請用此 Handle URI 來引用此文件: http://hdl.handle.net/11455/2420
標題: 受位移或頻率限制的最輕重量拓樸最佳化設計
Minimum weight topology optimization subject to displacement or frequency constraints
作者: 許劭睿
Hsu, Shao-Jui
關鍵字: topology optimization
拓樸最佳化設計
出版社: 機械工程學系所
引用: 1. BendsØe, M.P. and Kikuchi, N., “Generating optimal topologies in structural design using a homogenization Method”, Computer Methods in Applied Mechanics and Engineering, 71(1988),197-224 2. BendsØe, M.P., “Optimal Shape Design as a Material Distribution Problem”, Structural Optimization, Vol. 1, 1989, pp. 193-202 3. Mlejnek and Schirrmacher, R., “An engineering approach to optimal material distribution and shape finding”, Computer Methods in Applied Mechanics and Engineering, 106(1993), pp.1-26 4. Wang, B.P. and Lu, C.M. and Yang, R.J., “Topology Optimization Using MSC/NASTRAN”, MSC User Conference, Orlando S.L., 1994 5. Yang, R.J. and Chuang, C.H., “OTDULP” Computer & Structures, Vol.52, No.2, 1996, pp.265-275. 6. 林嘉洋,“可變設計空間的形勢最佳化”,國立中興大學機械工程研究所,民國87年6月 7. 謝嘉擎, “最佳清晰度之結構形勢最佳化設計”,國立中興大學機械工程研究所,民國86年6月 8. 陳至賢,“結構型態最佳化設計”,國立中興大學機械工程研究所,民國84年6月 9. 吳世昌,“結構多目標最佳化設計”,國立中興大學機械工程研究所,民國85年6月 10. Diaz, A. and Sigmund, O., “Checkboard Patterns in Layout imitation”, Structural Optimization, Vol.10,1995, pp.40-45 11. Hsu, Y.L. and Hsu, M.S. and Chen, C.T., “Interpreting results from topology optimization using density contours”, Computer and Structures, Vol. 79, 2001, pp.1049-1058. 12. Lin, C.Y. and Chou, J.-N. “A two-stage approach for structural topology optimization”, Advances in Engineering Software, Vol. 30, 1999, pp. 261-271. 13. Liu, X. and Yi, W.J. and Li, Q.S. and Shen, P.S., “Genetic evolutionary structural optimization”, Journal of Constructional Steel Research, Vol. 64,2008,pp.305-311. 14. Sandgren E. and Jensen E., and Welton J.W., “Topological design of structural components using genetic optimization methods”, Sensitivity Analysis and Optimization with Numerical Methods, ASME, Vol. 115, 1990, pp. 31-43. 15. Xie, Y.M. and Steven, G.P., “A simple evolutionary procedure for structural optimization”, Computer &Structures, 1993, Vol.49, pp.885-96. 16. Liang, Q.Q. and Xie, Y.M. and Steven, G.P., “Optimal topology selection of continuum structures with displacement constraints”, Vol.77, 2000, pp.635-644. 17. Kumar, A.V. and Gossard, D.C., “Synthesis of optimal shape and topology of structures, J Mech Des”, Vol.118, 1996, pp.68 -74. 18. Hsu, M.H. and Hsu, Y.L., “Interpreting three-dimensional structural topology results”, Computer and Structures, Vol.83, 2005, pp.327 -337. 19. Zuo, K.T. and Chen, L.P. and Zhang, Y.Q. and Yang, J.Z., “ Manufacturing- and machining-based topology optimization” ,Int J Adv Manuf Technol, Vol.27,2006 ,pp.531 -536. 20. Jasbir, S.A., Introduction to Optimum Design, McGraw-Hill Book Company, Singapore, 1989
摘要: 自從1988年BendsØe 以及 Kikuchi[1]提出均質法(homogenization method)求解拓樸結構最佳化問題(structural topology optimization problems)後,許多研究人員將此法發展做為開發結構初始設計之用。 本文主要是對結構重量的最小化為目標,在滿足位移或頻率束制條件下,配合正常化(normalized)材料密度關係式,並搭配幾種不同材料剛性之變化對正常化密度關係式,使用MATLAB撰寫序列二次規劃法(Sequential Quadratic Programming)之最佳化程式,並應用MSC/PATRAN及MSC/NASTRAN有限元素分析軟體作為前後級處理工具,進行結構拓樸最佳化設計。由於在最佳化結果中時常有拓樸形勢不清晰之現象,因此在目標函數中加入了懲罰函數以及使用高階元素進行改善,由多個實例所顯示的結果,導入懲罰函數使得結構的輪廓更為清晰。 比較使用重量和順從度做為目標函數的結果,使用重量為目標函數的優點是不必預估材料使用量,在慎選楊氏係數與設計變數關係式中α值的情況下,在懸臂梁的例子中有較佳之減重效果。
Since 1988 BendsØe and Kikuchi [1] published the homogenization method to solve structural topology optimization problems, more and more researchers have used this method to generate initial shapes of structures. In this thesis, the objective function is defined as minimum weight subject to two types of constraints: one is the displacement and the other one is the natural frequency. The normalized density of each finite element is adopted as the design variable. Some formulas representing the relationship between Young's modulus and the normalized density are used in the optimization process. The results are compared. A MATLAB program is written to use SQP optimizer to solve the optimization problems. While MSC/NASTRAN and MSC/PATRAN are used to do the pre- and post- processing. Because of the existence of uncertain elements, higher order elements or penalty function is employed to improve this drawback to make the structure clearer and recognizable. Compared with using minimum weight and minimum compliance as objective function, the biggest advantage of using minimum weight as the objective function is that there is no need to assign an amount of mass in the design space. By choosing an appropriate α in the formula relating Young's modulus and design variables, the weight saving is found in the cantilever plate case.
URI: http://hdl.handle.net/11455/2420
其他識別: U0005-0807201023164300
文章連結: http://www.airitilibrary.com/Publication/alDetailedMesh1?DocID=U0005-0807201023164300
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