Material Topology Optimization Design of Structures using SIMP Approach Part II : Initial Design Domain with Topology of Partial Solids

SIMP를 이용한 구조물의 재료 위상 최적설계 Part II : 부분적인 솔리드 위상을 가지는 초기 설계영역

  • 이동규 (독일 슈투트가르트대학교 토목공학과 구조역학연구소) ;
  • 박성수 (부산대학교 건축공학과) ;
  • 신수미 (부산대학교 건축공학과 BK21)
  • Published : 2007.02.28


Discrete topology optimization processes of structures start from an initial design domain which is described by the topology of constant material densities. During optimization procedures, the structural topology changes in order to satisfy optimization problems in the fixed design domain, and finally, the optimization produces material density distributions with optimal topology. An introduction of initial holes in a design domain presented by Eschenauer et at. has been utilized in order to improve the optimization convergence of boundary-based shape optimization methods by generating finite changes of design variables. This means that an optimal topology depends on an initial topology with respect to topology optimization problems. In this study, it is investigated that various optimal topologies can be yielded under constraints of usable material, when partial solid phases are deposited in an initial design domain and thus initial topology is finitely changed. As a numerical application, structural topology optimization of a simple MBB-Beam is carried out, applying partial circular solid phases with varying sizes to an initial design domain.


  1. 이동규, 신수미(2007) SIMP를 이용한 재료 위상 최적설계, Part I: 부분적인 구멍의 위상을 가지는 초기 설계영역, 한국전산구조공학회 논문집, 20(1), pp.9-19
  2. 이상진 (2000) 위상최적화에 대한 개론, 한국전산구조공학회 논문집, 13(3), pp.25-33
  3. 임오강, 이진석(1998) 균질재료와 벌칙인자를 이용한 위상 최적설계, 한국전산구조공학회 가을학술발표대회 논문집, pp.3-10
  4. Bendsoe, M.P., Kikuchi, N.(1988) Generating Optimal Topologies in Optimal Design using a Homogenization Method, Computer Methods in Applied Mechanics and Engineering, 71, pp.197-224
  5. Bendsoe, M.P.(1989) Optimal Shape Design as a Material Distribution Problem, Structural Optimization, 1, pp.193-202
  6. Dobbs, W., Felton, L.P.(1969) Optimization of Truss Geometry, Processing ASCE, 95(ST10). pp.2105-2118
  7. Dorn, W., Gom, R., Greenbergm, H. (1964) Automoryatic Design of Optimal Structures, Journal of Mechanics, 3. pp.25-52
  8. Eschenauer, H.A., Kobelev, V.V., Schmacher, A. (1994) Bubble Method for Topology and Shape Optimization of Structures. Structural Optimization, 8, pp.42-51
  9. Haug, E.J., Choi, K.K., Komkov, V. (986) Design Sensitivity Analysis of Structural Systems, Academic Press. Orlando. New York
  10. Michell. A.G.M. (1904) The Limits of Economy of Material in Frame Structures. Philosophical Magazine. 8. pp.589-597
  11. Mlejnek, H.P. (1992) Some Aspects of the Genesis of Structures. Structural Optimization. 5. pp.64-69
  12. Rozvany, G.I.N. (1972) Optimal Load Transmission by Flexure, Computer Methods in Applied Mechanics and Engineering. 1, pp.253-263
  13. Rozvany, G.I.N., Zhou, M., Birker, T. (1992) Generalized Shape Optimization without Homogenization. Structural Optimization. 4. pp.250-252
  14. Sigmund, O. (2001) A 99 line topology optimization code written in Matlab, Structural and Multidisciplinary Optimization, 21, pp.120-127