Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/2424
標題: 拓樸最佳化設計變數懲罰方式之探討
Exploration of penalty functions applied to design variables in topology optimization
作者: 李彥叡
Li, Yen-Jui
關鍵字: topology optimization;拓樸最佳化
出版社: 機械工程學系所
引用: 1. Bendsoe, M.P. and N. Kikuchi, Generating Optimal Topologies in Structural Design Using a Homogenization Method. Computer Methods in Applied Mechanics and Engineering, 1988. 71(2): p. 197-224. 2. Yang, R.J. and C.H. Chuang, Optimal Topology Design Using Linear-Programming. Computers & Structures, 1994. 52(2): p. 265-275. 3. Diaz, A.a.S., O., Checkerboard Patterns in Layout Optimization. Struct. Optim., 1995. 10: p. 40-45. 4. Bendsoe, M.P., Optimal Shape Design as a Material Distribution Problem. Structural Optimization, 1989. 1: p. 193-202. 5. Mlejnek, H.P., Some Aspects of the Genesis of Structures. Structural Optimization, 1992. 5(1-2): p. 64-69. 6. Wang B. P., L.C.M.a.Y.R.J., Topology Optimization Using MSC/NASTRAN. MSC User Conference, 1994. 7. 陳至賢, 結構形勢最佳化設計. 國立中興大學機械工程研究所碩士論文, 民國84年6月. 8. Tenek, L.H. and I. Hagiwara, Optimal Rectangular Plate and Shallow Shell Topologies Using Thickness Distribution or Homogenization. Computer Methods in Applied Mechanics and Engineering, 1994. 115(1-2): p. 111-124. 9. Nakamura, T. and M. Ohsaki, A Natural Generator of Optimum Topology of Plane Trusses for Specified Fundamental-Frequency. Computer Methods in Applied Mechanics and Engineering, 1992. 94(1): p. 113-129. 10. Kirsch, U., Optimal topologies of truss structures. Computer Methods in Applied Mechanics and Engineering, 1989. 72: p. 15 - 28. 11. Rozvany, G.I.N., et al., Optimal Topology of Trusses or Perforated Deep Beams with Rotational Restraints at Both Ends. Structural Optimization, 1993. 5(4): p. 268-270. 12. Sankaranarayanan, S., R.T. Haftka, and R.K. Kapania, Truss Topology Optimization with Simultaneous Analysis and Design. Aiaa Journal, 1994. 32(2): p. 420-424. 13. Kirsch, U., Optimal Topologies of Structures. Appl. Mech. Rev., 1989. 42(8): p. 223-239. 14. Zhou, M. and G.I.N. Rozvany, The Coc Algorithm .2. Topological, Geometrical and Generalized Shape Optimization. Computer Methods in Applied Mechanics and Engineering, 1991. 89(1-3): p. 309-336. 15. Zakhama, R., Wind load modeling for topology optimization of continuum structures. Structural and Multidisciplinary Optimization, July 2010. 42: p. 157-164. 16. Zuo, Z.H.a.X., Y.M. and Huang, X., Combining genetic algorithms with BESO for topology optimization. Structural and Multidisciplinary Optimization, June 2009. 38: p. 511-523. 17. U. Darling, O.S., and S. Bouwstra, Design and fabrication of compliant micromechanisms and structures withnegative poisson''s ratio. IEEE, 1999: p. 365-367. 18. Jiang, C., Evolutionary algorithm and its application in structural topology optimization. Proceedings of the 27th Chinese Control Conference, CCC, 2008: p. 10-14. 19. Salami M, Hendtlass T., A fast evaluation strategy for evolutionary algorithms. Applied Soft Computing, 2003. 2(3): p. 156-173.
摘要: 
自從Bendsoe與Kikuchi於1988年提出以均質法來求解結構型態最佳化問題後,相關研究便日益增多。本文亦將針對結構型態最佳化問題,考慮順從度的最小化並伴隨著材料使用量的束制條件。本研究以各元素之比密度為設計變數,每個設計變數介在0到1之間,0表示此元素不存在,因為其楊氏係數值為0;1表示此元素存在,因為其楊氏係數值並未改變,每個元素的楊氏系數為其比密度的函數。
本文嘗試著不同於SIMP ( Solid Isotropic Material with Penalization ) 理論的懲罰方法,分別使用五種函數,其特性是以設計變數的值0.5為分界,在設計變數介於0到0.5的前半段以懲罰的方法提高設計變數的值往0靠近的趨勢,若值為0則不懲罰;在設計變數介於0.5到1的後半段以鼓勵的方法提高設計變數的值往1靠近的趨勢,若值為1則不鼓勵,並使其呈現對稱與非對稱的數種情形來做測試,希望能藉由這樣的函數分佈情形,驅使較多數的設計變數盡量朝向0或1靠近。藉由上述的方法,在本研究一一驗證後,確實得到了幾條較為理想的函數。

After Bendsoe and Kikuchi introduced the homogenization method to solve the structural topology optimization problems, many research results have been reported. In this thesis, the objective is to generate a minimum compliance topology of a structure subject to a material constraint in a given design space. The design variable is the normalized density of each finite element in the design space, and the Young's modulus is assumed to be a function of the normalized density.
Five formulas with the features of penalization and encouragement are developed to compete with the commonly used method SIMP (Solid Isotropic Material with Penalization). The basic idea of these formulas is to penalize the design variables with value between 0 and 0.5 and encourage the design variables with value between 0.5 and 1. Through these efforts, the chance of most design variables approaching 0 or 1 will be increased. Based on the results of the numerical examples, some of the formulas proposed in this thesis indeed show some positive outcomes.
URI: http://hdl.handle.net/11455/2424
其他識別: U0005-0907201016573600
Appears in Collections:機械工程學系所

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