Improvement of the Phase Section Method for Multi-material Topology Optimization

Min-sung Kang; Cheolwoong Kim; Jeonghoon Yoo

doi:10.7734/COSEIK.2022.35.2.65

All Issue

2022 Vol.35, Issue 2 Next Page

Research Paper

Improvement of the Phase Section Method for Multi-material Topology Optimization 다중 물질 위상최적설계를 위한 페이즈섹션 설계법 개선

30 April 2022. pp. 65-71

PDF XML

Abstract

Recently, multi-material structural topology optimization is more critical because it provides reasonable solution to weight reduction challenges and can as well provide effective conceptual design. For conventional multi-material topology optimization (MMTO), the number of design variable increases when the number of candidate materials increases, and accordingly, a significant increase in computational time occurs. Therefore, MMTO with a single design variable, such as the phase section method (PSM) was proposed . This research is focused on improving the PSM, considering three major limitations: the composition ratio does not represent the area or volume ratio, design variables are not sufficiently concentrated to target values, and certain materials are created less than they are required. To address such limitations, the redefined composition ratio and adjusted parameters for better convergence are proposed. The validation of proposed modifications is verified via two- and three-dimensional numerical examples.

Keywords

topology optimization

multi-material

phase section method

single variable

composition ratio

최근에는 경량화 문제에 대한 합리적인 솔루션을 제공하고 유용한 개념설계를 제공할 수 있는 다중 재료 구조 위상최적화가 더욱 중요해지고 있다. 기존의 MMTO(Multi-Material Topology Optimization)의 경우 후보 물질의 수가 증가할수록 설계변수의 수도 증가하고, 결과적으로 계산 시간이 크게 증가한다. 따라서 PSM(Phase Section Method)과 같은 단일 설계변수를 갖는 MMTO가 제안되었다. 본 연구는 조성비가 면적이나 부피비를 나타내지 못하고, 설계변수가 목표치에 충분히 집중되지 않고, 특정 재료가 요구량보다 적게 생성되는 PSM의 세 가지 주요 제한점을 고려하여 이를 개선하는데 중점을 둔다. 이러한 한계를 극복하기 위해 재정의된 조성비와 더 나은 수렴을 위한 조정된 매개변수를 제안한다. 제안된 수정 사항의 유효성을 2차원 및 3차원 수치 예제를 통해 검증한다.

키워드

위상최적설계

다중 물질

페이즈 섹션 방법

단일변수

조성비

References

Bendsøe, M.P., Kikuchi, N. (1988) Generating Optimal Topologies in Structural Design using a Homogenization Method, Comput. Methods Appl. Mech. Eng., 71(2), pp.197~224. 10.1016/0045-7825(88)90086-2

Bendsøe, M.P., Sigmund, O. (1999) Material Interpolation Schemes in Topology Optimization, Arch, Appl. Mech., 69(9), pp.635~654. 10.1007/s004190050248

Choi, J.S., Yamada, T., Izui, K., Nishiwaki, S., Yoo, J. (2011) Topology Optimization using a Reaction-Diffusion Equation, Comput. Methods Appl. Mech. Eng., 200(29-32), pp.2407~2420. 10.1016/j.cma.2011.04.013

Go, J., Seong, H.K., Kim, H., Park, J., Yoo, J. (2018) RF Collimator Design Having Multi-Dielectric Structure Using the Phase Field Design Method, J. Comput Struct. Eng. Inst. Korea, 31(1), pp.47~52. 10.7734/COSEIK.2018.31.1.47

Seong, H.K., Kim, C.W., Yoo, J., Lee, J. (2019) Multiphase Topology Optimization with a Single Variable Using the Phase‐Field Design Method, Int. J. Numer. Methods Eng., 119(5), pp.334~360. 10.1002/nme.6052

Sigmund, O. (2001) A 99 Line Topology Optimization Code Written in Matlab, Struct. Multidisc. Optim., 21(2), pp.120~127. 10.1007/s001580050176

Takezawa, A., Nishiwaki, S., Kitamura, M. (2010) Shape and Topology Optimization based on the Phase Field Method and Sensitivity Analysis, J. Comput. Phys., 229(7), pp.2697~2718. 10.1016/j.jcp.2009.12.017

Zuo, W., Saitou, K. (2017) Multi-Material Topology Optimization using Ordered SIMP Interpolation, Struct. Multidisc. Optim., 55(2), pp.477~491.

Information

Publisher :Computational Structural Engineering Institute of Korea
Publisher(Ko) :한국전산구조공학회
Journal Title :Journal of the Computational Structural Engineering Institute of Korea
Journal Title(Ko) :한국전산구조공학회 논문집
Volume : 35
No :2
Pages :65-71
Received Date : 2021-11-22
Revised Date : 2021-12-27
Accepted Date : 2021-12-27
DOI :https://doi.org/10.7734/COSEIK.2022.35.2.65

Journal of the Computational Structural Engineering Institute of Korea ISSN:1229-3059(Print) 2287-2302(Online) 한국전산구조공학회 논문집

All Issue