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標題: 使用遺傳演算法的拓樸最佳化設計
Topology optimization using genetic algorithms
作者: 邱奕弘
Ciou, Yi-Hong
關鍵字: 遺傳演算法;Genetic Algorithms;拓樸最佳化;Topology Optimization
出版社: 機械工程學系所
引用: 1.Holland, J., Adaptation in Natural and Artificial Systems, The University of Michigan, Ann Arbor, MI, 1975. 2.Goldberg, D. E., Genetic Algorithms in Search, Optimization, and Machine Learning, Addison Wesley, Reading, MA, 1989. 3.Bendsøe, M. P. and Kikuchi, N., “Generating Optimal Topologies in Structural Design Using a Homogenization Method”, Computer Methods in Applied Mechanics and Engineering, Vol. 71, 1988, pp. 197-224. 4.Suzuki, K. and Kikuchi, N., “A Homogenization Method for Shape and Topology Optimization”, Computer Methods in Applied Mechanics and Engineering, Vol. 93, 1991, pp. 291-318. 5.Bendsøe, M. P., “Optimal Shape Design as a Material Distribution Problem”, Structural Optimization, Vol. 1, 1989, pp. 193-202. 6.Rozvany, G. I. N. and Zhou, M. and Birker, T., “Generalized Shape Optimization Without Homogenization”, Structural Optimization, Vol. 4, 1992, pp. 250-252. 7.Rozvany, G. I. N. and Bendsøe, M. P. and Kirsch, U., “Layout Optimization of Structures”, Applied Mechanics Reviews, Vol. 48, 1995, pp. 41-119. 8.Rozvany, G. I. N., “Aims, Scope, Methods, History and Unified Terminology of Computer-aided Topology Optimization in Structural Mechanics”, Structural and Multidisciplinary Optimization, Vol. 21, 2001, pp. 90-108. 9.Mlejnek, H. P., “Some Aspects of the Genesis of Structures”, Structural and Multidisciplinary Optimization, Vol. 5, 1992, pp. 64-69. 10.Mlejnek, H. P. and Schirrmacher, R., “An Engineer''s Approach to Optimal Material Distribution and Shape Finding”, Computer Methods in Applied Mechanics and Engineering, Vol. 106, 1993, pp. 1-26. 11.Yang, R. J. and Chuang, C. H., “Optimal Topology Design Using Linear Programming”, Computers and Structures, Vol. 52, 1994, pp. 265-275. 12.李彥叡, “拓樸最佳化設計變數懲罰方式之探討”, 國立中興大學機械工程研究所, 中華民國99年6月. 13.Maute, K. and Ramm, E., “Adaptive Topology Optimization”, Structural and Multidisciplinary Optimization, Vol. 10, 1995, pp. 100-112. 14.Maute, K. and Schwarz, S. and Ramm, E., “Adaptive Topology Optimization of Elastoplastic Structures”, Structural Optimization, Vol. 15, 1998, pp. 81-91. 15.吳世昌, “結構多目標最佳形態設計”, 國立中興大學機械工程研究所, 中華民國85年6月. 16.謝嘉擎, “最佳清晰度之形勢最佳化設計”, 國立中興大學機械工程研究所, 中華民國86年6月. 17.Rong, J. and Tang, G. and Liang, Q. Q. and Yang, Z., “A Topology Optimization Method for Three-dimensional Continuum Structures”, 6th World Congresses of Structural and Multidisciplinary Optimization, 2005, pp. 1-11. 18.Goldberg, D. E. and Samtani, M. P., “Engineering Optimization Via Genetic Algorithm”, ASCE, 1986, pp. 471-482. 19.Jenkins, W. M., “Towards Structural Optimization Via the Genetic Algorithm”, Computers and Structures, Vol. 40, 1991, pp. 1321-1327. 20.Sandgren, E. and Jensen, E. and Welton, J. W., “Topological Design of Structural Components Using Genetic Optimization Methods”, American Society of Mechanical Engineers, Applied Mechanics Division, Vol. 115, 1990, pp. 31-43. 21.Chapman, C. D. and Saitou, K. and Jakiela, M. J., “Genetic Algorithms as an Approach to Configuration and Topology Design”, Journal of Mechanical Design, Transactions of the ASME, Vol. 116, 1994, pp. 1005-1012. 22.Cappello, F. and Mancuso, A., “A Genetic Algorithm for Combined Topology and Shape Optimizations”, Computer Aided Design, Vol. 35, 2003, pp. 761-769. 23.Wang, S. Y. and Tai, K. and Wang, M. Y., “An Enhanced Genetic Algorithm for Structural Topology Optimization”, International Journal for Numerical Methods in Engineering, Vol. 65, 2006, pp. 18-44. 24.Eiben, A. E. and Smith, J. E., Introduction to Evolutionary Computing, Springer, 2008. 25.Carroll, D. L., FORTRAN Genetic Algorithm (GA) Driver, University of Illinois, 1999. 26.Hsu, Y. L. and Hsu, M. S. and Chen, C. T., “Interpreting results from topology optimization using density contours”, Computers and Structures, Vol. 79, 2001, pp. 1049-1058. 27.Liu, X. and Yi, W. J. and Li, Q. S., “Genetic evolutionary structural optimization”, Journal of Constructional Steel Research, Vol. 64, 2008, pp. 305-311. 28.Lin, C. Y. and Chou, J. N. and Li, Q. S., “A two-stage approach for structural topology optimization”, Advances in Engineering Software, Vol. 30, 1999, pp. 261-271. 29.Nha Chu, D. and Xie, Y. M. and Hira, A. and Steven, G. P., “Evolutionary structural optimization for problems with stiffness constraints”, Finite Elements in Analysis and Design, Vol. 21, 1996, pp. 239-251. 30.Li, Q. and Steven, G. P. and Xie, Y. M., “A simple checkerboard suppression algorithm for evolutionary structural optimization”, Structural and Multidisciplinary Optimization, Vol. 22, 2001, pp. 230-239.
鑒於使用傳統的最佳化方法求解結構拓樸最佳化問題時,往往最後所得到的拓樸結構會包含許多的灰階元素,但是實際上此種元素不應該存在。因此,本論文將使用遺傳演算法做為拓樸最佳化設計的方法來克服此一問題,以極小化順從度為設計目標,材料使用量為限制條件作為本論文的拓樸最佳化問題,使用的建模和分析軟體是MSC. Patran & Nastran。
由於使用遺傳演算法於結構拓樸最佳化時,將會遇到結構不連續而無法分析的問題,以及最佳化求解的時間過長之困擾,所以本論文提出脆弱材料結構與縮減設計空間的構想,藉以克服此兩種問題,文中將使用四個二維與一個三維的範例來驗證此兩種構想的可行性與實用性,同時也對遺傳演算法本身的相關參數設定進行分析,以比較拓樸最佳化結果的差異。由於棋盤式結構常會出現,本文也嘗試使用Li et al.[30]所提出的方法-平滑度技術來加以改善,結果顯示確實可清除棋盤式結構得到更有實用性之拓樸形狀。

When gradient-based search methods are used to solve topology optimization problems, gray elements may result. In reality, these elements should not exist. Therefore, this thesis tries to use genetic algorithm to find the optimum topology. The topology optimization problems are minimum compliance design subjected to the material constraint. The softwares used to create and analyze the models are MSC.Patran and MSC.Nastran.

Because of random search nature of genetic algorithm, disconnected topologies may appear and tremendous computational time is needed. These are the difficulties encountered in using GA to solve topology optimization problems. Two strategies are proposed in this thesis to overcome these two difficulties. One is to use a weak structure as a base structure to integrate the disconnected structures. The other one is to reduce the design space to save the computational time. Four 2-D and one 3-D design problems are illustrated to test these ideas. Different crossover probabilities are also used in GA to compare the topologies obtained. Because checkerboard pattern structure often appears, this thesis also employs Li et al.’s approach [30] to prevent its happening. The checkerboard patterns are indeed eliminated in all examples and useful topologies result.
其他識別: U0005-0612201221295900
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