Magnetic actuators
Gradient methods
Structural optimization
Cantilever beams
cantilever beams
Materials properties
Finite element method
finite element method
actuators
gradients
sensitivity

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications

Cite this

Choi, Jae Seok ; Yamada, Takayuki ; Izui, Kazuhiro ; Nishiwaki, Shinji ; Yoo, Jeonghoon. / Topology optimization using a reaction-diffusion equation. In: Computer Methods in Applied Mechanics and Engineering. 2011 ; Vol. 200, No. 29-32. pp. 2407-2420.
@article{14ac2f5ecacb41c7aa72b3be426cb30f,
title = "Topology optimization using a reaction-diffusion equation",
abstract = "This paper presents a structural topology optimization method based on a reaction-diffusion equation. In our approach, the design sensitivity for the topology optimization is directly employed as the reaction term of the reaction-diffusion equation. The distribution of material properties in the design domain is interpolated as the density field which is the solution of the reaction-diffusion equation, so free generation of new holes is allowed without the use of the topological gradient method. Our proposed method is intuitive and its implementation is simple compared with optimization methods using the level set method or phase field model. The evolution of the density field is based on the implicit finite element method. As numerical examples, compliance minimization problems of cantilever beams and force maximization problems of magnetic actuators are presented to demonstrate the method's effectiveness and utility.",
author = "Choi, {Jae Seok} and Takayuki Yamada and Kazuhiro Izui and Shinji Nishiwaki and Jeonghoon Yoo",
year = "2011",
month = "7",
day = "1",
doi = "10.1016/j.cma.2011.04.013",
language = "English",
volume = "200",
pages = "2407--2420",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0374-2830",
publisher = "Elsevier",
number = "29-32",

}

Topology optimization using a reaction-diffusion equation. / Choi, Jae Seok; Yamada, Takayuki; Izui, Kazuhiro; Nishiwaki, Shinji; Yoo, Jeonghoon.

In: Computer Methods in Applied Mechanics and Engineering, Vol. 200, No. 29-32, 01.07.2011, p. 2407-2420.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Topology optimization using a reaction-diffusion equation

AU - Choi, Jae Seok

AU - Yamada, Takayuki

AU - Izui, Kazuhiro

AU - Nishiwaki, Shinji

AU - Yoo, Jeonghoon

PY - 2011/7/1

Y1 - 2011/7/1

N2 - This paper presents a structural topology optimization method based on a reaction-diffusion equation. In our approach, the design sensitivity for the topology optimization is directly employed as the reaction term of the reaction-diffusion equation. The distribution of material properties in the design domain is interpolated as the density field which is the solution of the reaction-diffusion equation, so free generation of new holes is allowed without the use of the topological gradient method. Our proposed method is intuitive and its implementation is simple compared with optimization methods using the level set method or phase field model. The evolution of the density field is based on the implicit finite element method. As numerical examples, compliance minimization problems of cantilever beams and force maximization problems of magnetic actuators are presented to demonstrate the method's effectiveness and utility.

AB - This paper presents a structural topology optimization method based on a reaction-diffusion equation. In our approach, the design sensitivity for the topology optimization is directly employed as the reaction term of the reaction-diffusion equation. The distribution of material properties in the design domain is interpolated as the density field which is the solution of the reaction-diffusion equation, so free generation of new holes is allowed without the use of the topological gradient method. Our proposed method is intuitive and its implementation is simple compared with optimization methods using the level set method or phase field model. The evolution of the density field is based on the implicit finite element method. As numerical examples, compliance minimization problems of cantilever beams and force maximization problems of magnetic actuators are presented to demonstrate the method's effectiveness and utility.

UR - http://www.scopus.com/inward/record.url?scp=79955854798&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79955854798&partnerID=8YFLogxK

U2 - 10.1016/j.cma.2011.04.013

DO - 10.1016/j.cma.2011.04.013

M3 - Article

AN - SCOPUS:79955854798

VL - 200

SP - 2407

EP - 2420

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0374-2830

IS - 29-32

ER -