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2016 Vol.29, Issue 4
Topology Design Optimization using Projection Method

프로젝션 기법을 활용한 위상 최적설계

Ha Seung-Hyun†*
Department of Ocean Engineering, Korea Maritime and Ocean University, Busan, 49112, Korea
•*Corresponding author Ha, Seung-Hyun shha@kmou.ac.kr
2016. pp. 293-299
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Abstract

In this paper, a projection method is introduced which is used in topology design optimization. In the projection method, each active design variable is projected onto the design domain depending on the shape and size of the projection functions, and the finite element under this projection receives a solid material. Furthermore, the size of the projection function defines the minimum length scale of the structural members. Therefore, a designer can easily apply design constraints without complicated post-processing procedure. In addition, the projection method can be combined with the homogenization theory, and applied to material design problem for composite materials. Topology design optimization for the unit-cell of the periodic structures can maximize the effective material properties, which yields the optimal material distribution with maximum bulk or shear moduli under a given volume fraction.

본 논문은 확장된 프로젝션 기법을 사용한 위상 최적설계 방법을 다루고 있다. 다양한 형상과 길이 스케일을 가지는 프로젝션 함수를 개발해 위상 최적설계 기법에 적용시킴으로써, 복합재료의 설계에서 형상 및 크기가 미리 주어진 보강재의 최적 배치를 위상 최적설계를 통해 결정할 수 있음을 확인하였다. 또한 이와 같은 프로젝션 기법이 균질화법과 결합되어 체적탄성률 또는 전단탄성률 등의 유효 재료특성을 최대화시키는 단위 구조를 설계함으로써, 주기 구조를 가지는 복합재료에서 보강재의 최적 배치를 결정하고 그 유효 재료특성값을 수치적으로 계산할 수 있음을 여러 수치 예제들을 통해서 검증하였다.

Keywords
projection method, topology design optimization, length scale, composite materials, homogenization
프로젝션기법, 위상최적설계, 길이 스케일, 복합재료, 균질화법.
References
1
M.P., Bendsoe and N., Kikuchi, 1998. Generating Optimal Topologies in Structural Design using a Homogenization Method. Comput. Methods Appl. Mech. & Eng., 71, pp.197-224.
10.1016/0045-7825(88)90086-2
2
S.-H., Cha, S.-W., Lee and S., Cho, 2013. Experimental Validation of Topology Design Optimization. J. Comput. Struct. Eng., 26, pp.241-246.
10.7734/COSEIK.2013.26.4.241
3
J., Guedes and N., Kikuchi, 1990. Preprocessing and Postprocessing for Materials based on the Homogenization Method with Adaptive Finite Element Methods. Comput. Methods Appl. Mech. & Eng., 83, pp.143-198.
10.1016/0045-7825(90)90148-F
4
J.K., Guest, 2015. Optimizing the layout of Discrete Objects in Structures and Materials: A Projection- based Topology Optimization Approach. Comput. Methods Appl. Mech. & Eng., 283, pp.330-351.
10.1016/j.cma.2014.09.006
5
J.K., Guest, A., Asadpoure and S.-H., Ha, 2011. Eliminating Beta-Continuation from Heaviside Projection and Density Filter Algorithms. Struct. & Multidiscipl. Optim, 44, pp.443-453.
10.1007/s00158-011-0676-1
6
J.K., Guest, J.H., Prévost and T., Belytschko, 2004. Achieving Minimum Length Scale in Topology Optimization using Nodal Design Variables and Projection Functions. Int. J. Numer. Methods Eng., 61, pp.238-254.
10.1002/nme.1064
7
S.-H., Ha and J.K., Guest, 2014. Optimizing Inclusion Shapes and Paterns Inperiodic Materials using Discrete Object Projection. Struct. & Multidiscipl. Optim., 50, pp.65-80.
10.1007/s00158-013-1026-2
8
B., Hassani and E., Hinton, 1998. A Review of Homogenization and Topology Optimization II - Analytical and Numerical Solution of Homogenization Equations. Comput. & Struct., 69, pp.719-738.
10.1016/S0045-7949(98)00132-1
9
O. , Sigmund, 1994. Materials with Prescribed Constitutive Parameters: an Inverse Homogenization Problem. Int. J. Solids & Struct., 31, pp.2313-2329.
10.1016/0020-7683(94)90154-6
10
O., Sigmund, 2001. A 99 line Topology Optimization Code Written in Mathlab. Struct. & Multidiscipl. Optimi., 21, pp.120-127.
10.1007/s001580050176
11
O., Sigmund, 2007. Morphology-based Black and White Filters for Topology Optimization. Struct. & Multidiscipl. Optimi., 33, pp.401-424.
10.1007/s00158-006-0087-x
12
O., Sigmund and J., Peterson, 1998. Numerical Instabilities in Topology Optimization: A Survey on Procedures Dealing with Checkerboards. Mesh- dependencies and Local Minima, Struct. Optimi., 16, pp.68-75.
10.1007/BF01214002
13
K., Svanberg, 1987. The Method of Moving Asymptotes- a New Method for Structural Optimization. J. Numer. Methods Eng., 24, pp.359-373.
10.1002/nme.1620240207
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 : 29
  • No :4
  • Pages :293-299
  • Received Date : 2015-10-11
  • Revised Date : 2015-11-19
  • Accepted Date : 2016-07-19
  • DOI :https://doi.org/10.7734/COSEIK.2016.29.4.293
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