博碩士論文 91322022 詳細資訊




以作者查詢圖書館館藏 以作者查詢臺灣博碩士 以作者查詢全國書目 勘誤回報 、線上人數:60 、訪客IP:18.119.106.66
姓名 藍志浩(Chih-Hao Lan)  查詢紙本館藏   畢業系所 土木工程學系
論文名稱 考慮動態反應束制及關連性離散變數之結構最佳化設計
相關論文
★ PSO-DE混合式搜尋法應用於結構最佳化設計的研究★ 考量垂直向效應之多項式摩擦單擺支承之分析與設計
★ 以整合力法為分析工具之結構離散輕量化設計效率的探討★ 最佳化設計於結構被動控制之應用
★ 多項式摩擦單擺支承之二維動力分析與最佳參數研究★ 構件考慮剛域之向量式有限元素分析研究
★ 矩形鋼管混凝土考慮局部挫屈與二次彎矩效應之軸壓-彎矩互制曲線研究★ 橋梁多支承輸入近斷層強地動極限破壞分析
★ 穩健設計於結構被動控制之應用★ 二維結構與固體動力分析程式之視窗介面的開發
★ 以離心機實驗與隱式動力有限元素法模擬逆斷層滑動★ 以離心模型實驗探討逆斷層錯動下群樁基礎與土壤的互制反應
★ 九二一地震大里奇蹟社區倒塌原因之探討★ 群樁基礎之最低價設計
★ 應用遺傳演算法於群樁基礎低價化設計★ 應用Discrete Lagrangian Method於群樁基礎低價化設計
檔案 [Endnote RIS 格式]    [Bibtex 格式]    [相關文章]   [文章引用]   [完整記錄]   [館藏目錄]   [檢視]  [下載]
  1. 本電子論文使用權限為同意立即開放。
  2. 已達開放權限電子全文僅授權使用者為學術研究之目的,進行個人非營利性質之檢索、閱讀、列印。
  3. 請遵守中華民國著作權法之相關規定,切勿任意重製、散佈、改作、轉貼、播送,以免觸法。

摘要(中) 摘 要
本文主要針對含關連性離散變數、靜態和動態反應束制之結構輕量化設計問題,提出三種以離散拉格朗日法(Discrete Lagrangian Method, DLM)為基礎的搜尋策略,其中靜態反應束制包括位移、應力、挫屈應力及長細比束制,動態反應束制包括頻率及頻率反應振幅的束制。研究中,首先針對DLM中的拉格朗日乘子的更新公式提出修正,避免每次迭代可能必須反覆更新拉格朗日乘子的缺失。接著探討DLM應用於關連性離散變數以及動態反應束制條件下所遭遇的困難,並對此提出動態擴大鄰點搜尋及改善震盪現象策略。最後,為了確保DLM的求解品質,本研究亦提出一種藉由折減拉格朗日乘子啟動再搜尋的方法,使DLM有機會跳脫一個局部最佳解區域搜尋另一局部最佳解。數個結構輕量化設計問題將分別用來探討其適用性和影響求解品質與效率的相關參數,並藉由設計結果之比較,來探討本文所發展之三種搜尋法的優缺點。
摘要(英) Abstract
This research studies the minimum weight design of structures with linked discrete variables, static and dynamic response constraints. Three discrete Lagrangian based searching procedures are proposed in this report. The static response constraints include displacement, stress, buckling stress and slenderness ratio. The dynamic response constraints include frequency and frequency response amplitude. In this research, an update formula for the Lagrange multiplies is developed first. The difficulties in applying the DLM to solve for problems containing linked discrete variables and dynamic response constraints are then discussed. To resolve the difficulties, a dynamic extending neighborhood technique and an improving strategy for eliminating fluctuated searching trajectory are proposed. Finally, a restarting procedure for the DLM by scaling down the values of Lagrange multipliers is also proposed to help the search escaping from a local minimum to search for another one. The feasibility of three procedures is validated by several design examples. The results from comparative studies of the DLM against other discrete optimization algorithms are reported to show the solution quality of the proposed DLM procedures. The advantages and drawbacks of the three DLM algorithms are also discussed.
關鍵字(中) ★ 長細比束制
★ 關連性離散變數
★ 輕量化設計
★ 頻率反應振幅束制
★ 位移束制
★ 應力束制
★ 挫屈應力束制
★ 頻率束制
★ 離散拉格朗日法
關鍵字(英) ★ buckling stress constraints
★ linked discrete variable
★ slenderness ratio constraints
★ frequency constraints
★ minimum weight design
★ frequency response amplitude constraints
★ discrete Lagrangian method
★ stress constraints
★ displacement constraints
論文目次 目錄
中文摘要 I
英文摘要 III
目錄 V
表目錄 XI
圖目錄 XVII
第一章 緒論 1
1.1 研究動機與目的 1
1.2 文獻回顧 3
1.2.1 離散最佳化方法 3
1.2.2 動態反應束制 5
1.3 研究方法與內容 6
1.3.1 動態反應束制條件 7
1.3.2 拉格朗日乘子放大倍數 7
1.3.3 動態擴大鄰點搜尋策略 8
1.3.4 DLM演算法震盪現象之改善策略 8
1.3.5 DLM的再搜尋策略 8
第二章 DLM演算法 11
2.1 離散最佳化問題之數學模式 11
2.2 DLM理論回顧 12
2.2.1 加權離散拉格朗日函數 12
2.2.2 鄰點 12
2.2.3 離散梯度 13
2.2.4 離散鞍點 14
2.2.5 轉換函數 15
2.2.6 收斂準則與一階搜尋公式 15
2.2.7 一階搜尋公式之修改 17
2.2.8 DLM演算程序 20
2.3 合向量策略 22
2.4 動態擴大鄰點搜尋策略 24
2.5 動態擴大鄰點搜尋策略之數值算例 27
2.5.1 22桿平面桁架 27
2.5.2 10桿平面桁架(I) 30
2.6 DLM演算法震盪現象之改善策略 33
2.7 震盪現象改善策略之數值算例 36
2.7.1 3桿平面桁架 36
2.8 討論 40
第三章 設計程序 41
3.1 引言 41
3.2 固定鄰點之搜尋程序 42
3.3 動態擴大鄰點與改善震盪現象之搜尋程序 44
3.4 DLM的再搜尋程序 44
3.4.1 測試算例 45
3.4.1.1 25桿空間桁架(I) 48
3.4.2 討論 60
第四章 數值算例與參數研究 65
4.1 目標函數與束制條件 65
4.2 測試流程介紹 69
4.3 DLM-1與DLM-2之參數研究 70
4.3.1 10桿平面桁架(I) 71
4.3.1.1 DLM-1參數研究 71
4.3.1.2 DLM-2參數研究 75
4.3.1.3 結果比較 80
4.3.2 10桿平面桁架(II) 82
4.3.2.1 DLM-1參數研究 84
4.3.2.2 DLM-2參數研究 93
4.3.2.3 結果比較 101
4.3.3 10桿平面桁架(III) 105
4.3.3.1 DLM-1參數研究 106
4.3.3.2 DLM-2參數研究 110
4.3.3.3 結果比較 114
4.4 其他算例設計結果 116
4.4.1 25桿空間桁架(I) 116
4.4.2 25桿空間桁架(II) 120
4.4.3 25桿空間桁架(III) 123
4.4.4 25桿空間桁架(IV) 133
4.4.5 25桿空間桁架(V) 141
4.4.6 160桿空間桁架 143
4.4.7 200桿平面桁架(I) 147
4.4.8 200桿平面桁架(II) 151
4.4.9 單跨八層平面構架 154
4.4.10 單跨雙層平面構架 158
4.4.11 單跨七層平面構架 172
第五章 結論與建議 179
5.1 結論與建議 179
5.2 未來研究方向 182
參考文獻 183
附錄A 22桿平面桁架細部資料及設計結果 191
A.1 細部設計資料 191
A.2 DLM設計結果 192
附錄B 10桿平面桁架(I)細部資料及設計結果 193
B.1 細部設計資料 193
B.2 DLM設計結果(I) 195
B.3 DLM設計結果(II) 196
附錄C 3桿平面桁架細部資料及設計結果 197
C.1 細部設計資料 197
C.2 DLM設計結果 198
附錄D 25桿空間桁架(I)細部資料及設計結果 199
D.1 細部設計資料 199
D.2 DLM設計結果(I) 201
D.3 DLM設計結果(II) 203
附錄E 10桿平面桁架(II)細部資料及設計結果 205
E.1 細部設計資料 205
E.2 DLM設計結果 206
附錄F 10桿平面桁架(III)細部資料及設計結果 209
F.1 細部設計資料 209
F.2 DLM設計結果 210
附錄G 25桿空間桁架(II)細部資料及設計結果 211
G.1 細部設計資料 211
G.2 DLM設計結果 212
附錄H 25桿空間桁架(III)細部資料及設計結果 213
H.1 細部設計資料 213
H.2 DLM設計結果 215
附錄I 25桿空間桁架(IV)細部資料及設計結果 219
I.1 細部設計資料 219
I.2 DLM設計結果 221
附錄J 25桿空間桁架(V)細部資料及設計結果 225
J.1 細部設計資料 225
J.2 DLM設計結果 226
附錄K 160桿空間桁架細部資料及設計結果 227
K.1 細部設計資料 227
K.2 DLM設計結果 231
附錄L 200桿平面桁架(I)細部資料及設計結果 239
L.1 細部設計資料 239
L.2 DLM設計結果 242
附錄M 200桿平面桁架(II)細部資料及設計結果 247
M.1 細部設計資料 247
M.2 DLM設計結果 250
附錄N 單跨八層平面構架細部資料及設計結果 255
N.1 細部設計資料 255
N.2 DLM設計結果 260
附錄O 單跨雙層平面構架細部資料及設計結果 261
O.1 細部設計資料 261
O.2 DLM設計結果 265
附錄P 單跨七層平面構架細部資料及設計結果 267
P.1 細部設計資料 267
P.2 DLM設計結果 270
參考文獻 參考文獻
[1] Juang, D. S., Wu, Y. T., and Chang, W. T., “Optimum Design of Truss Structures using Discrete Lagrangian Method,” Journal of the Chinese Institute of Engineers, Vol. 25, No. 6, pp. 755?766 (2003).
[2] 莊德興、吳朗益,「離散拉格朗日法於群樁基礎低價化設計之應用,」中國土木水利學刊,第十五卷,第二期,第93?104頁 (2003)。
[3] 莊德興、張慰慈,「DLM?GA混合演算法於大型桁架離散最佳化設計之應用」,電子計算機於土木水利工程運用研討會論文集,臺北市 (2003)。
[4] 莊德興、張慰慈、吳泳達,「離散拉格朗日演算法及其在結構最佳設計之應用」,電子計算機於土木水利工程運用研討會論文集,臺北市 (2003)。
[5] Wu, Z., “The Discrete Lagrangian Theory ans its Application to Solve Nonlinear Discrete Constrain Optimization Problems,” Master Thesis, Department of Computer Science, University of Illinois at Urbana?Champaign (1998).
[6] Garlinkel, R. and Nemhauser, G., Integer Programming, John Wiley and Sons, New York, N. Y. (1992).
[7] Gupta, O. K. and Ravindran, A., “Nonlinear Mixed Integer Programming and Discrete Optimization,” Progress in Engineering Optimization, R. W. Mayne and K. M. Ragsdell, New York, N. Y. pp. 297?520 (1984).
[8] Ringertz, U. T., “On Methods for Discrete Structural Optimization,” Engineering Optimization, Vol. 13, pp. 47?64 (1988).
[9] Cha, J. Z. and Mayne, R. W., “Optimization with Discrete Variables via Quadratic Programming, Part 2: Algorithms and Results,” Transactions of the ASME, Vol. 111, No. 3, pp. 130?136 (1989).
[10] Sandgren, E., “Nonlinear Integer and Discrete Programming in Mechanical Design Optimization,” Journal of Mechanical Design, ASME., Vol. 112, No. 2, pp. 223?229 (1990).
[11] Tseng, C. H., Wang, L. W. and Ling, S. F., “A Numerical Study of the Branch and Bound Method in Structural Optimization,” Technical Report, Department of Mechanical Engineering, National Chiao Tung University, Hsinchu, Taiwan (1992).
[12] Schmit, L. A. and Fleury, C., “Discrete?Continuous Variable Structural Synthesis Using Dual Methods,” AIAA Journal, Vol. 18, No. 4, pp. 1515?1524 (1980).
[13] Olsen, G. and Vanderplaats, G. N., “A Method for Nonlinear Optimization with Discrete Variables,” AIAA Journal, Vol. 27, No. 11, pp. 1584?1589 (1989).
[14] Vanderplaats, G. N., “General Purpose Optimization Software for Engineering Design,” Proc., 3rd Air Force / NASA Symp. On Recent Adv. In Multi Disciplinary Anal. and Iptimization, San Francisco, C. A (1990).
[15] Kirkpatrick, S., Gelatt, C. D. and Vecchi, M. P., “Optimization by Simulated Annealing,” Science, Vol. 220, pp. 671?680 (1983).
[16] Trosset, M. W., “What is Simulated Annealing,” Optimization and Engineering, Vol. 2, pp. 201?213 (2002).
[17] Geman, S. and Geman, D., “Stochastic Relaxation, Gibbs Distributions and the Bayesian Restoration of Images,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 6, pp. 721?741 (1984).
[18] Hajek, B., “Optimization by Simulated Annealing: A Nece? ssary and Sufficient Condition for Convergence,” in Adaptive Statistical Procedures and Related Topics, J. Van Ryzin, Institute of Mathematical Statistics: Hayward, C. A., pp. 417?427 (1986).
[19] Hajek, B., “Cooling Schedules for Optimal Annealing,” Mathematics of Operations Research, Vol. 13, pp. 311?329 (1988).
[20] Holland, J. H., “Outline for a Logical Theory of Adaptive System,” Journal of the Association for Computing Machinery, Vol. 3, pp.297?314 (1962).
[21] Davis, J. S., Handbook of Genetic Algorithms, Van Nostrand Reinhold (1991).
[22] Whitley, D., “The Genitor Algorithm and Seiection Pressure: Why Rank?Based Allocation of Reproductive Trials is Best,” Proceeding of the Third International Conference on Genetic Algorithms, J. D. Schaffer, pp. 116?121, Morgan Kaufmann Publishers, San Mateo, California (1989).
[23] Wu, S. J. and Chow, P. T., “The Application of Genetic Alogirthms to Discrete Optimation Problems,” Journal of the Chinese Society of Mechanical Engineers, Vol. 16, No. 6, pp. 587?598 (1995).
[24] Wu, S. J. and Chow, P. T., “Integrated Discrete and Configuration Optimization of Trusses Using Genetic Algorithms,” Computers and Structures, Vol. 55, No. 4, pp. 695?702 (1995).
[25] De Jong, K. A., “An Analysis of the Behavior of a Class of Genetic Adaptive Systems,” Ph.D. Dissertation, University of Michigan, Dissertation Abstracts International, No. 36, Vol. 10, 5140B. (University Microfilms No. 76?9381) (1975).
[26] Wah, B. W. and Shang, Y., A Discrete Lagrangian?Based Global?Search Metod for Solving Satisfiability Problems, Proc. DIMACS Workshop on Satisfiability Problems, Theory and Applications, Du, D.Z., Gu, J., and Pardalos, P., AMS (1996).
[27] 紀炤良,「結構在頻率限制下之最佳設計」,碩士論文,國立台灣大學土木工程研究所,臺北 (1987)。
[28] Pantelides, C. P. and Tzan, S. R., “Optimal Design of Dynamically Constrained Structures,” Computers and Structures, Vol. 62, No. 1, pp. 141?149 (1997).
[29] Tong, W. H. and Liu, W. H., “An Optimization Procedure for Truss Structures with Discrete Design Variables and Dynamics Constrains,” Computers and Structures, Vol. 79, pp. 155?162 (2001).
[30] Choi, Y. H., Bae, B. T., Kim, S. T. and Kim, T. H., “Static, Dynamic, and Sectional Topology Optimization of Structures Using a Genetic Algorithm with Dynamic Penalty,” The 6th International Conference on Engineering Design and Automation, Maui, Hawaii, 2002, pp. 610?616 (2002).
[31] 張慰慈,「DLM?GA混合搜尋法於結構離散最佳化設計之應用」,碩士論文,國立中央大學土木工程研究所,中壢 (2003)。
[32] 吳泳達,「離散拉格朗日法於結構最佳化設計之應用」,碩士論文,國立中央大學土木工程研究所,中壢 (2003) 。
[33] 莊德興,「桁架之形狀與離散斷面的整合輕量化設計」,第七屆結構工程研討會論文集,桃園大溪 (2004)。
[34] Arora, J. S., Introduction to Optimum Design, McGraw?Hill, (1989).
[35] Erbatur, F., Hasancebi, O., Tutuncu, I. and Kilic, H., “Optimal Design of Planar and Space Structures with Genetic Algorithms,” Computers and Structures, Vol. 75, pp. 209?224 (2000).
[36] AISC, Manual of Construction: Allowable Stress Design, 9nd Edition, Chicago, Illinois (1989).
[37] Groenwold, A. A. and Stander, N., “Optimal Discrete Sizing of Truss Structures Subject to Buckling Constraints,” Structural Optimization, Vol. 14, pp. 71?80 (1997).
[38] Groenwold, A. A., Stander, N. and Snyman, J. A., “A Regional Genetic Algorithms for the Discrete Optimal Design of Truss Structures,” International Journal for Numerical Methods in Engineering, Vol. 44, No.6, pp. 749?766 (1999).
[39] Haug, E. J. and Arora, J. S., Applied Optimal Design: Mechanical and Structural Systems, John Wiley & Sons, (1979).
[40] Chopra, A. K., Dynamics of Structures Theory and Applications to Earthquake Engineering, Prentice?Hall, (2000).
[41] Arora, J. S. and Tseng, C. H. “Interactive Design Optimization,” Engineering Optimization, Vol. 13, pp. 173?188 (1988).
[42] Tseng, C. H., Wang, L. W. and Ling, S. F., “Enhancing Branch?and?Bound Method for Structural Optimization,” Journal of Structural Engineering, ASCE., Vol. 121, pp. 831?837 (1995).
[43] Camp, C., Pezeshk, S. and Cao, G., “Optimized Design of Two?Dimensional Structures Using a Genetic Algorithm”, Journal of Structural Engineering, ASCE., Vol. 124, No. 5, pp. 551?559 (1998).
[44] Nanakorn, P. and Meesomklin, K., “An Adaptive Penalty Function in Genetic Algorithms for Structural Design Optimiation,” Computers and Structures, Vol. 79, pp. 2527?2539 (2001).
[45] McGee, O. G. and Phan, K. F., “A Robust Optimality Criteria Procedure for Cross?Sectional Optimization of Frame Structures with Multiple Frequency Limits,” Computers and Structures, Vol. 38, pp. 485?500 (1991).
[46] Salajegheh, E., “Optimum Design of Structures with High?Quality Approximation of Frequency Constraints,” Advances in Engineering Software, Vol. 31, pp. 381?384 (2000).
指導教授 莊德興(Der-Shih Juang) 審核日期 2005-7-20
推文 facebook   plurk   twitter   funp   google   live   udn   HD   myshare   reddit   netvibes   friend   youpush   delicious   baidu   
網路書籤 Google bookmarks   del.icio.us   hemidemi   myshare   

若有論文相關問題,請聯絡國立中央大學圖書館推廣服務組 TEL:(03)422-7151轉57407,或E-mail聯絡  - 隱私權政策聲明