한국강구조학회 논문집 (Journal of Korean Society of Steel Construction)

한국강구조학회 (Korean Society of Steel Construction)
권호 표지

형상 최적설계를 위한 최적화 기법에 관한 연구

A Study on the Techniques of Configuration Optimization

  • 최병한 (전북대학교 부설 공학연구원 공업기술연구센타)
  • 투고 : 2004.10.15
  • 심사 : 2004.12.03
  • 발행 : 2004.12.27
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

본 연구는 구조물의 형상 최적화를 효율적이면서 보다 용이하게 수행할 수 있는 기법을 제안하고자 하였다. 구조물의 형상 표현과 설계변수 선택을 위해 설계요소 개념을 활용하여 설계변수 수를 과감하게 줄일 수 있었고, 등매개변수 사상기법을 이용하여 최적화 과정 중 형상의 변화에 따른 유한요소망을 자동생성 하였으며 효율적인 최적화 과정 수행을 위하여 결정론적 최적화 기법(개선된 허용방향법)과 스토캐스틱 최적화 기법(유전 알고리즘)을 사용하여 그 결과와 효율성을 비교하였다. 최적화 과정 중 구조해석은 유한요소법을 이용하며 구조물의 부피와 단면적 등을 목적함수로 하여 형상 최적화를 수행하였다. 또한 제작성과 시공성을 위한 최종형상 제시를 위하여 최적형상에 완화곡선 처리를 시도하였다. 이상의 연구를 강구조물을 대상으로 한 몇 가지 수치 예에 적용한 결과 설계과정을 보다 단순화시켰으며, 두 가지 기법 모두 최적해에 수렴함으로써 목적함수 값을 효과적으로 개선시킬 수 있었다. 따라서 본 연구는 그 타당성과 적용성이 있다고 판명된다.

This study describes an efficient and facile method for configuration optimum design of structures. One of the ways to achieve numerical shape representation and the selection of design variables is using the design element concept. Using this technique, the number of design variables could be drastically reduced. Isoparametric mapping was utilized to automatically generate the finite element mesh during the optimization process, and this made it possible to easily calculate the derivatives of the coordinates of generated finite element nodes w.r.t. the design variables. For the structural analysis, finite element analysis was adopted in the optimization procedure, and two different techniques(the deterministic method, a modified method of feasible direction; and the stochastic method, a genetic algorithms) were applied to obtain the minimum volumes and section areas for an efficient configuration optimization procedure. Futhermore, spline interpolation was introduced to present a realistic optimum configuration that meet the manufacturing requirements. According to the results of several numerical examples(steel structures), the two techniques suggested in this study simplified the process of configuration optimum design of structures, and yielded improved objective function values with a robust convergence rate. This study's applicability and capability have therefore been demonstrated.

키워드

참고문헌

  1. AIAA. J. v.24 no.5 Sensitivity Analysis of Discrete Structural Systems Adelman, H.M.;Haftka, R.T.
  2. Finite Elements in Analysis and Design v.29 Optimization of Finite Element Bidimensional Models: An Approach Based on Genetic Algorithms Annicchiarico, W.;Cerrolaza, M.
  3. AAA/ASME/ASCE/AHS 24th Structures. Structural Dynamics and Materials Conference. AIAA-83-0941 Shape Optimization of Two Dimensional Structures with Geometric Problem discription and Adaptive Mesh Refinement Bennett, J.A.;Botkin, M.E.
  4. AIAA J. v.23 no.3 Structural Shape Optimization with Geometric Description and Adaptive Mesh Refinement Bennett, J.A.;Botkin, M.E.
  5. AIAA J. v.20 Shape Optimization of Plate and Shell Structures Botkin, M.E.
  6. Int.J. Numerical Methods in Engineering v.26 Sensitivity Analysis with Plate and Shell. Finite Elements Brockman, R.A.;Lung, F.Y.
  7. Finite Elements in Analysis and Design v.15 A Comparative Study of Design Sensitivity Analysis by Using Commercial Finite Element Programs Chen, J.L.;Ho, J.S.
  8. Int.J.Numerical Methods in Engineering v.38 A Continuum Approach for Second-Order Shape Sensitivity of Elastic Solids with Loaded Boundaries Chen, Chin-Jung;Choi, K.K.
  9. Finite Elements in Analysis and Design v.6 Accuracy of Semi-Analytic Sensitivity Analysis Cheng, G.;Gu, Y.;Zhou, Y.
  10. Int.J.Numerical Methods in Engineering v.28 Sensitivity Analysis and Shape Optimization of Axisymme Structures Cheu, T.C.
  11. An Introduction to the Mechanics of Solids Dahl, Crandall;Lardner
  12. Mech.Struct. & Mach. v.16 no.40 Two Approaches to Sensitivity Analysis for Shape Variation of Structures Dems, K.;Haftka, R.T.
  13. Sructural Opt v.6 On Shape Sensitivity Approaches in the Numerical Analysis of Structures Dems, K.;Mroz, Z.
  14. Computers & Structures v.24 no.6 Shape Optimization of Structures : A Literature Survey Ding, Y.
  15. J.Strain Analysis v.10 no.2 Optimization of Shape to Minimize Stress Concentration Francavilla, A.;Ramakrishnan, C.V.;Zienkiewicz, O.C.
  16. Genetic Algorithms in Search, Optimization and Machine Learning Goldberg, D.E.
  17. Structural Opt v.3 Computational Aspects of Sensitivity Calculations in Linear Transient Structural Analysis Greene, W.H.;Haftka, R.T.
  18. Structural Opt v.6 Structural Modelling and Sensitivity Analysis of Shape Optimization Gu, Y.;Cheng, G.
  19. Computer Methods in Applied Mechanics and Engineering v.57 Structural Shape Optimization-A Survey Haftka, R.T.;Grandhi, R.V.
  20. AIAA J. v.24 no.7 First and Second Order Sensitivity Analysis of Linear and Nonlinear Structures Haftka, R.T.;Mroz, Z.
  21. Structural Opt v.3 On the Accuracy of Shape Sensitivity Haftka, R.T.;Barthelemy, B.
  22. Struct Multidisc. Opt v.21 Shape Sensitivity Analysis Using a Fixed Basis Function Finite Element Approach Hansen, J.S.;LIu, Z.S.;Olhoff, N.
  23. Int.J. Numer. Method Eng. v.18 Three-Dimensional Shape Optimization Hasan , Imam M.
  24. Int. J. Meth. Engng v.58 Topology Optimization of Trusses Using Genetic Algorithm, Force Method and Graph Theory Kaveh, A.;Kalatjari, V.
  25. Computers & Structures v.32 no.3/4 Finite Element Design Sensitivity Analysis and Its Integration with Numerical Optimization Techniques for Structural Design Kumar, V.;Lee, S-J;German, M.D.
  26. Eng Opt. v.19 Genetic Algorithms in Optimization Problems with Discrete and Integer Design Variables Lin, C.Y.;Hajela, P.
  27. J. Meth. Engng v.39 Genetic Algorithms as An Approach to Optimize Real-World Trusses Galante, Miguel
  28. Computers & Structures v.61 no.2 Practical Considerations in Two Dimensional Shape optimization of Elastic Continuum Naqib, R.A.;Zureick, A.;Will, K.M.
  29. Mech.Struct & Mach v.17 no.3 On Accuracy Problems for Semi-Analytical Sensitivity Analysis Pedersen, P.;Cheng, G.;Rasmussen, J.
  30. Electronics Letters v.31 no.18 Genetic Algorithm using Gradient-Like Reproduction Operator Pham, D.T.;Jin, G.
  31. Proc 3rd Congress on Expert Systems v.2 A Hybrid Genetic Algorithm Pham, D.T.;Jin, G.
  32. Computers & Structures v.60 no.2 An Integrated Approach to Structural Shape Optimization Pourazady, M.;Fu, Z.
  33. Struct. Mech. v.3 no.4 Structural Shape Optimization Using Penalty functions Ramakrishnan, C.V.;Francavilla, A.
  34. Structural Opt v.4 Shape Design Sensitivity Analysis of Structural Systems Santos, J.L.T.;Choi, K.K.
  35. Paper Presented at the U.S.-Japan Seminar Structural Synthesis : A Decade of Progress Schmit, L.A.
  36. Applied Mechanics Review v.21 no.10 Recent Development in Optimal Structural Design Sheu, C.Y.;Prager, W.
  37. Computer & Structures v.20 no.5 Sensitivity Analysis in Shape Optimization of Continuum Structures Wang, Shu-yu;Sun, Y.;Gallagher, R.H.
  38. Shape Optimization and Sequential Linear Programming. Chapter 7 of Optimum Structure Design Zienkiewicz, O.C.;Campbell, J.S.