臺灣博碩士論文加值系統

本文發展多階段拓樸最佳化技術從事結構靜、動態拓樸最佳化設計，其中結合密度指數遞增法以提升拓樸明確程度；以濾波器技術解決棋盤現象與網格依賴問題；改良適應性網格化技術以求得更細緻邊界之拓樸圖形；應用Bezier-curve之拓樸模組以消除動態結構時人工模態現象；文中除有傳統靜、動態拓樸最佳化設計範例外，更將所發展之技術推廣至結構支撐最佳化設計。最後本文整合各項技術成為一自動化的流程，以提供使用者一易於使用的拓樸最佳化設計工具。

The thesis focuses on how to design a structure for a minimal compliance and for highest natural frequencies by using the multi-stage topology optimization technique. Several techniques are utilized to overcome the difficulties encountered in the topology optimization. For example, the fixed-size filter technique is used to overcome the checkerboard and mesh-dependency problems. The Bezier-curve method is utilized to avoid the occurrence of the artificial modes in the problem of maximizing the structural natural frequencies. All the techniques are integrated into a single program and this program provides an automatic and user-friendly design tool for engineers. Several examples of minimizing the structural compliance and maximizing the natural frequencies subject to a limited material are given to demonstrate the effectiveness of this design tool.

第一章 緒論 9
1-1 前言 9
1-2 研究動機與目的 10
第二章 拓樸演進概述 11
2-1 文獻回顧 11
2-1-1 拓樸最佳化 11
2-1-2 均質化法 12
2-1-3 密度函數法 13
2-1-4 其他應用 16
2-1-5 文獻回顧總結 19
2-2 研究方法 20
第三章 拓樸最佳化設計 21
3-1 拓樸演算法概述 21
3-2 基本理論 22
3-2-1 傳統拓樸最佳化設計之流程 22
3-2-2 多階段拓樸最佳化設計之流程 23
3-3 理論分析 29
3-3-1 靜態目標函數與靈敏度分析 29
3-3-2 動態目標函數與靈敏度分析 30
3-3-3 靜動態結構拓樸之多重目標函數與靈敏度推導 31
第四章 濾波器技術之應用 33
4-1 梯度濾波器 33
4-1-1 棋盤現象 33
4-1-2 梯度非線性濾波器 33
4-1-3 梯度濾波器技術之範例 36
4-2 尺寸濾波器技術(FIX-SIZE-FILTER) 39
4-2-1 網格化問題(Mesh-dependency) 39
4-2-2 尺寸濾波器之原理 39
4-2-3 尺寸濾波器應用範例 41
第五章 邊界細緻化技術 44
5-1 傳統邊界細緻化 44
5-1-1 邊界鋸齒狀問題 44
5-2 改良之邊界細緻化方法 45
5-3 邊界拓樸細緻化之範例 47
第六章 提昇自然頻率之多階段拓樸最佳化 50
6-1 人工模態(ARTIFICIAL MODES) 50
6-2 使用 B-CURVE 之拓樸模組 51
6-3 消除人工模態之範例 52
第七章 多階段結構支撐拓樸最佳化設計 56
7-1 結構支撐拓樸設計 56
7-2 靜態支撐元素應用範例 57
第八章 結構拓樸設計應用範例 59
8-1 多階段拓樸最佳化之流程 59
8-2 結構靜態支撐設計應用範例 63
8-3 三維結構靜態支撐設計應用範例 66
8-4 提升自然頻率之結構支撐拓樸設計應用範例 70
第九章 總結與未來展望 75
9-1 總結 75
9-2 檢討與未來展望 76
9-2-1 尚待解決問題 76
9-2-2 未來發展趨勢 76

1Schmit, L. A., 1960, "Structural Design by Systematic Synthesis," Proceedings of the 2nd Conference on Eletronic Computation, ASCE, New York, pp. 105-122.
2Haftka, R. T. and Grandhi, R. V., 1986, "Structural Shape Optimization – A Survey," Computer Methods in Applied Mechanics and Engineering, 57, pp. 91-106.
3Bendse, M. P. and Kikuchi, N., 1988, "Generating Optimal Topologies in Structural Design Using a Homogenization Method," Computer Methods in Applied Mechanics and Engineering, 71, pp. 197-224.
4Mlejnek, H. P., 1992, "Some Aspects of the Genesis of Structures," Structural Optimization, 5, pp. 64-69.
5Baumgartner, A., Harzheim, L. and Mattheck, C., 1992, "SKO (Soft Kill Option)：The Biological Way to Find an Optimum Structure Topology," International Journal of Fatigue, 14, No. 6, pp. 387-393.
6Xie, Y. M. and Steven, G. P., 1993, "A Simple Evolutionary Procedure for Structural Optimization," Computers and Structures, 49, No.5, pp. 885-896.
7 IMSL Math/Library, 1994, Visual Numerics, Inc.
8Chen, T. Y., Wang, B. P. and Chen, C. H., 1995, "Minimum Compliance Design Using Topology Approach," 中國機械工程學會第十二屆學術研討會論文集, pp. 841-848.
9伊能教夫, 上杉武文, 1995, "Cellular Automaton Self-Organizing the Mechanical Structure (Generation of Various Types of Topological Structures and a Comparison)," 日本機械學會論文集(A 編), 61卷, 585號, pp. 241-246.
10Ma, Z. D., Kikuchi, N., Cheng H. C. and Hagiwara, I., 1995, "Topological Optimization Technique for Free Vibration Problems," Transactions of the ASME, 62, pp. 200-207.
11 Ma, Z. D., Kikuchi, N., Cheng H. C., 1995, "Topological Design for Vibrating Structures," Comput. Methods Appl. Mesh. Engrg. 121, pp. 259-280.
12Maute, K. and Ramm, E., 1995, "Adaptive Topology Optimization," Structural Optimization, 10, pp. 100-112.
13 黃崇銘, 1996, "自己組織化方法在機械結構元件拓樸最佳設計之研究,"國立成功大學機械工程研究所碩士論文,陳家豪.
14 Haber, R. B., Jog, C. S. and Bendse, M. P., 1996, "A New Approach to Variable Topology Shape Design Using a Constraint on Perimeter," Structure Optimization, 11, pp. 1-12.
15Maute, K. and Ramm, E., 1997, "Adaptive Topology Optimization of Shell Structures," American Institute of Aeronautics and Astronautics, 35, pp. 1767-1773.
16Fernandes, P., Guedes, J. M. and Rodrigues, H., 1999, "Topology Optimization of Three-Dimensional Linear Elastic Structures with a Constraint on Perimeter," Computers and Structures, 73, pp. 583-594.
17 韓乃智, 1997, "三維機械結構拓樸最佳化設計之研究," 國立成功大學機械工程研究所碩士論文,陳家豪.
18楊德慶, 1997, "桁架拓樸優化設計密度變量的兩種模式," 力與實踐論文集, 19卷, 5期, pp. 61-62,隋允康.
19 周政男, 1997, "兩階段拓樸最佳化策略," 中國機械工程學會第十四屆全國學術研討會論文集, pp. 637-645,林其禹.
20 Maute, K. and Ramm, E., 1997, "Adaptive Topology Optimization of Shell Structures," University of Stuttgart, 70569 Stuttgart, Germany
21 陳釧棠, 1998, "三維結構形態最佳化設計之研究," 私立元智大學機械工程研究所碩士論文,徐業良.
22 Li, Q., Steven, G. P., Querin, O. M., Y.M. Xie, 1999, “Shape and Topology Design for Heat Conduction by Evolutionary Structural Optimization”, International Journal of Heat and Mass Transfer, 42, pp. 3361-3371.
23 Min, S., Nishiwaki, S. and Kikuchi, N., 2000, "Unified Topology Design of Static and Vibrating Structures Using Multiobjective Optimization," Computers and Structures, 75, pp. 93-166.
24 姜冠禎, 2000, "拓樸最佳化設計系統整合之研究," 國立中正大學機械工程研究所碩士論文,鄭志鈞.
25 Rong, J. H., Xie, Y. M., Yang, X. Y. and Liang, Q. Q., 2000, "Topology Optimization of Structures under Dynamic Response Constraints," Journal of Sound and Vibration, 234, pp. 177-189.
26Hsu, Y. L., Hsu, M. S. and Chen, C. T., 2001, "Interpreting Results from Topology Optimization Using Density Contours," Computers and Structures, 79, pp. 1049-1058.
27Cheng, H. C., Chiang, K. N., and Chen, T. Y., 2001, "Topology Optimization of Elastic Structures for Stability," Journal of the Chinese Society of Mechanical Engineers, 22, pp. 391-398.
28 Sigmund, O., 2001, "A 99 Line Topology Optimization Code Written in Matlab," Struct. Multidisc. Optim., 21, pp. 120-127.
29 陳建昌, 2002, "多階段拓樸最佳化設計," 國立中正大學機械工程研究所碩士論文,鄭志鈞.
30 Liang, Q. Q., Steven G. P., 2002, "A Performance-Based Optimization Method for Topology Design of Continuum Structures with Mean Compliance Constraints," Comput. Methods Appl. Mech. Engrg., 191, pp. 1471-1789.
31 Yin L., Ananthasuresh G. K., 2002, "A Novel Topology Design Scheme for the Multi-Physics Problems of Electro-Thermally Actuated Compliant Mcromechanisms," Sensors and Actuators A 97-98, pp. 599-609.
32 Pedersen, N. L., 2002, “Topology Optimization of Laminated Plates with Prestress,” Computers and Structures, 80, pp. 559-570.
33 Buhl, T., 2002, “Simultaneous Topology Optimization of Structure and Supports,” Sturct Multidisc Optim 23, pp. 336-346.
34范成瑋, 2003, "拓樸最佳化法於動態結構設計之應用," 國立中正大學機械工程研究所碩士論文,鄭志鈞.
35Bruns, T. E. and Tortorelli, D. A., 2003, "An Element Removal and Reintroduction Strategy for the Topology Optimization of Structures and Complaint Mechanisms," International Journal for Numerical Methods in Engineering, 57, pp. 1413-1430.
36 何智強, 2004, "應用拓樸最佳化法於三維動態結構之設計," 國立中正大學機械工程研究所碩士論文,鄭志鈞.
37 Li, Y., Saitou, K., Kikuchi, N., 2004," Topology Optimization of Thermally Actuated Compliant Mechanisms Considering Time-Transient Effect," Finite Elements in Analysis and Design, 40, pp. 1317-1331.
38 莊福盛,黃文賓, "電腦cpu散熱片之拓樸最佳化設計策略," 國立台灣科技大學機械系, NSC89-2212-E-011-061,林其禹.
39 劉至行, "熱應力強度拓樸最佳化設計之研究," 國立成功大學機械工程研究所,陳家豪.
40 http://www.leadwell.com.tw/
41 http://www.cadmen.com.tw/
42 http://www.topopt.dtu.dk/
43 Shi, X., Wang, T., Yu, P., 2004,”A Practical Construction of G1 smooth Biquintic B-Spline Surfaces Over Arbitrary Topology,” Computer-Aided Design, 36, pp. 413-424.